JP5376482B1 - Quantum error correction method, quantum error correction device, and quantum information storage device - Google Patents

Abstract

A quantum error correction method is provided.
A method for correcting an error of a data qubit on a side of a lattice structure, comprising: preparing a Z error syndrome for a first Z error qubit at a vertex of the structure; A step of copying to the error qubit, a step of cooling the second Z error qubit and the cooling qubit under a Hamiltonian dependent on the Z error syndrome, and a step of feeding back the quantum state of the cooling qubit to the data qubit A step of preparing an X error syndrome for the first X error qubit having the same structure, a step of copying the X error syndrome to the second X error qubit, and a second X under a Hamiltonian dependent on the X error syndrome Cool error qubits and cooling qubits Method comprising the step, a step of feeding back the quantum state of the cooling qubits data qubit, the.
[Selection] Figure 4

Description

  The technical field relates to a quantum information storage technique, and more particularly, to a technique for correcting an error in quantum information carried by a qubit.

  Reliable information storage is very important for quantum information processing, and a standard approach to achieve this is to use a technique called quantum error correction (Non-patent Document 1).

  The quantum error correction procedure generally begins with a selective projection measurement of each qubit. The huge number of measurement results are processed by a classical computer. Finally, a feedback operation is selectively performed on each qubit based on the processing result. In this way, entropy that is to be increased in the qubit system can be reduced by returning to the state before the error occurs in the quantum information. By repeating this series of flows continuously, large-scale quantum information can be protected from external noise for a long time.

  Various error-tolerant quantum computing architectures have been proposed based on quantum error correction technology. In theoretical research, it is often assumed that classical information processing and input / output to a processing device are completed in an instant. In practice, however, classical processing takes a system time polynomial time, which eventually becomes a bottleneck that limits the size and speed of quantum information processing.

  In addition, it is experimentally very challenging to operate and measure one qubit quickly and accurately from a large number of entangled qubits. It is still unclear what kind of physical system has expandability that can be realized as a large-scale quantum information processing device.

  For example, in a monolithic architecture realized using artificial atoms such as quantum dots and superconducting qubits, a huge number of channels for selective manipulation and measurement while the qubits are close enough to allow entanglement. Need to be integrated. However, if the channels for operation and measurement are too close, a new noise source that is difficult to model will be introduced. In addition, the low individuality yield of mass-produced artificial atomic qubits makes integration difficult.

  On the other hand, in the distributed architecture, the qubits are isolated from each other and can be selectively operated and measured. However, it takes a long time to provide entanglement between such distant qubits. Although these traditional framework problems are believed to be solved by breakthroughs in control methods and material development, attempts to devise other new architectures will be very important.

P. W. Shor, Phys. Rev. A, 52, R2493, 1995.

  Conventionally proposed quantum error correction techniques require a large amount of processing (for example, calculation of required classical information processing) according to an increase in system size, in short, the number of qubits to which quantum error correction is applied. Load) and device scale (the number of operation channels for performing selective operations on qubits) are disadvantageous. In view of this, an embodiment of the present invention includes a quantum error correction method that can be performed without depending on the system size, a quantum error correction device that corrects a quantum error according to the method, and the quantum information storage device error correction device. A quantum information storage device (quantum information storage) is provided.

One aspect of the present invention is a quantum information storage in which a plurality of qubits are arranged in a lattice structure, and is configured by quantum information stored in a plurality of data qubits arranged on each side of the lattice structure A quantum error correction method in a quantum error correction device for correcting an error of a surface code to be performed,
By performing a first translationally symmetric and local first operation on the quantum information store, a plurality of first Z error qubits arranged at each vertex of the lattice structure are converted into a Z error syndrome of the surface code. A Z error extraction step for preparing a corresponding quantum state;
By performing a second translationally symmetric and local second operation on the quantum information storage, the quantum states of the plurality of first Z error qubits prepared by the Z error extraction step are converted into a plurality of first Z A Z error copy step of copying to a plurality of second Z error qubits arranged close to each of the error qubits;
By performing a third translationally symmetric and local third operation on the quantum information store, the quantum state of the second Z error qubit prepared by the Z error copy step is used to generate a Z error syndrome. A first cooling step for cooling a plurality of cooling qubits disposed proximate to the plurality of second Z error qubits and the plurality of data qubits under a dependent Hamiltonian;
By performing a fourth translationally symmetric and local fourth operation on the quantum information store, each quantum state of the plurality of cooling qubits prepared by the Z error cooling step is converted into a plurality of data qubits. Z error correction step to feed back to
By performing a comprehensive translational symmetric and local fifth operation on the quantum information storage, a plurality of first X error qubits arranged at each center of the lattice structure are subjected to an X error syndrome of the surface code. An X error extraction step of preparing a quantum state corresponding to
By performing a comprehensive translational symmetric and local sixth operation on the quantum information storage, the quantum states of the plurality of first X error qubits prepared by the X error extraction step are converted into a plurality of first X An X error copy step for copying to a plurality of second X error qubits arranged close to each of the error qubits;
By performing a comprehensive translational symmetric and local seventh operation on the quantum information store, the quantum state of the second X error qubit prepared by the X error copy step is used to generate an X error syndrome. A second cooling step for cooling the plurality of second X error qubits and the plurality of cooling qubits under a dependent Hamiltonian;
By performing a comprehensive translational symmetric and local eighth operation on the quantum information store, each quantum state of the plurality of cooling qubits prepared by the X error cooling step is converted into a plurality of data qubits. X error correction step to feed back to
Is a quantum error correction method.

  Another aspect of the present invention is a quantum error correction for correcting an error of a surface code constituted by quantum information stored in a plurality of data qubits of a quantum information storage according to a quantum error correction method according to an aspect of the present invention. Device.

  Still another aspect of the present invention is a quantum information storage device including the quantum error correction device according to one aspect of the present invention and a quantum information storage in which the quantum error is corrected by the quantum error correction device.

  According to one aspect of the present invention, it is possible to correct surface code errors through a first translationally symmetric and local first operation with respect to a quantum information store. Therefore, according to the same aspect, a quantum error correction method independent of the system size is provided.

(A): Diagram of a circuit for performing projection measurement and feedback operation of quantum information and an equivalent circuit realized by operation on qubit, (b): Projection measurement in large-scale qubit system and feedback operation based on classical processing (C): Circuit diagram when classical information processing is replaced with unitary operation, (d): Realization of cooling process using translationally symmetric and local operations Circuit diagram when (A): a diagram for explaining a surface code and its stabilizer operator, (b): a diagram for explaining a method for correcting a Z error, (c): a diagram for explaining a method for correcting a Z error, (d): The figure explaining the technique which corrects Z error (A): Diagram showing configuration of quantum system and classical system, (b): Diagram for explaining operations for extraction of face center syndrome and vertex syndrome, (c): Description of error syndrome copy operation (D): Diagram for explaining the operation for the cooling process (A)-(d): The figure explaining the flow of non-observation type | mold quantum error correction (MFQEC: Measurement-Free Quantum Error Correction) Diagram of operation flow of unobserved quantum error correction (MFQEC) Diagram of operation flow of unobserved quantum error correction (MFQEC) (A): Schematic diagram of a quantum information storage with a two-layer structure, (b): Schematic diagram of a quantum information storage with a single-layer structure Block diagram of quantum information storage device Blueprint of an example molecule for a single layer quantum information store

  Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

1. Outline According to an embodiment of the present invention, a new quantum error correction architecture and a quantum error correction device for realizing a highly reliable quantum information storage device are realized. In the quantum error correction apparatus according to the embodiment of the present invention, there is almost no increase in the scale of the quantum error correction apparatus and the necessary calculation load depending on the system size (for example, the number of qubits holding quantum information).

