EP4577954A1

EP4577954A1 - Method of operating a semiconductor spin qubit quantum computer

Info

Publication number: EP4577954A1
Application number: EP23708477.7A
Authority: EP
Inventors: Jörg Hendrik BLUHM; Matthias KÜNNE; Jan KLOS; Lars Reiner SCHREIBER
Original assignee: Forschungszentrum Juelich GmbH; Rheinisch Westlische Technische Hochschuke RWTH
Current assignee: Forschungszentrum Juelich GmbH; Rheinisch Westlische Technische Hochschuke RWTH
Priority date: 2023-02-28
Filing date: 2023-02-28
Publication date: 2025-07-02
Also published as: WO2024179671A1; CN120677490A

Abstract

A method of operating a quantum processor (10) comprising a plurality of gate electrodes arranged on a semiconductor heterostructure, wherein the plurality of gate electrodes comprises conveyor gate electrodes configured to be supplied with at least one voltage V to move at least one qubit, arranged in the semiconductor heterostructure, along the at least one path to a manipulation zone for manipulating the at least one qubit is disclosed. The method comprises the steps of calibrating the at least one voltage V supplied to the gate electrodes; determining at least one fidelity FM or an error syndrome S, relating to manipulating the at least one qubit at the manipulation zone; and adjusting the at least one voltage V.

Description

Title: METHOD OF OPERATING A SEMICONDUCTOR SPIN QUBIT QUANTUM COMPUTER Field of the disclosure [0001] The field of the present disclosure relates to the operation of quantum processors. Background of the disclosure [0002] Quantum processor architectures have to allow for scalability in order to achieve numbers of logical qubits sufficiently high to implement quantum computer chips that enable NISQ (noisy intermediate-scale quantum) era quantum computing or even universal quantum computing. In the case of spin qubit-based quantum computing, the qubits are preferably arranged in a two-dimensional plane. A downside of this two-dimensional architecture is the so-called fan-out problem, i.e., spatial requirements of the wiring for the control lines of the quantum processor between the quantum processor and a classical control circuit. These spatial requirements scale faster with the number of qubits than the size of the hitherto proposed spin qubit-based quantum processor architectures. [0003] Recently, an architecture for spin-qubits based on direct electron shuttling in Si/SiGe semiconductor heterostructures was proposed. The architecture includes shuttling paths along which qubits are transportable across, in principle, arbitrary distances such as of up to about 50 µm. The shuttling paths allow to arrange components of the quantum processor, such as loading zones, readout zones, and manipulation zones, at a distance from each other, which lowers crosstalk. Providing shuttling paths also enables operations modes that require comparatively small operation frequencies and reduced local magnetic field gradients. [0004] In these shuttling path-based architectures, high-fidelity shuttling is important for reliable computations. Such high-fidelity shuttling is compromised by, e.g., charge defects or low valley splitting along the shuttling path. The low valley splitting may lead to leakage out of the computational basis, e.g., two spin states, that is used for computation. [0005] There is a need for identifying spots in the quantum processor, e.g., in the shuttling path or other components of the quantum processor, where the reliability of qubit handling is reduced, which ultimately impacts on the performance of the quantum processor. Summary of the disclosure [0006] A method of operating a quantum processor (10) comprising a plurality of gate electrodes arranged on a semiconductor heterostructure, wherein the plurality of gate electrodes comprises conveyor gate electrodes configured to be supplied with at least one voltage V to move at least one qubit, arranged in the semiconductor heterostructure, along the at least one path to a manipulation zone for manipulating the at least one qubit is disclosed. The method comprises the steps of calibrating the at least one voltage V supplied to the gate electrodes; determining at least one fidelity FM or an error syndrome S, relating to manipulating the at least one qubit at the manipulation zone; and adjusting the at least one voltage V. [0007] The calibrating of the at least one voltage V may include defining a Rabi frequency Ω, a resonance frequency ν, or an exchange coupling J. [0008] The adjusting of the at least one voltage V comprises adjusting a Rabi frequency Ω, a resonance frequency ν, or an exchange coupling J. [0009] The adjusting of the at least one voltage V further comprises applying a DC voltage to the gate electrodes. [0010] The at least one voltage is applied to the at least one electrode subset of the conveyor gate electrodes or to at least one electrode of a top gate arranged above the conveyor gate electrodes. [0011] The method may further comprise moving the at least one qubit along at least one segment of the at least one shuttling lane. [0012] The method may further comprise varying a length of the at least one segment of the at least one shuttling lane. [0013] The determining of the at least one fidelity F may comprise performing the at least one action on the at least one qubit. [0014] The determining of the at least one fidelity FM comprises determining a fidelity FS of shuttling the at least one qubit. [0015] The determining of the at least one fidelity FM comprises gathering measurements relating to the at least one fidelity FM. [0016] The gathering of measurements may further include spin-to-charge conversion. [0017] The method may further comprise restricting the at least one voltage V within an associated predefined target range. Brief description of the drawings [0006] FIG.1 shows a schematic top view of a quantum processor. [0018] FIG.2 shows a schematic top view of a unit cell of the quantum processor shown in FIG.2. [0019] FIG.3A shows an aspect of a top view of a manipulation zone. [0020] FIG.3B shows a longitudinal cross-section of a further aspect of the manipulation zone. [0021] FIG.3C shows a longitudinal cross-section of a further aspect of the manipulation zone. [0022] FIG.3D shows a longitudinal cross-section of a further aspect of the manipulation zone. [0023] FIG.4 shows in the upper panel an effect on a shuttling voltage of applying adjustment voltage for changing a confinement of a qubit. FIG.4 shows in the lower panel an effect on a shuttling voltage of applying adjustment voltage for shifting a confinement a qubit.. [0024] FIG.5 shows a flowchart of a method of operating a quantum processor. [0025] FIG.6A shows a pair of path-defining gates arranged at at least one path for a qubit. [0026] FIG.6B shows a pair of segmented path-defining gates arranged at at least one path for a qubit. [0027] FIG.6C shows an example of a grayscale-coded valley-splitting landscape of a shuttling lane as well as possible trajectories for a qubit along the shuttling lane which circumvent a series of fidelity-reducing loci with reduced valley splitting. [0028] FIG.6D shows a longitudinal cross-section of an aspect of the shuttling-lane. Detailed description [0029] The present disclosure relates to a method of operating a quantum processor as well as to a method of manufacturing a quantum processor. [0030] The quantum processor may operate based on spin qubits. A spin qubit is a two-level quantum system of a spin degree of freedom. An example of a spin qubit is the two-level quantum system of the spin of an electron confined in a quantum dot. Another example is a hole spin qubit. Furthermore, a group of electrons, for example two or three electrons, may be used to implement a spin qubit, such as an S-T0 singlet-triplet system of two electrons in a quantum double-dot. [0031] The method of the present disclosure is applicable to any type of electrically controllable spin qubit implemented in a semiconductor heterostructure 12. Using an electron-based spin qubit involves bringing the electron spin into a known state. To this end, the state of the electron is initialized. In one aspect, a selected qubit is associated with the same electron throughout the performing of a quantum algorithm. In another aspect, a qubit implemented by a first electron may be initialized and, subsequently to an operation on the qubit, the qubit may be implemented by means of a second electron. In a further aspect, there are situations in which it is impossible to tell whether the qubit is implemented by the first electron or by the second electron, without compromising the performing of quantum algorithms. Likewise, the method of the present disclosure may be applied on any type of hole spin qubit. [0032] Using semiconductor materials to form a structure, e.g., a semiconductor heterostructure, for implementing the quantum processor facilitates manufacturing due to easy handling and low costs of the materials, such as in the case of silicon. There are established technologies for using silicon in computing hardware. A two- dimensional electron gas (2DEG) or a two-dimensional hole gas (2DHG) is confinable within the structure formed from the semiconductor materials in a quantum well 69 (see below and FIG.3B-3D and 6D). The 2DEG or the 2DHG may further be confined based on electrical potentials. The electric potentials may be static electric potentials or non-static electric potentials. The electrical potentials may form at least one quantum dot, in which at least one electron or hole of the 2DEG or 2DHG is trappable or confinable. The spin of the trapped (confined) at least one electron or hole is usable to implement spin qubits. Moving the electrical potentials results in moving the at least one quantum dot. The moving of the at least one quantum dot enables moving the trapped (confined) at least one electron/hole as well as the qubits associated with the trapped (confined) at least one electrons/holes. Altering a strength of the electrical potentials alters the degree of confinement of the trapped (confined) at least one electron or hole. [0033] The quantum processor may comprise a plurality of unit cells. A unit cell of the plurality of unit cells comprises components that perform at least one action or operation on one or more qubits located in the unit cell. The at least one action on the one or more qubits includes: loading of the one or more qubits into the unit cell; unloading of the one or more qubits from the unit cell; moving (shuttling) the one or more qubits within the unit cell or beyond the unit cell (i.e., to another one of the unit cell of the quantum processor); manipulating a quantum state of the one or more qubits; and readout of the quantum state of the one or more qubits. The manipulating of the one or more qubits comprises manipulating a single qubit or manipulating two qubits. The manipulating of the single qubit comprises rotating the spin of the single qubit, e.g., for driving transitions between a plurality of spin states. The plurality of spin states may comprise, e.g., a spin-up state and a spin-down state. The manipulating of the two qubits may serve to implement a CPHASE gate, a CNOT gate, and/or a SWAP gate. The manipulating of the two qubits may further serve to implement a SQRT(SWAP) gate. Implementing a CNOT gate and one or more single-qubit gates, such as rotations or phase shifts, are sufficient to implement a quantum computer. The CNOT gate may be realized as a CPHASE gate in spin- qubit-based quantum computers. However, the afore-mentioned two-qubit gates are merely examples. The manipulating may serve to implement any two-qubit gate. [0034] In one aspect, several actions performed on the one or more qubits by the components of the unit cell may be performed one after another as a sequence of actions. For example, two actions may be performed one after another. In another aspect, the several actions performed on the one or more qubits by the components of the unit cell may be performed in parallel. For example, the two actions may be performed in parallel. [0035] In one aspect, the several actions on the one or more qubits may be performed within a single one of the plurality of the unit cells or across several ones of the plurality of unit cells. [0036] In one aspect, the several actions may be performed as part of determining a gate fidelity (see below for more details). For example, the determining of the gate fidelity may comprise performing the sequence of actions on the one or more qubits. [0037] In another aspect, the several actions may be performed as part of performing an algorithm. For example, the performing of the algorithm may comprise performing the sequence of actions on the one or more qubits. [0038] The components are arranged within the unit cell. Some of the components are connected with each other. The components and the connections of the components thus form a layout or structure of the unit cell. Ones of the plurality of unit cells may have substantially the same structure, in which the same components are arranged and connected with each other in substantially the same way. Other ones of the plurality of unit cells may have differing structures, in which the components and/or the connections of the components differ. [0039] Aspects of the quantum processor are disclosed in international patent application no. WO 2021/052541 A1, the disclosure of which is incorporated herein by reference in its entirety. In this aspect, shown in FIGS.1 and 2, the quantum processor 10 comprises the semiconductor heterostructure 12. The semiconductor heterostructure 12 comprises several layers of differing material composition. The semiconductor heterostructure 12 may be a Si/SiGe or GaAs/AlGaAs heterostructure, however, the use of other materials in which a two-dimensional