  In the quantum information storage device according to the embodiment of the present invention, quantum information is encoded and held by a surface code in a two-dimensionally arranged qubit system. In the quantum error correction architecture according to the embodiment of the present invention, as a means of reducing the entropy increasing in the qubit system, an auxiliary attached to the qubit instead of the selective projection measurement and the classical information processing for the result. Use the engineered cooling process in the classical system. This process cooling process involves the preparation of interesting quantum states (M. Mueller et al., New J. Phys. 13, 085007, 2011) and dynamics simulation (B. Kraus et al., Phys. Rev. A 78, 042307, 2008, and F. Verstraete, MM Wolf, and JI Cirac, Nat. Phys. 5, 633, 2009), quantum relay (KGH Vollbrecht, CA Muschik, and JI Cirac, Phys. Rev. Lett. 107, 120502 , 2011).

  All procedures necessary for error correction in the quantum error correction architecture according to the embodiment of the present invention, including this cooling process, are performed translationally invariant and by local external operations. That is, the quantum error correction apparatus according to the embodiment of the present invention does not perform selective operation on each qubit, but performs comprehensive (non-selective) operation on a plurality of qubits, thereby performing quantum error correction. Realize the correction. Therefore, the quantum error correction apparatus according to the embodiment of the present invention has very high expandability because error correction can be realized using an extremely small number of operation channels even when the system size is increased. Unlike the conventional monolithic architecture and distributed architecture, the quantum error correction according to the present embodiment does not require a measurement channel for selectively measuring individual qubits, and the number of operation channels is very large. Less. Therefore, it is easy to make the qubits close to each other to be strongly coupled.

  In the quantum information storage device including the quantum error correction device according to the embodiment of the present invention, integration and scale-up are easier than in the past. As will be described later, when six types of qubits are regularly arranged in a two-layer two-dimensional plane in the quantum information storage, the number of channels for comprehensive operations for the six types of qubits necessary for quantum error correction. Only 6 are enough. The systematic design method of comprehensive control for realizing quantum error correction in this system is also shown below.

  In the system to which this embodiment is applied, it has been proved that the time required for the work cooling process does not depend on the system size. In addition, a simulation in which the quantum error correction is repeated 20 to 40 times in a system with the number of qubits in the order of 100 has been performed. However, the time constant for decreasing the reliability of quantum information increases exponentially according to the system size. The result is obtained.

2. Comprehensive control and topological surface codes Global control schemes have a long history, and it has been shown that universal quantum information processing is possible with only translational and local operations in a one-dimensional spin system. Recently, it has been shown that there is an error resilience threshold in a comprehensive control architecture that allows only selective manipulation and observation of boundary surfaces. Its value is 10 ⁻⁵ , achieved by a scheme based on concatenation of Bacon-Shor codes.

  For example, as shown in FIG. 1 (a), the projection measurement necessary for quantum error correction and the feedback operation 101 (the upper circuit in FIG. 1 (a)) are performed by a unitary operation 102a with an auxiliary bit and thereafter Can be replaced with the initialization 102b by cooling the auxiliary bit (the lower circuit in FIG. 1A).

  As shown in FIGS. 1B to 1D, in order to implement projection measurement and its feedback operation in a large-scale qubit system, it is necessary to perform a feedback operation using classical information processing of a huge measurement result ( FIG. 1 (b)).

  However, universal classical information processing is possible in systems where universal quantum information processing is possible. By utilizing this, as shown in FIG. 1C, the classical information processing 103 can be replaced with a unitary operation 104 in the auxiliary bit system.

  In the quantum error correction architecture according to the present embodiment, a surface code that is a local, translationally symmetric stabilizer code is used instead of concatenating a finite length code such as a Bacon-Shor code. This realizes an architecture that does not require interface selectivity. In this architecture, a cooling process can be used for classical information processing as well, and the quantum error correction architecture according to the present embodiment realizes the cooling process 105 using translationally symmetric local operations (FIG. 1). (D)).

  Next, surface codes and syndrome detection used in the quantum error correction architecture according to the present embodiment will be described with reference to FIGS.

As shown in FIG. 2A, the surface code 201 is defined on a system in which qubits 202 are placed on each side of a square lattice. Here, a stabilizer operator Af = Z ₁ Z ₂ Z ₃ Z ₄ composed of four qubits adjacent to a face having a square lattice is considered. Further, consider a stabilizer operator Bv = X ₁ X ₂ X ₃ X ₄ consisting of four qubits adjacent to a vertex having a square lattice. In the surface code 201, the encoded state | Ψ> is an eigenvalue (measured value when the system is measured by the stabilizer operator) in the stabilizer operator defined at all face centers and vertices on the lattice. Is defined as a simultaneous eigenstate with +1.

  A method for correcting the Z error will now be described with reference to FIGS. 2 (b) and 2 (c). Since the X error can be corrected by the same method, the description thereof is omitted here.

The syndrome of Z error is defined by the eigenvalue bv of the stabilizer operator Bv. Similarly, the syndrome of X error is defined by the eigenvalue af of the stabilizer operator Af. Assume that a plurality of Z errors 205 as shown in FIG. When the place where the error has occurred continues like a chain C, the eigenvalue bv of the stabilizer operator Bv207 at the apex of the terminal C becomes -1. This is because the error operator has an anti-exchange relation with the stabilizer operator Bv at the end. In order to recover the error state to the correct state, first, an error operator C _ML whose syndrome is the same as that of the chain C is estimated. This corresponds to estimating a chain with the same end (ie, estimating C _ML satisfying ∂C _ML = ∂C). The error correction is successful not only when the error operator C _ML = chain C but also when a small loop is formed when the error operator C _ML and the chain C are connected. Conversely, if the small loop is not formed, error correction is a failure.

Let p be the probability of error. At that time, the probability that the end of an error chain is the same as ∂C is expressed by equation (1).
Here, E is the number of qubits, and u _i ^C is +1 when i is included in C, and −1 when i is not included. The most plausible error operator C _ML whose end is ∂C is obtained by maximizing its posterior probability. This indicates that the error chain connecting the pair of two ends with the minimum Manhattan distance is most likely. Such a problem can be solved efficiently by a classical computer using the Edmond's minimum weight perfect matching (MWPM) algorithm, that is, in a polynomial function time of the system size. The threshold of 10.3% obtained using the MWPM algorithm when the syndrome measurement is perfect is close enough to the ideal threshold of 10.9%. In addition, even in the case of incomplete syndrome measurement, the threshold value 2.9% obtained using the MWPM algorithm is sufficiently close to the ideal threshold value 3.3%. However, in the MWPM algorithm, it is necessary to consider not only the probability of each error chain, but also the number of combinations of error chains of the same homology when connected to the actual error chain C. In this regard, the MWPM algorithm is not suitable for application to embodiments of the present invention.

  A quantum computer can emulate all classical information processing. However, the MWPM algorithm requires very complex processing written in a high-level language. Therefore, the merit of the surface code is reduced. Therefore, in the embodiment of the present invention, the cooling process described later is used in the process of quantum error correction (FIG. 2C and FIG. 2D).

3. Unobserved Quantum Error Correction In the quantum error correction architecture according to the embodiment of the present invention, an auxiliary classical many-body system (“qubit system” in FIG. 2C) associated with data qubits forming a surface code ( The “auxiliary bit system” in FIG. 2C is introduced. Here, “classical” means that quantum coherence between states is not actively used. The auxiliary classical many-body system includes, for example, Ising spins {| 0>, | 1>} located immediately above the data qubits on the sides of the square lattice. These are also referred to as “cooling spins”. The Hamiltonian H ({bv}) of the cooling spin system is considered to be a translationally symmetric and local one represented by the formula (2).

Here, H P _({bv}) represents the following formula, as shown in equation (3), the four-body interactions in the four cooling spin in contact with the apex (strength J).

H _F has the formula, as shown in equation (4), representing the interaction of each cooling spin and a magnetic field (coupling constant J, strength h).
The coupling coefficient here is given by Jv = bv · J. The negative sign follows the eigenvalue of the stabilizer operator of the qubit immediately below each cooling spin. The realization of such a syndrome-dependent four-body interaction will be described in detail later.

The cooling process in a quantum error correction architecture according to an embodiment of the present invention includes two competing dynamics. One is to limit the boundaries of the chain by H _P. The other is to minimize the weight by the magnetic field. If there is no error, Jv = J in all v, and the ground state is | 00 ... 0>. If there is even one error, the state is not the ground state. In the interaction at Jv = −1, the interaction works so that the number of | 1> in the four spins becomes an odd number. This means that the chain terminating at vertex v has lower energy.

Interaction H _F with magnetic field, | 0> and | 1 break the symmetry of the>, | work with trying to reduce the number of 1>. Due to these two restrictions (constraints), the same effects as those of the MWPM minimum-weight condition and the perfect matching condition can be obtained. Therefore, the ground state or low temperature spin configuration under this Hamiltonian (Equation (2)) is a good approximation of the results obtained with MWPM.

  After the cooling process, in order to feed back the spin configuration obtained in the auxiliary bit system (cooling qubit (cooling spin)) to the qubit system (data qubit), the cooling qubit (cooling spin) and The CZ gate may be comprehensively performed with the corresponding data qubit. The Z error can be corrected by a series of these procedures.

  Even in the case of X error, cooling under Hamiltonian H ({af}) (Equation (2)) according to the eigenvalue af of the stabilizer operator Af on the vertex, followed by a comprehensive feedback operation (for cooling as a control bit) Error correction can be similarly performed by a CNOT gate between a qubit (cooling spin) and a data qubit as a target bit. These cooling processes and feedback operations do not require any selective measurement or manipulation. These cooling processes and feedback operations can be realized with only comprehensive (non-selective) control. In this sense, the quantum error correction architecture according to the embodiment of the present invention is also referred to as “Measurement-Free Quantum Error Correction” (MFQEC).

  There is no particular limitation on the magnitude of the bond strength J. However, it has been confirmed by numerical simulation that it is advantageous to set J to about J = 2h in that a good spin configuration can be obtained in an appropriate time.

  Further, in the quantum error correction architecture according to the embodiment of the present invention, the time required to obtain the spin arrangement under sufficiently low temperature is a finite time that does not depend on the size of the system. Also in this respect, the quantum error correction architecture according to the embodiment of the present invention is sufficiently expandable with respect to the system size.

4). Implementation of Digitalized Cooling Process In the following, the cooling process under Hamiltonian H ({bv}) (equation (2)) including four-body interaction that depends on syndrome is described in detail. Describe how it will be realized.

  FIG. 3A is a diagram showing a structure having two layers of square lattices each including three types of particles. Hereinafter, the cooling process of MFQEC and the like will be described using this two-layer structure system. Here, the lower layer in the figure is referred to as a quantum system 301, and the upper layer is referred to as a classical system 303. The quantum system 301 includes three types of particles 301A, 301B, and 301C, and the classical system 303 includes three types of particles 303A, 303B, and 303C. In this case, each particle is a quantum information holding body having a single qubit.

  The particle 301 </ b> A that is the first quantum information holding body is located on the side of the square lattice forming the quantum system 301. The particle 301 </ b> B that is the second quantum information holding body is positioned at the apex of the square lattice forming the quantum system 301. The particle 301 </ b> C that is the third quantum information holding body is located at the center of the square lattice forming the quantum system 301.

  The particle 303A as the fourth quantum information holding body is located on the side of the square lattice forming the classical system 303. The particle 303B, which is the fifth quantum information holding body, is located at the apex of the square lattice forming the classical system 303. The particle 303 </ b> C that is the sixth quantum information holding body is located at the center of the square lattice forming the classical system 303.

  The qubit of the particle 301A is a data qubit. That is, the quantum information held by the particle 301A constitutes a surface code. The qubit of the particle 303A corresponding to the particle 301A immediately above the particle 301A is a cooling qubit (cooling spin).

  The qubit of the particle 301B is the first Z error qubit (Z error syndrome spin), and the qubit of the particle 303B corresponding to the particle 301B immediately above the particle 301B is the second Z error qubit (Z error). Syndrome spin auxiliary spin).

  Similarly, the qubit of the particle 301C is the first X error qubit (X error syndrome spin), and the qubit of the particle 303C corresponding to the particle 301C immediately above the particle 301C is the second X error qubit (X error). Syndrome spin auxiliary spin).

  In the quantum system 301 and the classical system 303, the particles (quantum information holding body) included in them act on one qubit gate and two qubit gates independently of other kinds of particles for each kind of particle. The quantum system 301 and the classical system 303 are configured by selecting the kind of particles. For example, a Hadamard gate can be applied to all of the particles 301A (data qubit) of the quantum system 301 independently of other types of particles. Further, for example, a CNOT (control NOT) gate is applied between the particle 301B (Z error syndrome spin) of the quantum system 301 and the particle 301C (X error syndrome spin) independently of other types of particles. Can do. For example, the particle 303A (cooling spin), the particle 303B (auxiliary spin of the syndrome spin for Z error), and the particle 303C (auxiliary spin of the syndrome spin for X error) of the classical system 303 are each independently described later. Operations can be performed.

  The MFQEC according to the embodiment of the present invention can be applied to systems other than the system having the two-layer structure as described above. For example, the MFQEC according to the embodiment of the present invention can be applied even to a system including only one layer that includes three types of particles (three types of quantum information holders) and forms a square lattice. . In that case, six types corresponding to the particles 301A, B, and C and the particles 303A, B, and C using plural types (two types) of internal degrees of freedom (nuclear spin and electron spin) of each of the three types of particles. A qubit may be realized.

  Hereinafter, a method of quantum error correction (MFQEC) according to an embodiment of the present invention will be described with reference to FIGS. 3 and 4 and FIGS. 5A and 5B. FIG. 4 is a schematic diagram showing the flow of especially the first half of quantum error correction according to the embodiment of the present invention, that is, Z error correction. Note that the X error correction flow is not shown because it can be easily understood from the illustrated Z error correction flow. 5A and 5B are flowcharts of quantum error correction according to the present invention.

Step (i): Initialization The states of the qubit of the particle 301B (Z error syndrome spin) and the qubit of the particle 301C (X error syndrome spin) (FIG. 3A, etc.) are initialized to | 0>. (FIG. 4A, step S1 in FIG. 5A).

Step (ii): Extraction of face-centered syndrome Between the qubit of the particle 301A (data qubit) and the qubit of the particle 301B (Z error syndrome spin), the data qubit 301A is used as a control bit and for Z error The CNOT gate operation is performed with the syndrome spin 301B as the target bit (the right side of FIG. 3B, the in-plane arrow of the quantum system 301 in FIG. 4B, step S2 in FIG. 5A).