electron gas (2DEG) or a two-dimensional hole gas (2DHG) can be formed, such as Si-MOS or Ge/SiGe, is possible. The semiconductor heterostructure may be undoped and/or strained. The semiconductor heterostructure 12 may serve as a substrate of the quantum processor 10. The semiconductor heterostructure 12 may comprise the 2DEG. The 2DEG or the 2DHG may be arranged or located in the quantum well 69 (see FIG.3B-D and 6D). The one or more qubits may be arranged in the quantum well 69. The one or more qubits may be arranged in the at least one quantum dot formed in the quantum well 69. The one or more qubits may be generated from the 2DEG. [0040] In one aspect, the semiconductor heterostructure 12 may further comprise a silicon cap 64, on which a dielectric or insulating layer 66 is arranged. FIG.6D shows the silicon cap in the case of shuttling lane 16. However, the silicon cap 64 may also be present in the case of the manipulation zone 20. The gate electrodes 50a, 50b may be arranged on top of the dielectric or insulating layer 66. [0041] In a further aspect, the semiconductor heterostructure 12 may further comprise a layer of strained silicon 63 (see FIG.3C and 6D). In yet a further aspect, the semiconductor heterostructure 12 may further comprise a layer of silicon dioxide 62 (see FIG.3C). [0042] In the aspect of the quantum processor 10 shown in FIGS.1 and 2, the components 16, 18, 20, 22, 24 are provided on at least one surface 14 of the semiconductor heterostructure 12. As can be seen in FIG.1, the shown aspect of the quantum processor 10 comprises one or more of each of the components 16, 18, 20, 22, 24. In another aspect, the quantum processor 10 may comprise one or more of only some of the component 16, 18, 20, 22, 24. [0043] The quantum processor 10 shown in FIGS.1 and 2 is a substantially two- dimensional device, as defined by the at least one surface 14. A third dimension of the quantum processor 10 is defined by a thickness of the semiconductor structure 12 and a thickness of the components 16, 18, 20, 22, 24. [0044] The plurality of unit cells of the quantum processor 10 comprises several of the unit cell 26 (shown in FIG.2). In the aspect shown in FIG.2, the unit cell 26 comprises the components 16, 18, 20, 22, 24. In another aspect of the disclosure, the unit cell 26 comprises merely some of the components 16, 18, 20, 22, 24. In yet a further aspect, the unit cell 26 may comprise more than one of at least one of the components 16, 18, 20, 22, 24. [0045] The components 16, 18, 20, 22, 24 comprise a plurality of gate electrodes 50 (see FIGS.3A and 3B) arranged on at least one surface 14 of the semiconductor heterostructure 12. The plurality of gate electrodes 50 may be arranged to define within the associated one of the components 16, 18, 20, 22, 24 at least one path 451, 452 within the quantum well 69 (see FIG.3A) along which the one or more qubits may be moved (shuttled). [0046] In FIGS.1 and 2, the at least one path 45 is shown to substantially be directed in two directions on the surface 14 that are substantially perpendicular to one another, resulting in structure of a plurality of paths 45 that is grid-like. The plurality of paths 45 connect the components 16, 18, 20, 22, 24. [0047] The plurality of gate electrodes 50 may further be arranged to move (shuttle) the one or more qubits along the at least one path 45. The movement (shuttling) may occur in either one of the two directions (back and forth) along the at least one path 45. The plurality of gate electrodes 50 may further be arranged for performing the at least one action on the one or more qubits, performed by the components 16, 18, 20, 22, 24. [0048] The plurality of gate electrodes 50 may be provided with voltages. The plurality of gate electrodes 50 may be made of metal. The plurality of gate electrodes 50 may be superconducting. The voltages may serve one or more purposes, such as defining the at least one path 45, moving (shuttling) the one or more qubits, and/or implementing the at least one action on the one or more qubits. The voltages may comprise DC (direct current) voltages and AC (alternating current) voltages. The voltages may comprise one or more stationary voltages and one or more non- stationary voltages. The voltages may be applied by means of DC lines, AC lines, and/or bias tees. [0049] One or more of the components 16, 18, 20, 22, 24 may further comprise at least one magnet 35, such as a micromagnet (see FIGS.3B-3D). The at least one micromagnet 35 may be placed on top of the component 16, 18, 20, 22, 24. The at least one micromagnet 35 provides a magnetic field. The magnetic field may have a zero gradient or a non-zero gradient. The at least one magnet 35 may have a distance from the quantum well 69 of 150nm. The at least one magnet may have dimensions of 400nm ×200nm ×20nm. The at least one magnet 35 may be arranged on a dielectric or insulating layer 68 (see FIGS.3B-3D). The dielectric or insulating layer 68 may be arranged on the conveyor gates 50b (see FIG.3B) or on a top gate 50d (see FIGS.3C and 3D and below). [0050] An external magnetic field ^_^ splits the plurality of spin states (e.g., the spin-up state and the spin-down state) used as a computational basis for the one or more qubits into spin-dependent energy levels (Zeeman splitting). The external magnetic field ^_^ may be provided by an external magnet, e.g., an electromagnet (not shown), that is placed in the vicinity of the quantum processor 10. The quantum processor 10 may at least partially be placed in the external magnetic field ^_^ provided by the external magnet. [0051] The one or more components 16, 18, 20, 22, 24 may further comprise means for providing electromagnetic radiation, e.g., microwaves, for manipulating the quantum state of the one or more qubits, e.g., switching the spins of the one or more qubits between the plurality of spin states. The electromagnetic radiation may be provided by means of one or more of the gate electrodes 50b. The spin of a qubit may be switched between, e.g., the spin-up and the spin-down state, or vice versa, by means of the electromagnetic radiation based on electron spin resonance (ESR). The frequency of the electromagnetic radiation may equal the energy difference of the separated energy levels. ESR provides a further way of manipulating the quantum state of the one or more qubits. The microwaves may have a frequency in the range of several hundred MHz to several hundred GHz. In one aspect, the frequency lies in the range of 9–10 GHz, but is not limited thereto. [0052] Providing an inhomogeneous magnetic field, e.g., by means of the at least one magnet 35, i.e., having a non-zero gradient, enables manipulating the quantum state of the one or more qubits, e.g., rotating the spin of the qubit. The rotating enables driving transitions between the plurality of spin states by means of a displacement of the one or more qubits in the inhomogeneous magnetic field based on, e.g., an AC electric field. The AC electric field may be provided by means of one or more of the gate electrodes 50b. This effect is called electric dipole spin resonance (EDSR). The displacement may make the qubit oscillate between the plurality of spin states (e.g., the spin states forming the computational basis such as the spin-up state and the spin-down state).For example, the qubit may oscillate such that the spin-up state can be switched to the spin-down state, and vice versa. [0053] Alternatively, the EDSR may be achieved in one of the semiconductor heterostructure 12 in which spin-orbit coupling is present. The semiconductor heterostructure 12 may be made from semiconductor materials that provide the spin- orbit coupling [0054] The plurality of gate electrodes 50 may be provided as one or more of gate electrode assemblies 50a, 50b, 50c, 50d. The plurality of gate electrodes 50 may comprise one or more laterally positioning gate electrodes (also termed "screening gates”) 50a (see FIG.3A and 6A) arranged to define and/or modify a lateral position of a trajectory 80 (see FIG.6C and 6D) in the quantum well 69 and/or at the at least one path 45 for moving (shuttling) the one or more qubits within the unit cell or beyond the unit cell. The trajectory 80 may be a trajectory of one or more potential wells (further described below), in which the one or more qubits are arrangeable. The one or more potential wells may thus be one or more travelling potential wells. The trajectory of the one or more potential wells 80 may thus correspond to a trajectory of the one or more qubits arranged at the least one path 45. Thus, the lateral position of the trajectory80 may correspond to a lateral position of the one or more potential wells and/or of the one or more qubits. Arranging the one or more qubits at the least one path 45 is to be understood to mean that the one or more qubits are arranged within the quantum well 69. [0055] The plurality of gate electrodes 50 may further comprise one or more shuttling gate electrodes (also termed “conveyor gates” or “finger gates” or “clavier gates”) 50b (see FIG.3A) arranged to move (shuttle) the one or more qubits along the at least one path 45 for moving (shuttling) the one or more qubits within the unit cell or beyond the unit cell. [0056] The plurality of gate electrodes 50 may further comprise at least one vertically positioning gate electrode (also termed “back gate”) 50c arranged to define and/or modify a vertical position of the trajectory 80 (see FIG.6D) in the quantum well 69 and/or at the at least one path 45 for moving (shuttling) the one or more qubits within the unit cell or beyond the unit cell. The vertical position of the trajectory 80 may correspond to a vertical position of the one or more potential wells and/or of the one or more qubits. [0057] The plurality of gate electrodes 50 may further comprise qubit-handling gate electrodes arranged for performing the at least one action on the one or more qubits. The qubit-handling electrodes include plunger gates and barrier gates. The plunger gates may be used to control the occupation of a quantum dot, to control a detuning in a double quantum dot, and/or to perform an exchange of two qubits. The barrier gates may be used to form a potential double-well and/or to control the tunnel barrier in a double quantum dot. [0058] The plurality of gate electrodes 50 may be arranged on the at least one surface 14 of the semiconductor heterostructure 12. The plurality of gate electrodes 50 may be arranged in layers that are separated by an insulating or dielectric layer 60 and the insulating or dielectric layer 66 (see FIG.3B-3D and 6D). In one aspect, the layers may be arranged in a direction substantially perpendicular to the direction of the at least one path 45. [0059] One or more of the insulating or dielectric layer 60, the insulating and dielectric layer 66, and/or the insulating or dielectric layer 67 may be planarized. A method of manufacturing the shuttling element 16 may comprise the step of planarizing one or more of the insulating or dielectric layer 60, the insulating and dielectric layer 66, and/or the insulating or dielectric layer 67. The insulating or dielectric layer 60 may be planarized during manufacturing before arranging the conveyor gates 50b on the insulating or dielectric layer 60. The planarizing facilitates using processes such as electron ray epitaxy, Deep UV, and/or spacer lithography. The planarizing reduces the thickness of one or more of the dielectric or insulating layers 60, 66, 67. For instance, the insulating or dielectric layers 66 and/or 60 may be planarized before manufacturing of the conveyor gates 50b to reduce the thickness of the insulating or dielectric layer 66 and/or 60, respectively. After planarization, the insulating or dielectric layers 66 and/or 60 are tightly placed on the semiconductor heterostructure 12. Planarizing the insulating or dielectric layers 66 and/or 60 results in the thickness of the insulating or dielectric layers 66 and/or 60 being reduced between the at least one path 45 and the conveyor gates 50b. In one aspect, the thickness of the insulating or dielectric layer 60 is required to cover a top surface and sides of the screening gates 50a. [0060] The component 16 serves to move (shuttle) the one or more quantum dots in the semiconductor heterostructure 12 for moving (shuttling) the one or more qubits within the unit cell or beyond the unit cell. The component 16 is also termed “shuttling lane”. Aspects of the shuttling lane 16 are disclosed in international patent application no. WO 2021/052531 A1, the disclosure of which is incorporated herein by reference in its entirety. [0061] The component 18 provides a junction at which the one or more quantum dots may be diverted into at least one branch (at least one second one of the at least one path 45) that branches off of the at least one path 45 for moving (shuttling) the one or more qubits within the unit cell or beyond the unit cell. The component 18 is also termed “T-junction”. The at least one path 45 and the at least one branch of the T- junction 18 may be arranged perpendicular or non-perpendicular to one another. In one aspect, the at least one path 45 and the at least one branch of the T-junction 18 may substantially form a T-shape. Aspects of the T-junction 16 are disclosed in international patent application no. WO 2021/052539 A1, the disclosure of which is incorporated herein by reference in its entirety. [0062] The component 20 is provided for manipulating qubits in quantum dots. The component 20 is also termed “manipulation zone”. The manipulation zone 20 enables manipulating one or more current spin states of the one or more qubits. Any one qubit has a current spin state. In one aspect, the plurality of spin states may comprise the current spin state. In another aspect, the