Step (iii): Copying the extracted syndrome to the classical system 303 The state of the quantum bit of the particle 303B (auxiliary spin of the syndrome spin for Z error) (FIG. 3A, etc.) is initialized to | 0> Between the qubit of the particle 301B (Z-error syndrome spin) and the qubit of the particle 303B (Z-error syndrome spin auxiliary spin), the Z-error syndrome spin 301B is used as a control bit to assist the Z-error syndrome spin. CNOT gate operation is performed with the spin 303B as the target bit (the right side of FIG. 3C, the arrow from the quantum system 301 to the classical system 303 in FIG. 4B, step S3 in FIG. 5A).

Step (iv): Cooling under H _P ({bv}) CNOT operation represented as U in FIG. 3 (d), ie qubit of particle 303A (cooling qubit (cooling spin)) and particle Between 303B quantum bits (auxiliary spins of syndrome spin for Z error), four cooling spins 303A are control bits and auxiliary spins 303B of syndrome spins for Z error surrounded by four cooling spins 303A are target bits. , CNOT gate operation U is performed. Then, a dissipation operation (attenuation by D (βJ) (described later)) is performed on the auxiliary spin 303B of the syndrome spin for Z error, and the CNOT operation U is performed. (FIG.3 (d), FIG.4 (c), step S4 of FIG. 5A).

Step (v): Cooling under _{H F} Next, as shown in the last part of FIG. 3 (d), between the auxiliary spin 303B syndrome spin 301B and Z errors for the syndrome spin for Z errors, CNOT gate operation is performed using the Z error syndrome spin 301B as a control bit and the Z error syndrome spin auxiliary spin 303B as a target bit, and the surrounding four cooling spins 303A are controlled using the Z error syndrome spin auxiliary spin 303B as a control bit. An operation for changing the parity (even / odd number of zero-kets), for example, a random CNOT operation (described later) is performed between the auxiliary spin 303B of the Z-error syndrome spin and the cooling spin 303A. Then, a dissipation operation (attenuation (described later) by D (βh)) is performed on the cooling spin 303A (FIG. 4C, step S5 in FIG. 5A).

Step (vi)
The operation from the above step (iii) to step (v), so that the cooling effect under each H _P and H _F can be sufficiently obtained, repeated a predetermined number of times determined in advance (step of FIG. 5A S6 ).

Step (vii): Z error correction by feedback CZ gate operation is performed between the cooling spin 303A and the data qubit 301A using the cooling spin 303A as a control bit and the data qubit 301A as a target bit (FIG. 4D). FIG. 5A, step S7).

  As described above, the error (Z error) included in the data qubit 301A is corrected by the operations from step (i) to step (vii). Hereinafter, steps (viii) to (xiii) relate to correction of X errors.

Step (viii): Extraction of vertex syndrome Between the data qubit particle 301A and the qubit of the particle 301C (syndrome spin for X error), the syndrome bit for X error 301C is used as a control bit, and the data qubit 301A is used as a target bit. Then, the HCNOT gate operation is performed (the diagram on the left side in FIG. 3B, step S8 in FIG. 5B). Here, the HCNOT gate operation means that the control bit (X error syndrome spin 301C) is first subjected to Hadamard gate, then CNOT gate operation is performed, and then the control bit (for X error) This refers to an operation of applying a Hadamard gate to the syndrome spin 301C) (the lower diagram in FIG. 3B).

Step (ix): Copying the extracted syndrome to the classical system 303 As in step (iii), the state of the quantum bit (auxiliary spin of the syndrome spin for X error) (FIG. 3A, etc.) of the particle 303C is changed. , | 0>, and target X-error syndrome spin auxiliary spin 303C between X-error syndrome spin 301C and X-error syndrome spin auxiliary spin 303C using X-error syndrome spin 301C as a control bit As a bit, a CNOT gate operation is performed (the diagram on the left side in FIG. 3C, step S9 in FIG. 5B).

Step _{(x): H P ({} af}) in the same manner as the cooling step (iv) under the auxiliary spin 303C qubits (cooling qubits (cooling spin)) and X error for syndrome spin particles 303A The CNOT gate operation is performed using the four cooling spins 303A as control bits and the auxiliary spin 303C of the syndrome spin for X error surrounded by the four cooling spins 303A as a target bit. Then, the dissipation operation (attenuation by D (βJ) (described later)) is performed on the auxiliary spin 303C of the syndrome spin for X error, and the above-described CNOT operation U is performed (step S10 in FIG. 5B).

Step (xi): Similar to the cooling step under _{H F} (v), performed CNOT gate operation between the auxiliary spin 303C of X error for Syndrome spin 301C and X error for syndromes spin, syndrome X-Error An operation of changing the parity of the surrounding four cooling spins 303A using the auxiliary spin 303C of the spin as a control bit, for example, a random CNOT operation (described later) between the auxiliary spin 303C of the syndrome spin for X error and the cooling spin 303A . Then, a dissipation operation (attenuation by D (βh) (described later)) is performed on the cooling spin 303A (step S11 in FIG. 5B).

Step (xii)
The operation from the above step (ix) to step (xi), as the cooling effect under each H _P and H _F can be sufficiently obtained, repeated a predetermined number of times determined in advance (step of FIG. 5B S12 ).

Step (xiii): X error correction by feedback CNOT gate operation is performed between the cooling spin 303A and the data qubit 301A using the cooling spin 303A as a control bit and the data qubit 301A as a target bit (step S13 in FIG. 5B). ).

  As described above, the error (X error) included in the data qubit 301A is corrected by the operations from step (ix) to step (xiii).

  A series of operations from step (i) to step (xiii) corresponds to one cycle of quantum error correction according to the embodiment of the present invention.

Hereinafter, the step (iv) (cooled under _{H P)} and step (v) (cooled under _{H F),} it will be described in more detail.

  Steps (iv) and (v) are intended to achieve cooling under the Hamiltonian H ({bv}) (Equation (2)). Steps (x) and (xi) are also aimed at achieving cooling under the Hamiltonian H ({af}).

_First, rewrites the H P ({bv}), using a spin operator Zv auxiliary spin 303B syndrome spin for Z errors, the shape such as the following equation does not depend on the eigenvalues bv (Equation (5)).

Next, in order to consider the dynamics of cooling, the interaction H _int between the classical system 303 and the environmental system is considered. Then, the time evolution V (t) of the whole system is
V (t) = e ^ [− i (H + H _int ) t],
It becomes.

  If the interaction between the classical system 303 and the environmental system is sufficiently small and the correlation time of the environmental system is sufficiently short, the whole system can be well approximated as being attenuated in a Markov process toward the thermal equilibrium state.

If we use Suzuki Trotter expansion and finely discretize the time evolution of V (t),
V (t) = e ^ [− i (H + H _int ) t]
_{~ [E ^ [- i (} H P + H int / 2) τ]
_{× e ^ [- i (H} F + H int / 2) τ]] ^ m,
It becomes. Here, t = τm.
Here, approximation
Is used.

Thus, by partially tracing the environmental system, the dissipation dynamics of the Markov process can be digitally simulated in a cooled spin system.
Here, ρA and ρB are density matrices of the classical system 303 and the environmental system, respectively.

L _P and L _F, respectively, corresponding to a Markovian dissipation under Hamiltonian H _P and H _F, Lindblad (Lindblad) Ultra operator
It is. Also here the operator
Is
It works to lower energy.

The ratio of attenuation to excitation (γ ₋ / γ ₊ ) is calculated by using the inverse β of the temperature of the environment and the energy gap h,
Given in.