current spin state may be a linear combination of the plurality of spin states. During the manipulating, the one or more current spin states may be changed. Aspects of the manipulation zone 20 are disclosed in WO 2021/052537 A1, the disclosure of which is incorporated herein by reference in its entirety. [0063] The component 22 serves to initialize the one or more spin states of the one or more qubits. When the one or more spin states have been initialized, any one of the one or more current spin states is equal to one of the plurality of spin states. After initialization, the one or more current spin states may remain unchanged during a relaxation time. The relaxation time describes transitions between the spin-up state and the spin-down state due to interactions with the environment, such as the lattice of the semiconductor heterostructure 12. The component 22 is also termed “initialization zone”. Aspects of the initialization zone 22 are disclosed in WO 2021/052538 A1, the disclosure of which is incorporated herein by reference in its entirety. [0064] The component 24 serves to read out the one or more spin states of the one or more qubits. When the one or more spin states have been read out, any one of the one or more current spin states prior to readout is known. The component 24 is also termed “readout zone”. Aspects of the readout zone 24 are disclosed in WO 2021/052536 A1, the disclosure of which is incorporated herein by reference in its entirety. [0065] In one aspect of the disclosure, the initialization zone 22 and the readout zone 24 are the same component. [0066] The quantum processor 10 is operated to perform algorithms, such as quantum algorithms. The performing of the algorithms includes performing the sequence of actions on the one or more qubits, as explained above. The at least one action is performed by the components 16, 18, 20, 22, 24 of the unit cells 26. [0067] The operating of the quantum processor 10 involves controlling the at least one action performed by the components 16, 18, 20, 22, 24. In one aspect of the disclosure, the at least one action is controlled by applying the voltages to the plurality of gate electrodes 50. The voltages may be set and/or adjusted to increase a fidelity F of the at least one action or of the sequence of actions. The fidelity F is a measure of how reliably the at least one action or the sequence of actions results in the outcome that is expected based on the design of the quantum processor 10 and on the voltages applied to the plurality of gate electrodes 50. To determine the fidelity F, the at least one action or the sequence of actions is repeated; subsequently the proportion of the repetitions is determined in which the actual outcome equals the expected outcome. The actual outcome includes the one or more current spin states that have been read out at the readout zone 24 after the at least one action or the sequence of actions. The expected outcome includes the one or more current spin states that are, based on known fidelities of the components 16, 18, 20, 22, 24 and/or the relaxation time of the one or more qubits, expected to be read out at the readout zone 24 after the at least one action or the sequence of actions. [0068] For example, the at least one action may comprise the moving (shuttling) of the one or more qubits along the at least one path 45 of the shuttling lane 16, e.g., to the manipulation zone 20, and the manipulating the quantum state of the one or more qubits in the manipulation zone 20. In this case, the fidelity F of performing the at least one action is a combination, i.e., the product, of a shuttling fidelity FS and a manipulation fidelity F_M, i.e., F = F_S × F_M. The manipulation fidelity F_M, relating to the manipulation zone 20, may then be calculated by dividing the fidelity F by the shuttling fidelity. The manipulation fidelity FM is understood to be a probability that the one or more current spin states of the one or more qubits are changed as expected during the manipulating. The shuttling fidelity F_S may be determined, for example, by repeatedly performing the sequence of actions: initialization of a qubit, moving (shuttling) of the qubit, and readout of the qubit; followed by determining whether the initialized spin state of the one or more qubits are equal to the one or more current spin states after shuttling and prior to readout; and finally calculating the proportion of the repetitions in which the one or more spin states were unaltered. The manipulation fidelity F_M may be determined, for example, by repeatedly performing the sequence of actions: initialization of the one or more qubits, moving (shuttling) of the one or more qubits, manipulation of the one or more qubits, and readout of the one or more qubits; followed by determining whether the one or more initialized current spin states of the one or more qubits are changed as expected; calculating the proportion of the repetitions in which the one or more current spin state are changed as expected, dividing the result by the shuttling fidelity FS. [0069] As explained above, determining the shuttling fidelity FS involves an initialization step and a readout step. In a manner analogous to the determination of the manipulation fidelity FM, the shuttling fidelity FS may be determined by determining a fidelity F that is a combination, i.e., a product, of an initialization fidelity, a shuttling fidelity, and a readout fidelity, and by subsequently dividing the fidelity F by the initialization fidelity and the readout fidelity. [0070] The fidelity F may further be a gate fidelity. The gate fidelity F is a measure of how closely the outcome of a gate operation (i.e., the sequence of actions by means of the components 16, 18, 20, 22, 24 on the one or more qubits that are associated with a gate the quantum processor 10 is designed to implement) matches the expected, e.g., theoretical, outcome based on the design of the quantum processor 10 and the components 16, 18, 2022, 24. The gate fidelity F may be determined by randomized benchmarking. [0071] The gate fidelity F may be determined by employing state and process tomography which both allow the reconstruction and/or estimation of single logic operations, e.g., a logic gate. Another way of determining the gate fidelity F may be uses randomized benchmarking (RB) or gate set tomography (GST). Both RB and GST are nearly calibration-free and allow the reconstruction and/or estimation of sets of logic operations, e.g., a sequence of initialization, multiple manipulations and subsequent measurement. Thus, both methods are resilient to state preparation and measurement (SPAM) errors. [0072] For standard RB, so-called Clifford gate operations are performed that evenly sample a Hilbert space. The benchmarking subsequently averages across errors. In one aspect, an electron is initialized to the spin-down state, followed by randomized sequences of multiple Clifford gates and a final Clifford gate which is chosen such that the final target state in the absence of errors is either spin-up or spin-down. Applying random sequences of imperfect Clifford gates may result in a depolarizing channel. Repeating the afore-described procedure, possibly with different numbers of Clifford gates, may allow the extraction of the gate fidelity F. [0073] Alternatively to increasing one or more fidelities, errors syndromes may be reduced. A syndrome S is measured by preparing a known state, e.g., |0^, applying a suitable sequence of gate operations, e.g., a π/2x rotation (a pi-half-x rotation), and determining the probability p(|0^) of obtaining the state |0^ by measuring the sequence 10³...10⁴ times. In the case of perfect gates, the probability will be p(|0^) = 0.5, corresponding to S = ^σz^ = 0. The prepared state is preferably an eigenstate. In other words, an error syndrome S is a measure for the deviation from the expected probability distribution of measurement outcomes for a specific sequence of gate operations. Appropriate error syndromes are chosen in such a way that relevant decoherence channels, i.e., sources for the loss of coherence, are identified. Minimizing the error syndromes by adjusting the voltages for the gate operations yields an overall improved performance of the quantum computer 10. [0074] As an example, increasing the manipulation fidelity FM of one or more qubits, e.g., the single qubit or the two qubits, at the manipulation zone 20 will be described. FIG.3A shows an aspect of the manipulation zone 20. The manipulation zone 20 comprises the screening gates 50a and the conveyor gates 50b arranged on the at least one surface 14 of the semiconductor heterostructure 12. In the aspect shown in FIG.3A, the at least one surface 14 comprises a top surface 141 of the semiconductor heterostructure 12. In the aspect shown in FIG.3B, the top surface 141 may be a top surface of dielectric or insulating layer 66 (further described below). [0075] The screening gates 50a are arranged to extend on either side of a first path 451 and a second path 452 as screening gates 50a-1 and 50a-2 (see also FIG.6A). In one aspect, as shown in FIGS.3A-3C, the screening gates 50a-1 and 50a-2 may extend continuously along the at least one path 45. In another aspect, the screening gates 50a-1 and 50a-2 may be interrupted. The screening gates 50a-1 and 50a-2 may be spaced apart by approximately 200nm. The screening gates 50a may be made from metal and may be manufactured by embedding the metal in the semiconductor heterostructure 12 or by local implantation of the semiconductor heterostructure 12. The screening gates 50a may be embedded in the dielectric or insulating layer 66 and/or in the dielectric or insulating layer 60. [0076] The dielectric or insulating layer 66 and/or in the dielectric or insulating layer 60 may be structured in the lateral direction D3. In one aspect, the dielectric or insulating layer 66 and/or in the dielectric or insulating layer 60 may be provided as two separate portions (not shown), the separate portions enveloping the two screening gates 50a-1 and 50a-2, and the semiconductor heterostructure 12 extending into a space (not shown) between the two portions along the lateral (or transverse direction) D3. The semiconductor heterostructure 12 thus may form a ridge (not shown) in the space between the two portions of the dielectric or insulating layer 66 and/or in the dielectric or insulating layer 60. [0077] The conveyor gates 50b may extend transversely across the first path 451 and/or the second path 452 (as shown in FIG.3A). For example, the conveyor gates 50b may extend in a lateral direction D3. The conveyor gates or finger gates 50b are arranged along the at least one path 45. [0078] In the aspect shown in Fig.3A, the conveyor gates 50b have a first conveyor gate assembly 50b1 and a second conveyor gate assembly 50b2. In FIGS.3A-D, the first conveyor gate assembly 50b1 and second conveyor gate assembly 50b2 are indicated by the braces at the top of the drawings. In addition, three electrodes belonging to the first conveyor gate assembly 50b1 and three electrodes belonging to the second conveyor gate assembly 50b2 are indicated in FIGS.3A-D for the sake of clarity. The first conveyor gate assembly 50b1 and/or the second conveyor gate assembly 50b2 is arranged to extend transversely across at least part of the first path 451 and/or the second path 452, respectively. The first conveyor gate assembly 50b1 and the second conveyor gate assembly 50b2 are arranged at an interface 25 such that the first path 451 and the second path 452 meet at the interface 25 (see FIGS. 3A and 3B). [0079] The first path 451 and the second path 452 meet at the interface 25 such that a first qubit, trapped in first quantum dot and shuttled along the first path 451 to the interface 25, and a second qubit, trapped in a second quantum dot and shuttled along the second path 452, can undergo at least one two-qubit action (or operation) at the interface 25. The one or more potential wells may comprise one or more first potential wells. The first qubit may be shuttled (moved) along the first path 451 by the one or more first travelling potential wells. The one or more first travelling potential wells may be generated by applying the voltages to the first conveyor gate assembly 50b1. Likewise, the one or more potential wells may comprise one or more second potential wells. The second qubit may be shuttled (moved) along the second path 452 by the one or more second travelling potential wells. The one or more second travelling potential wells may be generated by applying the voltages to the second conveyor gate assembly 50b2. [0080] The at least one two-qubit action (or operation) at the interface 25 are enabled by forming at the interface ones of the one or more potential wells that are stationary (“one or more stationary potential wells”). The one or more stationary potential wells may comprise at least one first stationary potential well and at least one second stationary potential well. [0081] The at least one first stationary potential well may be arranged at the interface 25. For instance, the at least one first stationary potential well may be adjacent to the interface. The at least one first stationary potential well may be generated by the first conveyor gate assembly 50b1. Likewise, the at least one second stationary potential well may be arranged at the interface 25. For instance, the at least one second stationary potential well may be adjacent to the interface. The at least one second stationary potential well may be generated by the second conveyor gate assembly 50b2. [0082] The first qubit may be trapped in the at least one first stationary potential well. Likewise, the second qubit may be trapped in the at least one second stationary potential well. When the at least one first