Also, an operation to dissipate one qubit
Is assumed, the cooling dynamics e ^ (τL _F ) is the dissipative dynamics to the cooling spin 303A.
It is realized with.

In order to realize L _P by comprehensive control (non-selective operation on particle group), first, the following operator
think of. If the parity of ZvΠZ is odd, the auxiliary spin 303B of Z syndrome syndrome spin (error syndrome copy) is flipped.

  In order to reduce the energy of the cooling spin 303A, it is sufficient if the cooling spin 303A can be flipped randomly when a copy of the error syndrome is flipped.

Therefore, in order to know whether or not the error syndrome copy has been flipped, the Z error syndrome spin 301B is used as a control bit between the Z error syndrome spin 301B and the auxiliary spin 303B of the Z error syndrome spin. The CNOT gate operation is performed with the auxiliary spin 303B of the syndrome spin as the target bit. If a copy of the error syndrome is flipped, the auxiliary spin 303B of the Z error syndrome spin is | 1>. If the error syndrome copy is not flipped, the auxiliary spin 303B of the Z error syndrome spin is | 0>. Then, the operation of changing the parity of the surrounding four cooling spins 303A using the auxiliary spin 303B of the Z error syndrome spin as a control bit, for example, random CNOT between the auxiliary spin 303B of the Z error syndrome spin and the cooling spin 303A. Perform the operation. The CNOT gate operation between the Z error syndrome spin 301B and the auxiliary spin 303B of the Z error syndrome spin and the random CNOT operation between the auxiliary spin 303B of the Z error syndrome spin and the cooling spin 303A are summarized. R ~ _CNOT . After R ~ _CNOT , the operation of c ^ is effectively equivalent to the operation of a ^.

A method for realizing a dissipative operation by c ^ in which a Lindblad super operator is expressed as L to _P will be described.

The operator c ^ is determined by the operation U (FIG. 3 (d)).
Is converted as follows. This is a single quantum up / down operation for a qubit at a square lattice vertex. Therefore, by combining the results and R ~ _CNOT, dissipative operation L _P is realized as follows.
here,
It is. From the above, digitized (discretized) cooling under the Hamiltonian H ({bv}) can be realized by comprehensive operation (global control).

Next, the requirements that the physical parameters should meet are discussed. Here, the physical parameters are dissipation rates (decay rates) Γ ₁ = 1 / T ₁ and Γ ₂ = 1 / T ₂ for the particles 301A, 301B, and 301C of the quantum system 301. In this case, Γ ₁ >> Γ ₂ is assumed.

The dissipation rate of the particles 303B and 303C of the classical system 303 is represented by γ˜ || H _int ||, and if the coupling strength between qubits is g, the time required for gate operation is limited to 1 / g. Is done.

In the above-described cooling dynamics derivation process, Markov approximation is used. Therefore, it is assumed that J, h >> γ. In addition, Jγτ ² << 1, hγτ ² << 1 from the approximation (Expression (6)) used in Suzuki Trotter expansion. Assuming J, h to 10γ, and Jγτ ^{2 to} 0.1, the time width τ when digitally (time discretely) simulating the cooling process is τ to 0.1 / γ.

On the other hand, according to the numerical simulation (Monte Carlo simulation) conducted by the inventor, the cooling process requires 10 ³ Monte Carlo steps. In each Monte Carlo step, spins are flipped in parallel by a metropolis algorithm, and the step is physically given by a relaxation time 1 / γ. Therefore, the time required for the cooling process is estimated to be t _cool = 10 ³ / γ. The cooling process, since it is divided by the time width of τ~0.1 / γ, the number of divisions _{becomes m = t cool} / _τ~10 ^4. In each digitized cooling process, 10 gate operations are implemented, so in addition to the cooling time, a gate operation time t _g = 10 m / g is required.

From the above, the cooling process
t _cycle = t _cool + t _g -10 ³ / γ + 10 ⁵ / g,
Takes time.

In addition, in order for MFQEC to work well, it is required to suppress the error probability p of qubits to p-10 ⁻² or less. Since Γ ₁ << Γ ₂ , considering only the Z error probability due to T ₂ relaxation,
p = 1-e ^ (- Γ 2 t cycle) ~Γ 2 t cycle ~10 -2
⇔ Γ ₂ × (10 ³ / γ + 10 ⁵ / g) to 10 ⁻²
Γ Γ ₂ <10 ⁻⁵ γ and Γ ₂ <10 ⁻⁷ g,
It becomes. The former, dissipation time of the auxiliary bit (classical system 303) have shown that fast only 10 ⁵ times greater than the relaxation time _{T 2} of the qubit (quantum system 301). The latter, the gate time g is, it means that 10 ⁷ times faster than the coherence time of the quantum system 301.

  As described above, the quantum error correction method according to the embodiment of the present invention performs the quantum error correction using the cooling process realized by the comprehensive control. In this method, all operations and the Hamiltonian of each system are local and translationally symmetric in the two-dimensional system, and do not require any observation of individual quantum information carriers in the qubits. Therefore, in the quantum error correction method according to the embodiment of the present invention, the number of operation channels for performing operations on the quantum bits of the quantum information holding body does not increase with an increase in system size. Therefore, the quantum error correction method according to the embodiment of the present invention can realize quantum error correction with an extremely small number of operation channels regardless of the system size.

In other words, the quantum error correction method according to the embodiment of the present invention is:
In a quantum information storage in which a plurality of qubits are arranged in a lattice structure, a surface code error composed of quantum information stored in a plurality of data qubits 301A arranged on each side of the lattice structure A quantum error correction method in a quantum error correction apparatus for correcting
By performing a first translationally symmetric and local first operation on the quantum information storage, a plurality of first Z error qubits 301B arranged at each vertex of the lattice structure have a Z error syndrome of a surface code. A Z error extraction step (step (ii)) for preparing a quantum state corresponding to
By performing a second translationally symmetric and local second operation on the quantum information storage, the quantum states of the plurality of first Z error qubits 301B prepared by the Z error extraction step are changed to a plurality of first states. A Z error copy step (step (iii)) of copying to a plurality of second Z error qubits 303B arranged close to each of the 1Z error qubits 301B;
By performing a third translationally symmetric and local third operation on the quantum information store, using the quantum state of the second Z error qubit 303B prepared by the Z error copy step, the Z error syndrome A first cooling step (step (iv)) for cooling a plurality of cooling qubits 303A arranged in proximity to the plurality of second Z error qubits 303B and the plurality of data qubits 301A under a Hamiltonian depending on Step (v));
By performing the fourth translationally symmetric and local fourth operation on the quantum information storage, the quantum states of the plurality of cooling qubits 303A prepared by the Z error cooling step are converted into a plurality of data quanta. Z error correction step (step (vii)) that feeds back to bit 301A;
By performing a comprehensive translational symmetric and local fifth operation on the quantum information storage, a plurality of first X error qubits 301C arranged at each face center of the lattice structure are subjected to an X error of the surface code. An X error extraction step (step (viii)) for preparing a quantum state corresponding to the syndrome;
By performing a comprehensive translational symmetric and local sixth operation on the quantum information storage, the quantum states of the plurality of first X error qubits 301C prepared by the X error extraction step are converted into a plurality of first states. An X error copy step (step (ix)) for copying to a plurality of second X error qubits 303C arranged close to each of the 1X error qubits 301C;
The X error syndrome is obtained using the quantum state of the second X error qubit 303C prepared by the X error copy step by performing a comprehensive translational symmetric and local seventh operation on the quantum information storage. A second cooling step (step (x), step (xi)) for cooling the plurality of second X error qubits 303C and the plurality of cooling qubits 303A under a Hamiltonian depending on
By performing a comprehensive translational symmetric and local eighth operation on the quantum information storage, each quantum state of the plurality of cooling qubits 303A prepared by the X error cooling step is converted into a plurality of data quanta. And an X error correction step (step (xiii)) that feeds back to the bit 301A.