stationary potential well and the at least one second stationary potential are arranged at the interface 25, the first qubit trapped in the least one first stationary potential well and the second qubit trapped in the at least one second potential well may undergo the at least one two-qubit action (or two-qubit operation). [0083] For example, at the interface 25 a potential barrier may be formed by means of the first conveyor gate assembly 50b1 and the second conveyor gate assembly 50b2 between the at least one first stationary potential well and the at least one second stationary potential well. For example, the potential barrier may be formed by an electrode subset 50b1-4 (described below) of the first conveyor gate assembly 50b1 and an electrode subset 50b2-1 (described below) of the second conveyor gate assembly 50b2. [0084] A lowering/raising of the potential barrier may increase/decrease a tunnel coupling across the potential barrier (also referred to as “tunnel barrier”). In one aspect, the height of the potential barrier may be adjusted by pulsing, e.g., by non- adiabatic pulsing. The energy level in the at least one first stationary potential well and in the at least one second stationary potential well may or may not be different relative to one another, which is referred to as a detuning. The detuning may be zero or non-zero. The detuning may be generated by means of the first conveyor gate assembly 50b1 and the second conveyor gate assembly 50b2. For example, the detuning may be generated by an electrode subset 50b1-3 (described below) of the first conveyor gate assembly 50b1 and an electrode subset 50b2-2 (described below) of the second conveyor gate assembly 50b2. [0085] The tunnel coupling and the detuning determine an exchange coupling J between the first qubit trapped in the first stationary potential well and the second qubit trapped in the second stationary potential well. The exchange coupling J enables the first qubit and/or the second qubit to tunnel through the potential barrier into the at least one first stationary well or the at least one second stationary potential well. [0086] The first conveyor gate assembly 50b1 has electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4 (indicated in FIGS.3A-D by indices 1, 2, 3, 4 above the conveyor gates of the corresponding electrode subset). The ones of the conveyor gates 50b that belong to one of the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4 are marked with the same index at the top of FIGS.3A-3D, i.e., the index 1, 2, 3, or 4. The number of electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4 shown in FIG.3A is four. Likewise, the second conveyor gate assembly 50b2 has electrode subsets 50b2-1, 50b2-2, 50b2-3, 50b2-4 (indicated in FIG.3A-D by indices 1, 2, 3, 4 above the conveyor gates of the corresponding subset). The ones of the conveyor gates 50b that belong to one of the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4 are marked with the same index at the top of FIGS.3A-3D, i.e., the index 1, 2, 3, or 4. As shown in FIGS.3A and 3B, the interface 25 is located at one conveyor gate of the electrode subset 50b1-4 of the first conveyor gate assembly 50b1 and at one conveyor gate of the electrode subset 50b2-1 of the second conveyor gate assembly 50b2. The number of electrode subsets 50b2-1, 50b2-2, 50b2-3, 50b2-4 shown in FIG.3A is four. However, the number of the electrode subsets of the first conveyor gate assembly 50b1 and/or the second conveyor gate assembly 50b2 may differ from this example and be, e.g., three or five. Any number of the electrode subsets of the conveyor gates 50b may be chosen, as long as the one or more travelling potential wells for moving (shuttling) a qubit (see below) can be generated. [0087] The one or more travelling potential wells provide the confinement to trap an electron or hole, the strength of which is sufficiently strong to overcome disorder during moving (shuttling) in the quantum well 69, and the height of which provide barriers between adjacent potential well to suppress tunnelling. The trapped one or more electrons or holes adiabatically follow a sufficiently slow translation of the potential. The disorder is due to one or more of defects at boundaries of the layers of the semiconductor heterostructure 12, defects within the layers of the heterostructure 12, and/or defects within the dielectric layers 60, 66 and/or 67. The defects at the boundaries of the layers of the semiconductor heterostructure 12 include charge defects at interfaces between layers made from semiconductor materials and the dielectric or insulating layers 60 and/or 66. These charge defects are randomly distributed, e.g., at the interfaces. A density of the charge defects was set to 5E10/cm². Transitions to excited orbital states of the electron confined in the one or more travelling potential wells are caused by the disorder. In a moving frame of the one or more travelling potential wells, the disorder that quasi-statically fluctuates turns into dynamic noise that couples the orbital levels. Setting the shuttling velocity is set to v = 10 m/s results in a reduced orbital excitation rate and a below-threshold phase error. [0088] In one aspect, the conveyor gates 50b may be arranged at the at least one path 45 in a manner, in which juxtaposed ones of the conveyor gates 50b extend differently far in the lateral (or transverse) direction D3 (as shown in FIG.3A). In another aspect the conveyor gates 50b may extend equally far in the lateral (or transverse direction) D3. [0089] The conveyor gates 50b may be arranged in a substantially equidistant manner with a substantially constant conveyor gate spacing between any two neighboring conveyor gates 50b. If a conveyor gate width, i.e., an extension of the conveyor gates 50b in the longitudinal direction D3, of the conveyor gates 50b is substantially constant, also a conveyor gate pitch, which is the sum of the conveyor gate spacing and the conveyor gate width, is substantially constant. In one aspect of the disclosure, the conveyor gate pitch may be approximately 80nm. The conveyor gates 50b may be arranged in a periodic manner. In one aspect, the conveyor gates 50b of any one of the electrode subsets 50b-1, 50b-2, 50b-3, 50b-4 may be arranged in a substantially equidistant manner from each other based on a spatial period of the periodically arranged conveyor gates. In another aspect, any two conveyor gates 50b belonging to any selected one of the electrode subsets 50b-1, 50b-2, 50b-3, 50b-4 have one conveyor gate of each of the other non-selected ones of the electrode subsets arranged therebetween. The periodical arrangement of the conveyor gates 50b facilitates industrial manufacturing of the shuttling path 16. [0090] The conveyor gates belonging to any one of the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4, shown in FIG.3A, are electrically connected to each other by an electrical connection (not shown). The conveyor gates of any selected electrode subset from the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4 are electrically disconnected from (or not electrically connected to) the conveyor gates of the corresponding non-selected electrode subsets. The electrical connection may be provided by a metal strip arranged parallel to the screening gates 50a. The electrode subsets of the conveyor gates 50b1 and/or 50b2 with indices 1 and 3 may have the electrical connection on one side of the at least one path 45 (above the at least one path 45 as seen in FIG.3A). The electrode subsets of the conveyor gates 50b with indices 2 and 4 may have the electrical connection on the other side of the at least one path 45 (below the at least one path 45 as seen in FIG.3A). In one aspect of the disclosure, the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4 may be arranged at different levels in the stacking direction D1. For example, the metal strip connecting the conveyor gates of the electrode subset 50b1- 1 or 50b2-1 may be arranged on one side of the at least one path 45 at a higher level in the stacking direction D1 than the metal strip connecting the conveyor gates of the electrode subset 50b1-3 or 50b2-3, respectively; and/or the metal strip connecting the conveyor gates of the electrode subset 50b1-2 or 50b2-2 may be arranged on the other side of the at least one path 45 at a higher level in the stacking direction D1 than the metal strip connecting the conveyor gates of the electrode subset 50b1-4 or 50b2-4, respectively. The electrode subsets 50b-1, 50b-2, 50b-3, 50b-4 may each be arranged at the level at which the corresponding metal strip is arranged. In another aspect, the metal strips may be all arranged on one side of the at least one path 45. In a further aspect, ones of the metal strips connecting the conveyor gates of the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4 may be electrically connected to the conveyor gates of the corresponding electrode subset by vias; and the conveyor gates of the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4 may be arranged at substantially one level in the stacking direction D1. [0091] The electrical connection of the conveyor gates of any one of the electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4 enables providing a single voltage to the corresponding electrode subset of conveyor gates of the first conveyor gate assembly 50b1 or the second conveyor gate assembly 50b2. In other words, the number of voltage signals applied to the conveyor gates 50b is given by the number of electrode subsets chosen. As a result, the number voltage signals applied to screening gates 50a and the conveyor gates 50b is independent of a length of the shuttling element 16. In the example shown in FIGS.3A and 3B, the number of electrode subsets is four. However, the number may be smaller or larger than four. For example, using three electrode subsets may achieve moving the one or more qubits by means of the travelling potential well. [0092] The at least one magnet 35 provides a magnetic field (not shown). The magnetic field may be an inhomogeneous magnetic field. The magnetic field of the magnetic field provided by the at least one magnet 35 may have a non-zero magnetic field strength at the quantum well 69. The magnetic field may have a longitudinal component of non-zero longitudinal magnetic field strength at the quantum well 69 along a shuttling direction (or longitudinal direction) D2. The magnetic field may have a transverse component of non-zero transverse magnetic field strength at the quantum well 69 along the lateral (or transverse) direction D3. [0093] Furthermore, the magnetic field of the at least one magnet 35 may have a transverse component of non-zero transverse magnetic field strength and transverse to the external magnetic field ^_^. This transverse component of the magnetic field may have a gradient in the shuttling direction D2. In addition or alternatively, the magnetic field of the at least one magnet 35 may have a parallel component of non- zero parallel magnetic field strength and parallel to the external magnetic field ^_^. This parallel component of the magnetic field may have a gradient in the shuttling direction D2. [0094] This enables the magnetic field acting on the one or more qubits, when the one or more qubits are trapped in a potential well in the quantum well 69 where the magnetic field strength is non-zero. With the inhomogeneous magnetic field of the at least one magnet 35, the EDSR (see above) may be used to rotate the one or more spins of the one or more qubits. [0095] As shown FIGS.3A-D, the at least one magnet 35 may comprise a first magnet 35-1 and a second magnet 35-2. An example of the first magnet 35-1 is a first micromagnet. An example of the second magnet 35-2 is a second micromagnet. [0096] The first magnet 35-1 may be arranged at the first conveyor gate assembly 50b1. The first magnet 35-1 may be arranged at a distance from the interface 25. A first magnetic field of the first magnet 39-1, which may be inhomogeneous, has a first magnetic field strength (having a longitudinal component and/or a transverse component, as described above) that has a non-zero value at a first portion 69-1 of the quantum well 69. In one aspect, the first magnetic field strength substantially vanishes at the interface 25. [0097] The second magnet 35-2 may arranged at the first conveyor gate assembly 50b1. The second magnet 35-2 may be arranged in a vicinity of the interface 25. In one aspect, the second magnet 35-2 may be arranged at the first conveyor gate assembly 50b1 and the second conveyor gate assembly 50b2. In other words, the second magnet 35-2 may extend across the interface 25 in the shuttling direction (or longitudinal direction) D2. [0098] A second magnetic field of the second magnet 39-2, which may be inhomogeneous, has a second magnetic field strength (having a longitudinal component and/or a transverse component, as described above) that has a non-zero value at a second portion 69-2 of the quantum well 69. The second portion 69-2 may be located in the vicinity of the interface 25. In one aspect, the second portion 69-2 of the quantum well 69 may be located on both sides of the interface 25 along the shuttling direction (or longitudinal direction) D2. The second magnetic field strength may have a non-zero value at the interface 25. [0099] In another aspect of the disclosure, the manipulation zone 20 may comprise solely the first magnet 35-1 or solely the second magnet 35-2. [00100] In a further aspect of the disclosure, the manipulation zone 20 may comprise the top gate 50d (see FIG.3C and 3D). The top gate 50d may extend in the lateral (transverse) direction D3. The top gate may extend in the shuttling direction (or longitudinal direction) D2. The top gate 50d may cover at least part of the first path 