In the quantum error correction method according to the embodiment of the present invention,
The third operation (corresponding to the process of FIG. 4C) is an operation that simulates the temporal development of the interaction between a plurality of cooling qubits adjacent to the apex (operation U in FIG. 3D). And an operation for simulating the time evolution of energy dissipation of the plurality of cooling qubits (operation D in FIG. 3D) and an operation for simulating the time evolution of energy dissipation of the second Z error qubit (FIG. 3 ( d) operation D),
The seventh operation is similar to each operation included in the third operation, and is an operation that simulates the time evolution of the interaction between a plurality of cooling qubits adjacent to the face center, and a plurality of cooling qubits. The operation of simulating the time evolution of the energy dissipation of the second X error and the operation of simulating the time evolution of the energy dissipation of the second X error qubit may be included.

5. Physical implementation (configuration of quantum information storage device with quantum error correction device)
Finally, the configuration of a quantum information storage device (quantum information storage) capable of performing a quantum error correction method (non-observation type quantum error correction) according to an embodiment of the present invention will be described. In the above explanation, the role of each layer is clearly separated using the two-layer configuration of the classical system 303 and the quantum system 301, and furthermore, a model in which one quantum information holding body constitutes one qubit is used. It explained by. Therefore, in the above description, six types of quantum information carriers (particles (301A to C, 303A to C)) are used. However, the quantum information storage device can be physically realized by a single layer structure of three kinds of quantum information holding bodies (particles) arranged on a square lattice. In this case, particles (atoms) each having a plurality (two) of qubits are used for each quantum information holding body.

  In the present specification, the term “quantum information holding body” is a term that collectively includes one or two or more qubits that can hold a quantum state in each qubit. For example, the quantum information holder includes electrons. At this time, the electron as the quantum information holding body has, for example, an internal degree of freedom (spin) as a quantum bit. Further, for example, the quantum information holding body includes atoms. At this time, the atom as the quantum information holding body has, for example, a first internal degree of freedom (nuclear spin) as the first qubit and a second internal degree of freedom (electron spin) as the second qubit. Prepare. That is, an atom is a quantum information holding body that can use two internal degrees of freedom as two types of qubits. In this case, in a particle (such as an atom) as a quantum information holding body, its vibrational state, rotational state, and orbital state can also be used as qubits. Furthermore, a substance such as a molecule or a nanoparticle that is relatively stable while having an unpaired electron is an example of a quantum information carrier.

  In addition, a qubit using a superconducting circuit including one or more qubits can be used as a quantum information holding body. A quantum dot qubit can also be used as a quantum information holding body. That is, artificial atoms such as superconducting qubits and quantum dot qubits are examples of quantum information carriers.

  In addition, the vibration state of an object having a macroscopic scale (for example, a cantilever device configured with a macroscopic scale) can also become a qubit by being quantized. Therefore, an object having such a macroscopic scale is also an example of a quantum information holder. In addition, for example, a photon in a cavity and strongly bonded to a substance has a quantum state associated with the state of the substance. Thus, such photons can also be used as qubits. Therefore, a photon is also an example of a quantum information holder.

  FIG. 6B is a schematic diagram showing a configuration of a quantum information storage device (quantum information storage) 601 having a single layer structure. For comparison, FIG. 6A shows the quantum information storage device having the two-layer structure used in the above description.

  The quantum information storage device 601 shown in FIG. 6B includes, for example, three types of particles 601A, 601B, and 601C (quantum information holders) such as atoms containing two types of qubits such as electron spin and nuclear spin. Consists of. In the following, two qubits with two internal degrees of freedom of each particle are called nuclear spin and electron spin, but qubits may be realized using other internal degrees of freedom of atoms, This may be mimicked by artificial atoms such as qubits and semiconductor qubits.

  The electron spins 601AE, 601BE, and 601CE have different energies in the respective particles 601A, 601B, and 601C. The respective electron spins 601AE, 601BE, and 601CE serve as a cooling spin (for example, 601AE), a syndrome auxiliary spin for Z error (for example, 601BE), and a syndrome auxiliary spin for X error (for example, 601CE).

  The nuclear spin 601AN associated with the cooling spin 601AE functions as a data qubit, and the nuclear spin 601BN associated with the Z error syndrome auxiliary spin 601BE functions as a Z error syndrome spin and is associated with the X error syndrome auxiliary spin 601CE. The nuclear spin 601CN works as a syndrome spin for X error.

  The nuclear spins 601AN, 601BN, and 601CN may be spins having the same type of energy in the three types of particles 601A, 601B, and 601C.

  There is an interaction between adjacent electron spins and between electron spins and nuclear spins in the same particle, and there may be no interaction between nuclear spins and between electron spins and nuclear spins not in the same particle.

  Here, the on / off of the interaction between adjacent electron spins and between the electron spin and the nuclear spin in the same particle may be switched to the on state by an external action. Alternatively, these interactions may work constantly. In that case, it is only necessary to selectively switch to an off state (decoupling) by an external action.

  When the above-described cooking error correction method is used in such a quantum information storage device 601, if steps (i), (ii), and (viii) are changed (a SWAP operation is added) as follows, Good.

  First, in step (i), the Z error syndrome auxiliary spin 601BE is initialized to | 0>, and then the Z error syndrome spin 601BN and the Z error syndrome auxiliary spin 601BE are SWAPed. The same applies to the X error syndrome auxiliary spin 601CE and the X error syndrome spin 601CN.

  For step (ii), the data qubit 601AN is first SWAPed to the cooling spin 601AE. Then, a CNOT gate is applied between the cooling spin 601AE and the Z error syndrome auxiliary spin 601BE using the cooling spin 601AE as a control bit and the Z error syndrome auxiliary spin 601BE as a target bit. Thereafter, the Z error syndrome auxiliary spin 601BE is SWAPed to the Z error syndrome spin 601BN.

  For step (viii), the data qubit 601AN is first SWAPed to the cooling spin 601AE. Then, the above-described HCNOT gate is applied between the X error syndrome auxiliary spin 601CE and the cooling spin 601AE with the X error syndrome auxiliary spin 601CE as the control bit and the cooling spin 601AE as the target bit. Thereafter, the syndrome auxiliary spin 601CE for X error is SWAPed to the syndrome spin 601CN for X error.

  In addition, the 1-qubit gate operation for the nuclear spin uses the accompanying interaction with the electron spin. By doing so, it is possible to remotely control the one-qubit gate operation of the nuclear spin by only irradiating the electron spin with the electromagnetic wave without irradiating the nuclear spin with the electromagnetic wave.