451 and/or the second path 452. In one aspect, at least in the lateral (transverse) direction D3, the top gate 50d completely covers the first path 451 and/or the second path 452. [00101] In yet another aspect of the disclosure, the top gate electrode 50d may be arranged above the conveyor gates 50b with a dielectric or insulating layer 67 arranged therebetween (see FIGS.3C and 3D). The dielectric or insulating layer 67 may be partially arranged on the dielectric or insulating layer 60 (see FIGS.3C, 3D, and 6D). Portions of the dielectric or insulating layer 67, which are arranged between the conveyor gates 50b, may be arranged on the dielectric or insulating layer 60 (see FIGS.3C, 3D, and 6D). The dielectric or insulating layer 67 may be structured, e.g., segmented or profiled, in the shuttling direction D2 (see FIG.6D). The dielectric or insulating layer 67 insulates the conveyor gates 50b that belong to different ones of the subsets 50b-1, 50b-2, 50b-3, 50b-4 from each other. In one aspect of the disclosure, the dielectric or insulating layers 60 and 67 are a single dielectric or insulating layer 60, 67, in which the conveyor gates 50b are embedded. [00102] The top gate 50d may be applied with a constant voltage. In a further aspect, the voltage applied to the top gate 50d may be modified on the one or more actions on the one or more qubits. For example, the voltage applied to the top gate 50d may be modified for shuttling the one or more qubits, for initializing the one or more qubits, for reading out of the one or more qubits, for manipulating the one or more qubits. In another example, the voltage applied to the top gate 50d may be modified according to sequence of actions on the one or more qubits, for instance as part of performing an algorithm. In yet a further aspect, the voltage applied to the top gate 50d may be modified periodically or non-periodically. The periodically modifying and/or the non-periodically modifying of the voltage applied to the top gate 50d may depend on the action performed on the one or more qubits. The periodically modifying of the voltage applied to the top gate 50d includes adding a square wave, a sawtooth wave, a superposition of sine waves. The periodically modifying of the voltage applied to the top gate 50d includes adding a stepwise increment to the voltage applied to the top gate 50d. The stepwise increment may depend on the one or more actions performed on the one or more qubits. [00103] In one aspect, the top gate 50d may have a planar top surface (not shown). In another aspect of the disclosure, the top gate 50d may be structured. An example of the structured top gate 50d is a segmented top gate 50d (see FIG.3D) and/or a top gate 50d with a surface profile (or profiled top gate). As shown in FIG. 3D, the top gate 50d may be structured, e.g., segmented and/or profiled, along the shuttling direction (or longitudinal direction) D2. Additionally or alternatively to the longitudinal structuring, the top gate 50d may be structured, e.g., segmented and/or profiled, along the lateral direction (or transvers direction) D3. In the aspect shown in FIG.3D, the top gate 50d comprises a plurality of electrodes 50d-1, 50d-2, …, 50d- 12. [00104] The top gate 50d enables increasing the conveyor gate pitch between the conveyor gates 50b whilst maintaining the ability to shuttle the one or more qubits along the at least one path 45. Furthermore, the structured, e.g., segmented, top gate 50d shown in FIG.3D enables adjusting or tuning the Rabi frequency of the EDSR, generated by the magnetic field of the at least one magnet 35 and the applied AC electric field, by applying one or more adjustment voltages to one or more of the plurality of electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d (see below). [00105] In an aspect of the disclosure, the at least one surface 14 may further comprise a back surface 142. The at least one back gate 50c may be arranged on the back surface 142 of the semiconductor heterostructure 12 opposite the top surface 141 (see FIG.3D). The back surface 142 may be arranged at a bottom of the semiconductor heterostructure. The back surface 142 may be arranged opposite the top surface 141. The back surface 142 may be a surface of the layer of silicon dioxide 62 (described above). [00106] The at least one back gate 50c may extend along the shuttling direction (or longitudinal direction) D2. The at least one back gate 50c may further extend laterally (or transversely to the at least one path 45). For example, the at least one back gate 50c may further extend along the lateral (or transverse) direction D3 transverse to the at least one path 45. The at least one back gate 50c may overlap with or intersect the screening gates 50a in the lateral direction D3. The at least one back gate 50c may be arranged opposite the screening gates 50a. A voltage may be applied to the at least one back gate 50c to provide an electrical potential to modify the confinement at the quantum well 69. [00107] In one aspect of the disclosure, the at least one back gate 50c may be structured, e.g., segmented and/or profiled, along the shuttling direction D2. In another aspect of the disclosure, the at least one back gate 50c may be structured, e.g., segmented and/or profiled, along the lateral direction D3 transverse to the at least one path 45. In a yet a further aspect of the disclosure, the at least one back gate may be structured along the shuttling direction D2 and the lateral direction D3. [00108] As shown in FIGS.3B-D and 6D, the screening gates 50a and the conveyor gates 50b are separated by the insulating or dielectric layer 60. As explained above, the insulating or dielectric layer 60 may be planarized during manufacturing before arranging the conveyor gates 50b on the insulating or dielectric layer 60. The four electrode subsets of the conveyor gates 50b are separated by further insulating or dielectric layers or material (not shown). Furthermore, a dielectric or insulating layer 66 may be provided on the semiconductor heterostructure 12 (see FIG.3B-3D and 6D). The insulating or dielectric layer 66 separates the screening gates 50a and the semiconductor heterostructure 12. The screening gates 50a may be provided on the insulating layer 66. [00109] The manipulation zone 20 is configured to manipulate the one or more qubits at the least one magnet 35. During the operation of the quantum processor 10, the manipulation zone 20 will be used to manipulate the one or more qubits. The manipulating may be a single-qubit action or two-qubit action. [00110] In one aspect of the disclosure, the single-qubit action is the rotating of the one or more qubits by means of the EDSR, which is based on moving, by applying the AC electric field, one or more wave functions of the one or more electrons (or holes) trapped (confined) in the potential well that is located in the first portion 69-1 of the quantum well 69, where the first magnetic field strength of the inhomogeneous first magnetic field of the first magnet 35-1 is non-zero. The AC electric field may be generated by a microwave signal, e.g., applied to one or more of the conveyor gates 50b. The resulting Rabi frequency is given by ^ = ⁽^^_^^_^ ^⁄ 2^ ⁾⁽^^_^ ^⁄ ^^ ⁾ , where g is the g-factor, µB the Bohr magneton, E0 an amplitude of the AC electric field, ^^_^ ^⁄ ^^ a gradient in the shuttling direction D2 (represented by x) of the magnetic field of the at least one magnet 35 transverse to the external magnetic field ^_^ (the transverse component of the magnetic field of the at least one magnet 35 described above), and κ the curvature of the confining potential well, which in the first approximation may be described by a parabolic potential ⁽1⁄ 2 ⁾ ^^^{^}around a minimum of the confining potential well at ^ = 0. The strength of the confining potential and the orbital level splitting are determined by the curvature κ. From the equation for the Rabi frequency Ω it can be seen that a change ^^ in the curvature κ of the confining potential well results in a change ^^ in the Rabi frequency Ω given by ^^ = ^ ⁽^^⁄ ^ ⁾ ^^. [00111] In one aspect of the disclosure, the one or more qubits are moved (shuttled) in an oscillatory manner at a location of a maximum of the gradient in the shuttling direction D2 of the magnetic field of the at least one magnet 35 transverse to the external magnetic field ^_^. For high fidelity single-qubit gates, an amplitude of the oscillatory moving of the one or more qubits is estimated to be on the order of 20 nm, which is significantly larger than for conventional EDSR, where the amplitudes are on the order of a few picometers. The higher amplitude allows for using weaker magnetic field gradients, which in turn increases the overall robustness against charge noise. [00112] The change ^^ in the curvature κ of the confining potential may be generated by applying one or more adjustment voltages to one or more of the plurality of electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d. [00113] We consider an adjustment voltage ΔV applied to a single electrode (termed hereafter “tuning gate”) of the plurality of electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d. This tuning gate may be located at the first portion 69-1 or at the second portion 69-2 of the quantum well 69. The tuning gate may be located in the vicinity of the potential well in which the one or more qubits are trapped. For instance, in the case of FIG.3D, the tuning gate may be one of the electrodes 50d-2, 50d-3, 50d-6, 50d-7, or 50-d8 of the top gate 50d, but is not limited thereto. If the potential well in which the one or more qubits are trapped is located in the first portion 69-1 or the second portion69-2, the Rabi frequency for rotating the one or more qubits may be changed. The adjustment voltage ΔV applied to the tuning gate results in an adjustment potential that may be modelled as a potential generated by a dipole line oriented perpendicular to the shuttling direction D2 (i.e., oriented in the lateral or and pointing in the stacking direction D1: ^_^^^ = ^_^^^,^ ⁽^^{^}⁄ ⁽^^{^} + ^^{^) )}, where ^_^^^,^ is a prefactor proportional to the adjustment voltage ΔV applied to the tuning gate relative to the voltages applied to plurality of gate electrodes 50 and the width of the tuning gate, ^ is the position along the shuttling direction D2, and ^ is a distance between the dipole line and the at least one path 45. Furthermore, the potential well in which the one or more qubits are trapped may be modelled as ^_^ = ^_^^ cos ^^^^ − ^_^ ⁽^⁾^^, where ^ = 2^⁄ ^ , ^ is the spatial period, ^_^^ is a prefactor determined by the voltages applied to the conveyor gates 50b, and ^_^ is a position along the shuttling direction D2 of the minimum of the potential well in which the one or more qubits are trapped. [00114] In order to maintain the one or more qubits trapped in the potential well, there is an upper bound for the adjustment voltage ΔV applied to the tuning gate. The upper bound for the adjustment voltage ΔV may correspond to an upper bound for the prefactor given by ^^_^^^,^^ < ⁽4.8 ^^⁄ ^ ^)|^_^^ ^|. The adjustability or tunability of the Rabi frequency Ω is quantified by the ratio of the confining strengths (or curvatures) of the adjustment potential and the shuttling potential, i.e., by the ratio of the second derivative ^^{^}^_^^^⁄ ^^^{^} and ^^{^}^_^⁄ ^^^{^} . The upper bound for the adjustment voltage estimated above leads to an adjustability (or adjustment range) or tunability (or tuning range) of the Rabi frequency Ω of 0.25 ^⁄ ^ . For typical values of ^ = 50^^ and λ = 300nm, the tuning range of the confinement strength is thus by a factor 1.5 larger than the confinement due to the shuttling potential ^_^ alone. For a deconfining adjustment (or deconfining tuning) of the Rabi frequency Ω, it is advisable to remain below the upper bound in order to retain a shape of the potential well that has a harmonic minimum. Further considerations lead to the conclusion that an amplitude of the displacement of the one or more qubits in the inhomogeneous magnetic field are bound by approximately 15nm in order to ensure that the potential well may be approximated by the first order quadratic potential that is described by the curvature κ. [00115] Examples of the adjustment potential ^_^^^ as well as the resulting sum of the adjustment potential ^_^^^ and the shuttling potential ^_^ (which may also be referred to as “adjusted potential well”) are shown in the upper panel of FIG.4, where values of ^ = 50^^ and λ = 300^^ were chosen. Two examples of the adjusted potential well are shown with the adjustment voltage weakening the confinement (“deconfining”) or strengthening the confinement (“confining”). The corresponding non-adjusted potential well is shown with the adjustment voltage not changing the confinement (“unperturbed”). The solid lines indicate the adjusted potential well. The dashed lines indicate the adjustment or tuning potential ^_^^^ . A Gaussian charge density indicating the spatial distribution of the one or more qubits that are trapped in the potential well is shown. As explained above, the adjusted potential well results in the adjusted Rabi frequency Ω. [00116] In another aspect of the disclosure, in the case of the presence of a non-zero gradient ^^_∥ ^⁄ ^^ in the shuttling direction D2 of a magnetic field of the at least one magnet 35 parallel to the external magnetic field ^_^ (the parallel component of the magnetic field of the at least one magnet 35 described above), the splitting of the spin-dependent energy levels by means of the external magnetic field ^_^ may be adjusted by changing an average position of the minimum of the potential well by means of another one of the adjustment potential . This adjustment potential may be generated by applying the adjustment voltage ΔV to one or more of the electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d. The applying of the adjustment voltage may result in the changing of an average position of the one or more qubits trapped in the potential well. [00117] We consider adjustment voltages ΔV applied to two electrodes (“tuning gates”) of the one or more of the electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d. The two tuning gates may be located in the vicinity of the potential well in which the one or more qubits are trapped. For instance, in the case of FIG.3D, the two tuning gates may be chosen from the electrodes 50d-2, 50d-3, 50d-6, 50d-7, or 50- d8 of the top gate 50d, but are not limited thereto. In one aspect, the two tuning gates may be located around the position of the potential well. For example, the two tuning gates may be located at a distance of the minimum of the potential well along the shuttling direction D2. The two tuning gates may comprise a first tuning gate located in FIG.3D on the left of the minimum of the potential well, and a second tuning gate located in FIG.3D on the right of the minimum of the potential well. If the potential well in which the one or more qubits are trapped is located in the first portion 69-1 or the second portion 69-2, the afore-mentioned choice of the two tuning gates will result in a changed average position of the potential well, e.g., the minimum of the potential well, in which the one or more qubits are trapped. The changed average position of the potential well results in a changed magnetic field generating the spin- dependent energy levels ^_^ + ^^_^ with ^^_^ = ⁽ ^^_∥ ^⁄ ^^ ⁾ ^^. As a result of the changed magnetic field the resonance frequency ^ = ⁽^^_^ ^⁄ ℎ ⁾^_^ changes by ^^ = ⁽^^_^ ^⁄ ℎ ⁾^^_^. [00118] One example of the adjustment potential ^_^^^ as well as the adjusted potential well are shown in the lower panel of FIG.4, where values of ^ = 50^^ and λ = 300^^ were chosen. An example of the adjusted potential well is shown with the adjustment voltage changing the position of the minimum of the potential well (“shifting”). The corresponding non-adjusted potential well is shown with the adjustment voltage not changing the position of the minimum of the potential well (“unperturbed”). The solid lines indicate the adjusted or non-adjusted potential well. The dashed lines indicate the adjustment or tuning potential ^_^^^ , which is here the sum of potentials generated by dipole lines with opposing values of the adjustment voltages applied thereto. Furthermore, a Gaussian charge density indicating the spatial distribution of the one or more qubits that are trapped in the potential well is shown. As explained above, the adjusted potential well results in the adjusted resonance frequency. [00119] The considerations regarding upper bounds of the adjustment voltages similarly apply in the case of adjusting the resonance frequency in order not to compromise shuttling of the one or more qubits. Similar assumptions (see above) lead to maximal shifts of the sum of minimum of the potential well and the displacement of the one or more qubits trapped within the potential well by about 15nm. [00120] In a further aspect of the disclosure, the potential barrier (or tunnel barrier) and the detuning at the interface 25 may be adjusted. The adjustment voltages ΔV may be applied to one or more of the electrodes 50d-1, 50d-2, …, 50d- 12 of the top gate 50d. For instance, one of the adjustment voltages ΔV may be applied to the electrode 50d-8 to increase or decrease the tunnel coupling across the potential barrier (tunnel barrier). Others of the adjustment voltages ΔV may be applied to the electrodes 50d-7 and 50d-9 to change the detuning between the at least one first stationary potential well and the at least one second stationary potential well. [00121] In another aspect of the disclosure, the adjusting voltages may be applied to the conveyor gates 50b instead of to one or more of the electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d. In the aspects of the disclosure shown in FIGS.3B and 3C, the conveyor gates 50b have electrode subsets 50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4 that are independently supplied with voltages. In the aspect shown in FIG.3D, at least three electrodes belonging to the electrode subsets 50b1-2, 50b1-3, 50b1-4 are located at the first portion 69-1 of the quantum well 69. Furthermore, at least three electrodes belonging to the electrode subsets 50b1-3, 50b1-4, 50b2-1 are located at the second portion 69-2 of the quantum well 69. One or more of the electrode subsets may be supplied with an AC voltage for shuttling the potential wells and with adjustment voltages (DC voltages) for adjusting the manipulation parameters in a similar manner as when the adjustment voltages are applied to the electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d. [00122] Additionally, the adjusting voltages may be applied to the top gate 50d and/or to the back gate 50c. [00123] The foregoing examples of adjusting the Rabi frequency ^, the resonance frequency ^, or the exchange coupling J explain how the manipulation fidelity F_M may be increased by adjusting parameters relating to the manipulating of the one or more qubits (or “manipulation parameters”). The manipulation parameters comprise the Rabi frequency ^, the resonance frequency ^, and the exchange coupling J. The adjusting of the manipulation parameters enables overcoming the effect of fidelity-reducing loci or disorder in the quantum well 69. The fidelity-reducing locus 70 may be the result of, for example, a manufacturing impurity, a manufacturing defect, a charge defect, a crystal defect, and/or a locally reduced valley splitting. The fidelity reducing locus 70 may further be the result of the non-zero magnetic field strength, parallel to the external magnetic field ^_^, of the at least one magnet 35, which may affect the Rabi frequency Ω (as can be seen from, e.g., formula (2) in Kloeffel and Loss, Prospects for Spin-Based Quantum Computing, 2012). [00124] When it is determined that the manipulation fidelity FM does not meet the requirements for a reliable operation of the quantum processor 10, adjusting one or more of the manipulation parameters enables increasing the manipulation fidelity FM. [00125] Furthermore, in addition to the manipulation zone 20, the shuttling lane 16 will be used during the operation of the quantum processor 10. The shuttling lane 16 will be used to move the one or more qubits, e.g., from the initialization zone 22 to the manipulation zone 20 and thence to the readout zone 24. During this sequence of actions on the one or more qubits, the two gates 50a-1, 50a-2 (see FIG.6A) of the screening gates 50a of the shuttling lane 16 (FIG.6D shows an aspect of the shuttling lane) may in one aspect of the disclosure be provided with the same voltage of, e.g., 0V. The conveyor gates 50b are provided with AC voltages to provide the one or more travelling potential wells in which the one more qubits may be moved (shuttled). The AC voltages provided to the conveyor gates 50b may be sine-wave voltages or more general waveforms. The AC voltages provided to the conveyor gates 50b may be phase-shifted between the subsets of conveyor gates 50b-1, 50b- 2, 50b-3, 50b-4. The phase shifts of the conveyor gates 50b-2, 50b-3, 50b-4 with respect to the conveyor gates 50b-1 may be set to π/2, π, and 3π/2, respectively. However, other settings for the phase shifts are conceivable. The phase shifts may deviate from being set to multiples of π/2. [00126] A lateral or transverse position along the lateral or transverse direction D3 of the trajectory 80 (see FIG.6C) of the one or more qubits along the at least one path 45 (extending along the x-axis of FIG.6C) is defined by the voltage applied to the two gates 50a-1, 50a-2 (see, e.g., FIG.6A) of the screening gates 50a. If the voltage applied to the gate 50a-1 and the voltage applied to the gate 50a-2 are substantially equal, one or more lateral positions of the generated one or more potential wells (i.e., of one or more minima of the one or more potential wells) will be substantially in the middle of the two gates 50a-1, 50a-2. If on the other hand the voltage applied to the gate 50a-1 and the voltage applied to the gate 50a-2 differ, the lateral position of the generated one or more potential wells (i.e., of the one or more minima of the one or more potential wells) will be off the middle of the two gates 50a- 1, 50a-2. The differing voltages on the gates 50a-1, 50a-2 may be the result of changing either the voltage applied to the gate 50a-1 or the voltage applied to the gate 50a-2 by the addition of an adjustment voltage ΔV. In other words, the voltage applied to either the gate 50a-1 or the gate 50a is changed to V+ΔV. For example, in the case of the heterostructure 12 being an undoped Si/SiGe heterostructure, if the voltage applied to the gate 50a-1 is decreased relative to the voltage applied to the other gate 50a-2, the one or more positions of the generated one or more potential wells (i.e., of the one or more minima of the one or more potential wells) will be moved towards the other gate 50a-2. In case the heterostructure 12 is doped, such as when using GaAs/AlGaAs, increasing the voltage applied to the gate 50a-1 moves the one or more potential wells towards the other gate 50a-2. In this way, the trajectory 80 of the one or more qubits along the at least one path 45 may be shifted laterally (i.e., in a transverse direction with respect to the at least one path 45). [00127] In one aspect of the disclosure, the lateral shifting of the trajectory 80 of the of the one or more qubits may be transient (termed “local shift” in FIG.6C). The transient lateral shifting is the result of a time-varying adjustment voltage ΔV(t) being added to the voltage applied to the gate 50a-1 or the voltage applied to the gate 50a- 2. In other words, the trajectory 80 deviates only temporally from the lateral position that was initially set during a calibration (i.e., y-position of 0 nm in the example shown in FIG.6C). The temporal lateral shifting results for example in the trajectory 80-1 shown in FIG.6C. [00128] In one aspect, the time-varying adjustment voltage ΔV(t) may be an AC voltage, such as a square pulse or a square wave. If several fidelity-reducing loci 70 are on average found to be distanced along the at least one path 45 (along the x-axis in FIG.3C) from one another by an average distance of 1000 nm (or 1 µm), and the shuttling speed at which the one or more qubits are shuttled along the at least one path 45 is 10 nm/ns (or 10 m/s), then on average the one or more qubits take a time of 100 ns to travel a distance equal to the average distance. The time-varying adjustment voltage ΔV(t) may thus last for the time of 100 ns. For instance, half the period of the square wave may be chosen to be equal to the time of 100ns. In other words the square wave may be chosen to have a frequency of 5 MHz. [00129] In a further aspect of the disclosure, the adjustment voltage comprises a DC voltage that is added to the AC voltage applied to the conveyor gates 50b. The DC voltage may be applied to the conveyor gates 50b in addition to, or alternatively to the adjustment voltage ΔV(t) applied to the screening gates 50a. The further adjustment voltage may provide an alteration of the confinement provided by the conveyor gates 50b, e.g., enhance the confinement when the one or more qubits are in the vicinity of a fidelity-reducing locus 70 (see below). [00130] The lateral shifting of the lateral position of the trajectory 80-1 enables circumventing a fidelity-reducing locus 70 in the shuttling lane 16. When the one or more qubits pass the fidelity-reducing locus 70 in the shuttling lane 16, the shuttling fidelity F may be reduced. The reduced shuttling fidelity F results in a less reliable shuttling of the one or more qubits along the shuttling lane 16. FIG.6C shows a greyscale-coded valley-splitting landscape with valley-splitting energies between 0 µeV and 300 µeV (lighter shaded areas corresponds to higher valley-splitting energies; darker shaded areas correspond to lower valley-splitting energies). Fidelity- reducing loci 70 are located where the valley-splitting energy is between 0 µeV and approximately 30-50 µeV (shown by the paler shaded areas within dark shaded areas). In the example shown in FIG.6C, the trajectory 80-1 circumvents several fidelity-reducing loci 70 positioned at the y-position of 0 nm. The fidelity-reducing loci 70-1, 70-2, 70-3, …, 70-10 are indicated by arrows and in some cases additionally by white dotted elliptical markings. In the example shown, the deviation Δy from the lateral position of the trajectory 80 initially set during a calibration (i.e., the y-position of 0 nm set during a calibration step 100 described below) peaks at approximately 20 nm in one lateral direction (extending along the positive y-axis in FIG.6C) and at approximately -20 nm in the opposite lateral direction (extending along the negative y-axis in FIG.6C). In another case, the maximum values for the deviation Δy in the two lateral directions (along the positive and the negative y-axis, respectively) may differ from 20 nm and -20nm, respectively. [00131] The lateral shifting of the lateral position y of the trajectory 80-1 further enables continuous adjustment of the lateral position y of the trajectory 80-1 by means of a time-varying adjustment voltage ΔV(t). The time-varying adjustment voltage ΔV(t) results in a time-varying deviation Δy(t). The continuous adjustment may be required in the case of fluctuations in the voltages applied to the plurality of gate electrodes 50. [00132] In an aspect of the disclosure, similar to the lateral shifting described above, one or more vertical positions of