  Therefore, the quantum error correction apparatus selectively irradiates the whole quantum information storage apparatus 601 with an electromagnetic wave having three kinds of frequencies in accordance with the gate operation procedure defined by the quantum error correction method according to the embodiment of the present invention. It is realized by a device capable of

In other words, in the quantum error correction method according to the embodiment of the present invention,
The plurality of data qubits and the plurality of cooling qubits arranged on each side of the lattice structure are two types of a plurality of first quantum information holding bodies (first particles 601A) arranged on each side. Internal degrees of freedom (nuclear spin 601AN and electron spin 601AE),
The plurality of first Z error qubits and the plurality of second Z error qubits arranged at each vertex of the lattice structure are a plurality of second quantum information holding bodies (second particles 601B) arranged at each vertex. 2 types of internal degrees of freedom (nuclear spin 601BN and electron spin 601BE)
The plurality of first X error qubits and the plurality of second X error qubits arranged on each face center of the lattice structure include a plurality of third quantum information holding bodies (third Two kinds of internal degrees of freedom (nuclear spin 601CN and electron spin 601CE) of the particle 601C) may be used.

  FIG. 7 shows that the entire quantum information storage device 601 is comprehensively irradiated with electromagnetic waves having three kinds of frequencies according to the gate operation procedure defined by the quantum error correction method according to the embodiment of the present invention as described above. It is a block diagram of the quantum information storage apparatus 701 provided with the quantum error correction apparatus 703 which can do.

  A quantum information storage device 701 including a quantum error correction device according to an embodiment of the present invention includes the above-described single-layer quantum information storage 705 as a quantum information storage. Then, the quantum error correction device 703 irradiates the quantum information storage 601 comprehensively with the electromagnetic wave EMW1 having the frequency f = f1 to thereby form the first particle 601A (first quantum information holding body) and the second particle. 601B (second quantum information holding body) and first that can perform a comprehensive operation only on the plurality of first particles 601A among the third particles (third quantum information holding body). A plurality of the first particles 601A, the second particles 601B, and the third particles by comprehensively irradiating the quantum information storage 601 with the operation device 711 and the electromagnetic wave EMW2 having the frequency f = f2. By comprehensively irradiating the quantum information storage 601 with the second operator 712 capable of performing a comprehensive operation only on the second particle 601B and the electromagnetic wave EMW3 having the frequency f = f3. A third operator 713 that can perform a comprehensive operation only on the plurality of third particles 601C among the particles 601A, the second particles 601B, and the third particles, and a first operator 711 Controller for controlling on / off of electromagnetic wave irradiation of each of the second operation unit 712 and the third operation unit 713 based on the quantum error correction method according to the embodiment of the present invention (in accordance with the gate operation procedure defined by the method) Instrument control unit) 715. The frequency f1 of the electromagnetic wave EMW1 is, for example, applied to the coupling (coupling) between the electron spins 601AE of the adjacent first particles 601A by irradiating the electron spins 601AE of the first particles 601A (first quantum information holding body). ) (Frequency of coupling). For example, the frequency f2 of the electromagnetic wave EMW2 is applied to the coupling (coupling) between the electron spins 601BE of the adjacent second particles 601B by irradiating the electron spins 601BE of the second particles 601B (second quantum information holding body). ) (Frequency of coupling). For example, the frequency f3 of the electromagnetic wave EMW3 is applied to the coupling (coupling) between the electron spins 601CE of the adjacent third particles 601C by irradiating the electron spins 601CE of the third particles 601C (third quantum information holding body). ) (Frequency of coupling). The controller 715 here may be a processor (microcontroller, central processing unit (CPU), etc.) used in classical information processing. The gate operation procedure determined by the quantum error correction method according to the embodiment of the present invention is stored in a storage device (memory) included in the controller 715. Note that the storage device may be outside the controller 715.

  Finally, a physical system of electron spin and nuclear spin that realizes the quantum information storage (quantum information storage) 601 will be described.

Relaxation time T ₂ of the nuclear spins of silicon (Si) single crystal is that more than 30 seconds has been confirmed by experiment. Here, it is assumed that the nuclear spin T ₂ is 10 seconds or less. Then, the coupling | bonding for implement | achieving 2 quantum bit gates is calculated | required the intensity | strength of 1 MHz or more.

  Since the Rabi frequency that can be realized by irradiating the electron spin with electromagnetic waves is about 1 GHz, the coupling strength between the electron spins is less than 100 MHz considering that the coupling can be freely decoupled. It is preferable that For example, when the distance between localized electron spins is 1 nm, a dipole interaction of about 44 MHz works between the two, and the strength is inversely proportional to the distance between electron spins. From these, the desired distance between electron spins can be estimated.

  In the above description, each of the first operating unit 711, the second operating unit 712, and the third operating unit 713 irradiates the quantum information storage unit 601 with an electromagnetic wave having an appropriately selected frequency, thereby A comprehensive operation can be performed on only the first particles 601A, only the plurality of second particles 601B, or only the plurality of third particles 601C. However, in the embodiment of the present invention, the method for performing the operation is not limited to the irradiation of electromagnetic waves. For example, by changing the state of the field surrounding the quantum information holding body, or changing the electrical environment of the quantum information holding body (for example, applied bias voltage), a plurality of quantum information holding bodies Comprehensive operations can be performed.

  So far, implementation in a system that forms a two-dimensional square lattice has been described. However, as long as the data qubit (A ′) is on the side, the Z error syndrome spin (B ′) is at the apex, and the X error syndrome spin (C ′) is at the center, The surface code can be implemented in various lattice shapes such as a two-dimensional honeycomb lattice and even in a three-dimensional cubic lattice shape. For example, if three types of electron spins can be arranged on the side (A ′), vertex (B ′), and face center (C ′) of a honeycomb lattice having a side of 3 nm, between A ′ and B ′, and , A′-C ′ have a dipole interaction of 13 MHz and 2.5 MHz, respectively, and a quantum information storage (quantum information storage) having these lattice shapes is also preferable.

  For example, some free radical molecules have a very long electron spin decoherence time, such as trityl radical, nitrogen-encapsulated fullerene, and lithium (Li) phthalocyanine. These can be used for the quantum bits of the quantum information storage 705 according to the embodiment of the present invention. In that case, an appropriate nuclear spin qubit is attached by isotopically controlling atoms in the molecule. Then, by modifying these molecules to form a two-dimensional polymer or a two-dimensional supramolecule, electron spins can be arranged in a lattice shape. FIG. 8 is a diagram showing a design diagram of an example of the molecule 801 for quantum information storage made in this way. The supramolecular structure of the trityl radical 803 (first quantum information carrier) and the nitrogen-encapsulated fullerene 805 derivative (second quantum information carrier) serves as a skeleton, and another molecule (here, lithium (Li)) is formed in the gap. Phthalocyanine 807 (third quantum information carrier) is captured. That is, in this example, the two-dimensional lattice structure of the quantum information storage 705 is formed by a supramolecular structure including a trityl radical 803 and a nitrogen-containing fullerene 805 derivative. Then, the lithium phthalocyanine 807 is arranged at the face center position of the two-dimensional lattice structure, and the quantum information storage 705 is configured. Therefore, in this case, the first particle 601A is nitrogen, the second particle 601B is carbon in a radical state, and the third particle 601C is lithium. In such a structure, the length of one side of the lattice is about 3 nm, and the above condition is satisfied, and the quantum error correction method (non-observation type quantum error correction (MFQEC)) according to the embodiment of the present invention can be operated correctly.

  Note that the quantum information storage 705 is not limited to the example of FIG. Each of the first quantum information holder, the second quantum information holder, and the third quantum information holder includes an unpaired electron and a relatively stable molecule, or an unpaired electron. Any nanoparticle may be used. In other words, the first to third quantum information holders may be molecules or nanoparticles each having a paramagnetic electron. Nanoparticles include, for example, diamond and silicon carbide.

  In this case, the lattice structure of the quantum information storage 705 is formed to include at least one of the first quantum information holding body, the second quantum information holding body, and the third quantum information holding body. It may be formed by a supramolecular structure or a polymer structure.