the one or more potential wells may be shifted vertically, i.e., in a stacking direction D1 (described below). Thereby, a vertical position of the trajectory 80-3 (a position along the stacking direction D1) may be altered. When the voltage applied to the at least one back gate 50c is changed, the confinement of the one or more potential wells is altered. The voltage applied to the at least one back gate 50c may be changed relative to the voltage applied to the screening gates 50a. Depending on the location of the at least one fidelity-reducing locus 70 (indicated by an asterisk in FIG.6D), the vertical position of the trajectory 80 may be altered upwards or downwards in the stacking direction D1. Thereby, the at least one fidelity-reducing locus 70 may be circumvented, and the reliability (i.e., the fidelity) of the shuttling lane 16 may be increased. [00133] The determination of the shuttling fidelity F enables identifying positions of the fidelity-reducing loci 70 at the trajectory 80-1 or 80-3 (e.g., along and/or in the vicinity of the trajectory 80-1 or 80-3). During the identification of the positions of the fidelity-reducing loci 70, the applied voltages V are iteratively adjusted. Thereby, the lateral position of the trajectory 80-1 and/or the vertical position of the trajectory 80-3 is iteratively adjusted. The identification of the positions of the fidelity-reducing loci 70 results in a method of controlling the shuttling lane 16. [00134] In one aspect of the disclosure, the lateral shifting and/or the vertical shifting of the trajectory 80 may be used at the manipulation zone 20 for moving the one or more qubits to a manipulation position that does not coincide with a fidelity reducing locus 70. [00135] The method according to the disclosure of adjusting voltages applied to the plurality of gate electrodes 50 achieves a method of controlling the quantum processor 10. [00136] In a step 100, the voltages V applied to the gate electrodes 50 are calibrated. In the calibration, the voltages V applied to the screening gates 50a are set to, for example, 0V, which corresponds to the lateral position of the trajectory 80- 1, i.e., the y-position in FIG.6C, being set to 0 nm. The voltages applied to electrodes of the top gate 50d or to the electrode subsets50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2- 1, 50b2-2, 50b2-3, 50b2-4 of the conveyor gates 50b during the manipulating of the one or more qubits may for example be set based on prior knowledge. [00137] In a step 110, the voltages V are restricted to a target range associated with the voltages V. While the voltages V are calibrated, the voltages V are kept within the target range. The target range of voltages applied to the gate electrodes 50, e.g., the screening gates 50a, ones of the electrodes 50d-1, 50d-2, …, 50d-12 of the top gate 50d, or ones of the electrode subsets50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4 of the conveyor gates 50b, may be predefined based on previously gathered data. The previously gathered data may be statistically processed and may be stored in a database. [00138] In a step 200, the manipulation fidelity FM of the manipulation zone 20 is determined. If the manipulation fidelity F_M is below a predefined threshold, e.g., F_M < 99.9% or 99.99%, there is a need for adjustment of the manipulation parameters by applying adjustment voltages ΔV to the gate electrodes 50. If the manipulation fidelity F_M is equal to or greater than the predefined threshold of 99.9%, the voltages applied to the gate electrodes 50 of the manipulation zone 20 do not require any further adjustments. [00139] The step 200 of determining the manipulation fidelity F_M may include determining a combined fidelity F = F_S × F_M that is the combination of the shuttling fidelity FS and the manipulation fidelity FM. The step 200 of determining the manipulation fidelity FM may further include determining the shuttling fidelity FS. The step 200 of determining the manipulation fidelity F_M may further include calculating the manipulation fidelity FM from the combined fidelity F by dividing the combined fidelity F by the shuttling fidelity FS. [00140] The step 200 of determining the manipulation fidelity F_M may include a step 210 of gathering measurements. These measurements may be indicative of whether the manipulating of the one or more qubits in the manipulation zone 20 was successful. These measurements may be made at ones of the components 16, 18, 20, 22, 24 that are in proximity to the manipulation zone 20, the fidelity of which is being determined. The measurements may relate to a measured quantity that senses, or is affected by, a success of the sequence of actions on the at least one qubit performed during the determining of the manipulation fidelity F_M. As explained above, the sequence of actions may comprise initializing the one or more qubits at the initialization zone 22, shuttling the one or more qubits to the manipulation zone 20, manipulating the one or more qubits at the manipulation zone 20, and shuttling the one or more qubits to the readout zone 24. In one aspect of the disclosure, the step 210 of gathering measurements may relate to the determining the combined fidelity F = F_S × F_M. The gathering of measurements may take place after the sequence of actions on the at least one qubit performed during the determining of the combined fidelity F = FS × FM. In another aspect, the gathering of measurements may additionally take place after the sequence of actions on the at least one qubit performed during the determining of the shuttling fidelity F_S. [00141] For example, the initialization zone 22 and/or the readout zone 24 may be arranged in the vicinity of the manipulation zone 20, e.g., at ends of the shuttling lane 16 which is arranged between the manipulation zone 20 on the one hand and the initialization zone 22 and/or the readout zone 24 on the other hand. The initialization zone 22 may comprise a single-electron transistor (SET). An electrical current through the SET may be measured. Likewise, the readout zone 24 may comprise an SET. As explained above, in one aspect the initialization zone 22 and the readout zone 24 are the same component. An electrical current through the readout zone 24 comprising the SET may be measured. The measuring of the electrical current through the SET of the initialization zone 22 and/or of the readout zone 24 may comprise a step of spin-to-charge conversion. The step of spin-to- charge conversion may involve the principle of Pauli-spin-blockade or spin- dependent tunnelling. The step 210 of gathering the measurements, e.g., the measuring of the electrical currents through the SET of the initialization zone 22 and/or through the SET of the readout zone 24, enables analyzing the measurements (see step 300 below). [00142] In another aspect, the step 210 of gathering measurements may comprise one or more of the following single-shot readout techniques: quantum point contact (QPC), single electron transistor (SET), sensing dot (SD), baseband readout using transistor circuits, radio-frequency quantum point contact (rf QPC), radio- frequency single electron transistor (rf SET), radio-frequency sensing dot (rf SD), and/or single-electron box (SEB). These readout techniques enable charge detection after spin-to-charge conversion to conduct spin readout. The spin-to-charge conversion step may be based on Pauli spin blockade or spin-dependent tunnelling. The afore-mentioned single-shot readout techniques do not require a continuous gathering of measurements. One example of the continuous gathering of measurements is the measuring of the current through the SET/SD (see above). [00143] Furthermore, as explained above, the determining of the shuttling fidelity involves the repeating of the following sequence of actions: initialization of a qubit; moving (shuttling) of the qubit; readout of the qubit; and determining whether the initial spin state of the qubit is equal to the final spin state after shuttling. The shuttling fidelity is equal to the proportion of successful runs of this sequence of actions. [00144] The determining of the manipulation fidelity FM may involve the repeating of the following sequence of actions: the initialization of the one or more qubits; the moving (shuttling) of the one or more qubits, the manipulating of the one or more qubits; the moving (shuttling) of the one or more qubits; the readout of the one or more qubits; and the determining whether the one or more current spin states after the sequence of actions are equal to the expected current spin states. The manipulation fidelity FM is equal to the proportion of successful runs of this sequence of actions. [00145] The initialization of the qubit may be based on the Pauli spin blockade. [00146] The moving (shuttling) of the one or more qubits may comprise moving the one or more qubits by a chosen or predefined distance along the shuttling lane 16. In one aspect, the chosen or predefined distance covers a segment of the shuttling lane 16, the segment having a length equal to the predefined distance. [00147] The distance the one or more qubits travel may be chosen by presetting one or more frequencies f and/or one or more durations t of the AC voltages, which the conveyor gates 50b are provided with (see above). The AC voltages provide the travelling potential well for moving (shuttling) the qubit. The one or more frequencies f and/or the one or more durations t determine the distance travelled by the travelling potential well. The distance travelled by the travelling potential well during one period T = 2π/ω = 1/f is determined by a spacing of the conveyor gates 50b. In particular, the distance is determined by the spacing of the conveyor gates 50b-1, 50b-2, 50b-3, 50b-4 in the electrode subsets of the conveyor gates. In general, the distance travelled is determined by the one or more preset durations t as well as by the spacing of the conveyor gates 50b. [00148] The moving (shuttling) may include iteratively changing the distance travelled by the travelling potential well. In other words, the length of the segment of the shuttling lane 16, along which the travelling potential well is moved, is varied. The iteratively changing of the distance travelled may include iteratively changing the one or more frequencies f and/or the one or more durations t of the AC voltages. [00149] In one aspect, the length of the segment (i.e., distance travelled by the travelling potential well) may be changed by increasing the length of the segment. [00150] In another aspect, the length of the segment (i.e., the distance travelled by the travelling potential well) may be changed by reducing the length of the segment. [00151] In one aspect, the iteratively changing of the distance travelled by the travelling potential well (i.e., of the length of the segment) may result in covering an entire length of the shuttling path 16. [00152] In another aspect, the iteratively changing of the distance travelled by the travelling potential well may result in identifying the position of the fidelity- reducing locus 70. For example, the distance travelled by the travelling potential well (i.e., the length of the segment of the shuttling lane 16) may vary in a nested manner about the position of the fidelity-reducing locus 70. [00153] In a step 300, the measurements gathered during the step 210 of determining the manipulation fidelity FM are analyzed. The step of analyzing the measurements may comprise analyzing measurement gathered during the determining of the shuttling fidelity FS. In one aspect, a time course of the electrical current through the SET of the initialization zone 22 and/or a time course of the electrical current through the SET of the readout zone 24 may be classified according to a presence of a feature indicative of a failure of the manipulating and/or of the shuttling of the one or more qubits. In another aspect, the measurements gathered by the single-shot techniques may be analyzed and classified according to a presence of a feature indicative of the failure of the manipulating and/or of the shuttling of the one or more qubits. The feature indicative of the failure of the manipulating and/or of the shuttling of the one or more qubits may be a characteristic of the measurements gathered in step 210. [00154] In the case of the measurement of currents through the SET, the feature indicative of the failure includes abrupt changes, such as a sudden reduction or a sudden increase, of the electrical current through the SET. In the case of the single-shot techniques, the feature indicative of the failure includes changes in, e.g., a current across the QPC/SET/SD, a (quantum) conductance of the QPC/SET/SD, a voltage across the SET/SD that is capacitively-coupled , or a rf (radio-frequency) response based on shifts in a quantum capacitance of the QPC/SET/SD. The rf response may relate to an amplitude, a phase, and-or a reflection coefficient of a rf signal. [00155] The distance travelled by the qubit and associated with the feature indicative of the failure of the shuttling indicates an x-position along the at least one path 45 of the shuttling lane 16 based on the AC voltage applied to the conveyor gates 50b The one or more frequencies f and the one or more durations t of the AC voltage determine the shuttling speed of, and the distance travelled by the one or more qubits through the shuttling lane 16, respectively. Thereby, the x-position of the fidelity-reducing locus 70 associated with said failure may be determined. [00156] In a step 400, the x-position of the feature indicative of the failure of the shuttling is identified as a fidelity-reducing locus 70, e.g., one of the fidelity-reducing loci 70-1, 70-2, 70-3, … in FIG.6C, if a sufficiently large proportion of the gathered time courses through the SET of the initialization zone 22 and/or the time courses of the electrical current through the SET of the readout zone 24 (i.e., a sufficiently large proportion of the gathered measurements) contain the feature indicative of the failure of the shuttling. [00157] In a step 500, the voltages V applied to the screening gates 50a are adjusted to circumvent the identified fidelity-reducing locus 70. The voltages V are adjusted by adding the adjustment voltage ΔV, as explained above. [00158] In a step 510, the voltages V are restricted to the predefined target range associated with the voltages V. While the voltages V are adjusted, the voltages V are kept within the target range. The previously gathered data (i.e., gathered measurements) may be statistically processed and may be stored in a database. [00159] After step 500, the method returns to step 200 to determine the shuttling fidelity based on the adjusted voltages V. [00160] The method described above may be extended to several ones of voltages applied to the plurality of gate electrodes 50 for operating the quantum processor 10. [00161] The method of operating the quantum processor 10 comprises the calibration step 1100, in which the voltages V, which are applied to the plurality of gate electrodes 50, are calibrated. The calibration of the plurality of voltages V takes into account the target ranges for the plurality of voltages V. The target ranges may be predefined based on previously collected data from measurements and experiments. [00162] In a step 1110, the voltages V are restricted to the predefined target range associated with the voltages V. While the voltages V are calibrated, the voltages V are kept within the target ranges. [00163] When the plurality of the voltages V are calibrated, at least one interaction between ones of the plurality of voltages among each other is accounted for. The at least one interaction may be expressed as a boundary condition or as a functional relationship. The functional relationship may take into account the target ranges. [00164] For example, in the case of the shuttling lane 16 shown in FIGS.3A and 3B, the voltages applied to the screening gates 50a and to the conveyor gates 50b generate electric fields (in the case of voltages V being DC voltages) and/or electromagnetic fields (in the case of voltages V being AC voltages). The generated fields superpose each other, e.g., at trajectory 80, and lead to a resultant electric field and/or a resultant electromagnetic field. The effect of this superposition, i.e., the interaction, needs to be considered with regard to the material composition as well as the targeted behaviors of the shuttling lane 16. Other interaction among the voltages applied to the gate electrodes 50 will be present and possibly depend on the actual design of the quantum processor 10. [00165] In one aspect of the disclosure, the calibration step 1100 may be implemented using machine learning. In particular, a first recurrent neural network (RNN) may be used to calibrate the voltages applied to the gate electrodes 50. The first RNN is trained on historical data, e.g., voltages applied to the gate electrodes 50 during previous operations of the quantum processor 10, such as experiments. The target ranges and/or measurements gathered during previous determinations of the fidelities (step 1200 below) may further be used for training the first RNN. The first RNN may further be continuously updated during an operation of the quantum processor 10, i.e., the voltages applied to the gate electrodes 50 used during the operation of the quantum processor 10 may be included in the historical data. [00166] A convolutional neural network (CNN) and/or a fully connected neural network (FCNN) is used as a discriminator to determine whether the applied voltages are to be calibrated or adjusted. The CNN and/or the FCNN is trained on historical data collected in previous experiments, on the target ranges for the voltages, as well as on measurements gathered during previous determinations of the fidelities (step 1200 below). [00167] The method of operating the quantum processor 10 comprises the step 1200, in which a plurality of fidelities F is determined. The plurality of fidelities comprises fidelities regarding ones of the components 16, 18, 20, 22, 24 for at least some of the plurality of unit cells 26. The plurality of fidelities further comprises gate fidelities for gates that the quantum processor 10 is designed to implement. [00168] Ones of the fidelities F are associated with predefined thresholds, e.g., 99.9% or 99.99%. If the predefined thresholds are not met, i.e., F<99.9% or F<99.99%, there is a need for adjustment of the voltages V applied to the gate electrodes 50. If the shuttling fidelities, on the other hand, are equal to or greater than the associated predefined thresholds, the voltages applied to the screening gates 50a of the shuttling lane 16 do not require any further adjustments. [00169] Determining the fidelities involves the repeating of the sequences of actions for the components 16, 18, 20, 22, 24 for the at least some of the plurality of unit cells 26. Furthermore, the sequences of actions defining the gate operations of the gates are repeated. In all cases, the fidelities are given by the proportions of successful repetitions. [00170] As explained above, determining the fidelities may, for at least some of the fidelities, involve the step 1210 of gathering measurements. When a final readout of the one or more current spin states of the one or more qubits is involved in the sequences of actions (for the components or for the gates), an electrical current through an SET (single-electron transistor) of the readout zone 24 may be measured to determine the one or more current spin states of the one or more qubits. [00171] In a step 1300, the measurements gathered during the step 1210 of determining the fidelities F are analyzed. For example, for each one of the fidelities, time courses of the electrical currents through the SET of the initialization zone 22, associated with said fidelity, and/or the time courses of the electrical current through the SET of the readout zone 24, associated with said fidelity, may be classified according to features indicative of failure of the associated action. As explained above, the features indicative of the failure include abrupt changes, such as a sudden reduction or a sudden increase, of the electrical current through the associated SETs. The time associated with the feature indicative of the failure can be associated with a position, as explained above. If the determined position coincides with the position of the plunger gate or of the barrier gates, the determined position may indicate that an exchange interaction for a two-qubit interaction, provided by the voltages applied to the plunger gates, or a tunnel barrier for initialization and/or readout, provided by the voltages applied to the barrier gates, need to be adjusted by adjusting the associated voltages. [00172] In an identification step 1400, the determined position associated with the feature indicative of the failure is identified as a fidelity-reducing locus 70, if a sufficiently large proportion of the associated time courses contain the feature indicative of the failure. The proportion is sufficiently large when the fidelity F is not equal to or greater than the predefined threshold associated with the fidelity. [00173] In a step 1500, the voltages V applied to the gate electrodes that are located at or close to the determined position are adjusted to reduce the effect of the identified fidelity-reducing locus 70. The voltages V are adjusted by adding the adjustment voltage ΔV, as explained above. [00174] In a step 1510, the voltages V are restricted to a target range associated with the voltages V. While the voltages V are adjusted, the voltages V are kept within the target ranges. The previously gathered data may be statistically processed and may be stored in a database. [00175] In one aspect of the disclosure, the adjustment step 1500 may be implemented using machine learning. In particular, a second RNN may be used to calibrate the voltages applied to the gate electrodes 50. The second RNN is trained on historical data, e.g., voltages applied to the gate electrodes 50 during previous operations of the quantum processor 10, such as experiments. The target ranges and/or measurements gathered during previous determinations of the fidelities (step 1200 below) may further be used for training the second RNN. The second RNN may further be continuously updated during an operation of the quantum processor 10, i.e., the voltages applied to the gate electrodes 50 used during the operation of the quantum processor 10 may be included in the historical data. [00176] The CNN and/or the FCNN is trained on historical data gathered in previous experiments, on the target ranges for the voltages, as well as on measurements gathered during previous determinations of the fidelities (step 1200). [00177] In one aspect of the disclosure, the first RNN used in the calibration step 1100 and the second RNN used in the adjustment step 1500 may be a single recurrent neural network. Combining the first RNN and the second RNN may depend on a number of inputs to the first RNN or the second RNN. Furthermore, the combining the first RNN and the second RNN may depend on information received from the CNN and/or the FCNN. [00178] In an optional discrimination step 1600, the adjusted voltages V+ΔV, the target ranges, and the actions to be performed are used as input to a convolutional neural network and/or a fully connected neural network in order to decide whether the voltages are to be recalibrated, i.e., whether the method is to return to step 1100. [00179] The usefulness of employing neural networks is due to facilitating processing time-series of measurements, two-dimensional structures of measurements (measurement and/or correlation matrices), and/or correlated measurements. [00180] After step 1500, optionally after step 1600, the method returns to step 200 to determine the shuttling fidelity based on the adjusted voltages V. [00181] The method may further comprise a step 1700 of determining a density of the fidelity-reducing loci 70. If the method for operating the quantum processor 10 results in the density of fidelity-reducing loci 70 being elevated (e.g., being larger than a predefined threshold value) in a portion of the quantum processor 10, such as along one of the shuttling lanes 16, or in the entire quantum processor 10, the elevated density may point to a property of a manufacturing process of the quantum processor 10 or of the materials used in the manufacturing process. In this case, the quantum processor 10 may be manufactured such that the screening gates 50a-1 and 50a-2 (see FIGS.3A and 3B) arranged thereon are segmented into electrically disconnected segments 50a-11, 50a-12 and 50a-21, 50a-22, respectively, as shown in FIGS.4A and 4B.

Claims

Claims 1. A method of operating a quantum processor (10) comprising a plurality of gate electrodes (50) arranged on a semiconductor heterostructure (12), wherein the plurality of gate electrodes (50) comprises conveyor gate electrodes (50b) configured to be supplied with at least one voltage V to move at least one qubit, arranged in the semiconductor heterostructure (12), along the at least one path (45) to a manipulation zone (20) for manipulating the at least one qubit, wherein the method comprises the steps of ^ calibrating (100, 1100) the at least one voltage V supplied to the gate electrodes (50); ^ determining (200, 1200) at least one fidelity F_M or an error syndrome S, relating to manipulating the at least one qubit at the manipulation zone (20); ^ adjusting (500, 1500) the at least one voltage V. 2. The method of claim 1, wherein the calibrating (100, 1100) of the at least one voltage V includes defining a Rabi frequency Ω, a resonance frequency ν, or an exchange coupling J. 3. The method of claim 1 or 2, wherein the adjusting (500, 1500) of the at least one voltage V comprises adjusting a Rabi frequency Ω, a resonance frequency ν, or an exchange coupling J. 4. The method of any one of claims 1 to 3, wherein the adjusting (500, 1500) of the at least one voltage V further comprises applying a DC voltage to the gate electrodes (50). 5. The method of any one of claims 1 to 4, wherein the at least one voltage is applied to the at least one electrode subset (50b1-1, 50b1-2, 50b1-3, 50b1-4, 50b2-1, 50b2-2, 50b2-3, 50b2-4) of the conveyor gate electrodes (50b) or to at least one electrode of a top gate (50d) arranged above the conveyor gate electrodes (50b) 6. The method of any one of claims 1 to 4, further comprising moving the at least one qubit along at least one segment of the at least one shuttling lane (16). 7. The method of claim 5, further comprising varying a length of the at least one segment of the at least one shuttling lane (16) 8. The method of any one of claims 1 to 7, wherein the determining (200, 1200) of the at least one fidelity F comprises performing the at least one action on the at least one qubit. 9. The method of any one of claims 1 to 8, wherein the determining (200, 1200) of the at least one fidelity FM comprises determining a fidelity FS of shuttling the at least one qubit. 10.The method of any one of claims 1 to 9, wherein the determining (200, 1200) of the at least one fidelity FM comprises gathering measurements (1210) relating to the at least one fidelity F_M. 11.The method of claim 10, wherein the gathering (1210) of measurements includes spin-to-charge conversion. 12.The method of any one of claims 1 to 11, wherein the method further comprises restricting (110, 510, 1110, 1510) the at least one voltage V within an associated predefined target range.