  The key to the realization of highly reliable large-scale quantum information storage is the architecture of unobserved quantum error correction by comprehensive control and the implementation in a highly scalable physical system. In this respect, the quantum error correction method according to the embodiment of the present invention and the quantum information storage device using the same are extremely advantageous.

101: feedback operation 102a: initialization by cooling auxiliary bit 102b: auxiliary bit unitary operation 103: classical information processing 104: auxiliary bit system unitary operation 105: cooling process 201: surface code 202: quantum bit 205: Z error 207 : Stabilizer operator 301 at the top of terminal C of chain C: Quantum system 303: Classical system 301A: First quantum system particle (data qubit)
301B: Second quantum particle (syndrome spin for Z error)
301C: quantum system third particle (syndrome spin for X error)
303A: Classical first particle (cooling spin)
303B: Classical second particle (auxiliary spin of syndrome spin for Z error)
303C: Classical third particle (auxiliary spin of syndrome spin for X error)
601: Quantum information storage device (quantum information storage)
601A: first particle 601AE: first electron spin (cooling spin)
601AN: First nuclear spin (data qubit)
601B: second particle 601BE: second electron spin (Z-error syndrome auxiliary spin)
601BN: Second nuclear spin (Z-error syndrome spin)
601C: third particle 601CE: third electron spin (syndrome auxiliary spin for X error)
601CN: Third nuclear spin (Syndrome spin for X error)
701: Quantum information storage device 703 provided with a quantum error correction device 703: Quantum error correction device 705: Quantum information storage device 711: First operation device 712: Second operation device 713: Third operation device 715: Controller (operation device control) Part)
801: molecule for quantum information storage 803: trityl radical 805: nitrogen-containing fullerene 807: lithium (Li) phthalocyanine

Claims (7)

In a quantum information storage in which a plurality of qubits are arranged in a lattice structure, an error in the surface code composed of quantum information stored in a plurality of data qubits arranged on each side of the lattice structure A quantum error correction method in a quantum error correction apparatus for correcting
By performing a first translationally symmetric and local first operation on the quantum information storage, a plurality of first Z error qubits arranged at the respective vertices of the lattice structure are converted into Z of the surface code. A Z error extraction step of preparing a quantum state corresponding to the error syndrome;
By performing a second translationally symmetric and local second operation on the quantum information store, the quantum states of the plurality of first Z error qubits prepared by the Z error extraction step are obtained. A Z error copy step of copying to a plurality of second Z error qubits arranged close to each of the plurality of first Z error qubits;
By performing a third translationally symmetric and local third operation on the quantum information store, using the quantum state of the second Z error qubit prepared by the Z error copy step, A first cooling step of cooling a plurality of cooling qubits arranged in proximity to the plurality of second Z error qubits and the plurality of data qubits under a Hamiltonian dependent on Z error syndrome;
The plurality of cooling qubits prepared by the Z error cooling step are subjected to a comprehensive translational symmetric and local fourth operation with respect to the quantum information storage. Z error correction step for feeding back to the data qubits of
By performing a comprehensive translational symmetric and local fifth operation on the quantum information storage, a plurality of first X error qubits arranged at the center of each lattice structure are assigned to the surface code. An X error extraction step of preparing a quantum state corresponding to the X error syndrome;
By performing a comprehensive translational symmetric and local sixth operation on the quantum information storage, the quantum states of the plurality of first X error qubits prepared by the X error extraction step are obtained as described above. An X error copy step of copying to a plurality of second X error qubits arranged close to each of the plurality of first X error qubits;
By performing a comprehensive translational symmetric and local seventh operation on the quantum information store, using the quantum state of the second X error qubit prepared by the X error copy step, A second cooling step of cooling the plurality of second X error qubits and the plurality of cooling qubits under a Hamiltonian dependent on X error syndrome;
By performing a comprehensive translationally symmetric and local eighth operation on the quantum information store, the quantum states of each of the plurality of cooling qubits prepared by the X error cooling step are obtained. And an X error correction step of feeding back to the data qubits. The third operation includes an operation for simulating time evolution of interaction between the plurality of cooling qubits adjacent to the apex, and an operation for simulating time evolution of energy dissipation of the plurality of cooling qubits. And an operation for simulating the time evolution of energy dissipation of the second Z error qubit,
The seventh operation simulates time evolution of interaction between the plurality of cooling qubits adjacent to the face center and time evolution of energy dissipation of the plurality of cooling qubits. The quantum error correction method according to claim 1, comprising: an operation; and an operation for simulating the time evolution of energy dissipation of the second X error qubit. The plurality of data qubits and the plurality of cooling qubits arranged on each side of the lattice structure are two kinds of internal free of the plurality of first quantum information holding bodies arranged on each side. Degree,
The plurality of first Z error qubits and the plurality of second Z error qubits arranged at each vertex of the lattice structure are two types of a plurality of second quantum information holding bodies arranged at the vertices. Internal degrees of freedom,
The plurality of first X error qubits and the plurality of second X error qubits arranged on each face center of the lattice structure are formed by a plurality of third quantum information holding bodies arranged on the face centers. The quantum error correction method according to claim 1, wherein there are two types of internal degrees of freedom. A quantum error correction apparatus for correcting an error of a surface code constituted by quantum information stored in a plurality of data qubits of a quantum information storage according to the quantum error correction method according to claim 3,
Of the plurality of first quantum information holding bodies, the plurality of second quantum information holding bodies, and the plurality of third quantum information holding bodies, only the plurality of first quantum information holding bodies A first controller capable of performing comprehensive operations;
Of the plurality of first quantum information holding bodies, the plurality of second quantum information holding bodies, and the plurality of third quantum information holding bodies, only the plurality of second quantum information holding bodies A second controller capable of performing comprehensive operations;
Of the plurality of first quantum information holding bodies, the plurality of second quantum information holding bodies, and the plurality of third quantum information holding bodies, only the plurality of third quantum information holding bodies A third controller capable of performing comprehensive operations;
A quantum error correction apparatus comprising: an operator controller that controls the first operator, the second operator, and the third operator according to the quantum error correction method according to claim 3.
The first quantum information carrier, the two kinds of internal degrees of freedom having a nuclear spin and an electron spin;
In the operation, the first operation unit irradiates the quantum information storage unit with an electromagnetic wave having a first frequency, and changes the strength of coupling between electron spins of the adjacent first quantum information holding bodies. ,
In the operation, the second operation unit irradiates the quantum information storage unit with an electromagnetic wave having a second frequency, and changes the strength of the coupling between the electron spins of the adjacent second quantum information holding bodies. ,
In the operation, the third operation unit irradiates the quantum information storage unit with an electromagnetic wave having a third frequency to change the strength of the coupling between the electron spins of the adjacent third quantum information holding bodies. The quantum error correction apparatus according to claim 4. A quantum error correction device according to claim 4,
A plurality of first quantum information holders disposed on each side of the lattice structure; a plurality of second quantum information holders disposed at the vertices of the lattice structure; and the lattice structure A plurality of the third quantum information holding bodies arranged on each of the face centers of the quantum information storage,
A quantum information storage device. The lattice structure of the quantum information storage is formed including at least one of the first quantum information holding body, the second quantum information holding body, and the third quantum information holding body. Formed by a supramolecular structure or a polymer structure,
The first quantum information holding body, the second quantum information holding body, and the third quantum information holding body are each a molecule having an unpaired electron or a nanoparticle having an unpaired electron. Item 7. The quantum information storage device according to Item 6.