CN114528999B

CN114528999B - Optical pulse generation method for performing high-fidelity control on ensemble qubits

Info

Publication number: CN114528999B
Application number: CN202210110994.7A
Authority: CN
Inventors: 延英; 陈添凤; 莫泽; 邱嘉旻; 彭宏; 乐猛
Original assignee: Suzhou University
Current assignee: Suzhou University
Priority date: 2022-01-21
Filing date: 2022-01-21
Publication date: 2024-07-12
Anticipated expiration: 2042-01-21
Also published as: CN114528999A

Abstract

The invention belongs to the field of quantum computation, and discloses a light pulse generation method for performing high-fidelity control on an ensemble quantum bit in order to improve the robustness and the fidelity of quantum control, wherein in an ensemble nitrogen vacancy central system, a time-containing schrodinger equation of a three-energy-level system is reversely solved based on a non-transition quantum driving theory, a microwave field between two ground-state energy levels is eliminated as a target, and a representation form of a time evolution operator is designed through the introduction of a degree-of-freedom parameter; the amplitude and the phase of two light pulses are designed through the reverse direction of a time evolution operator; inputting the light into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as those of the light pulse, driving an acousto-optic modulator in a continuous laser light path by using the radio signal to obtain +1 level or-1 level deflection output light, and generating a group of bicolor light pulses; the generated bicolor light pulse is vertically incident into a three-energy-level quantum system medium, and the bicolor light pulse interacts with the quantum system medium to generate any superposition state of quantum bits.

Description

Optical pulse generation method for performing high-fidelity control on ensemble qubits

Technical Field

The invention belongs to the field of quantum control and quantum computing, and particularly relates to an optical pulse design theory capable of quickly and highly robustly creating a quantum bit superposition state.

Background

The age of classical physical development is mature at the end of the nineteenth century, and the life of people is changed over the sky. With the development of informatics, the continuous and deep research of big data, artificial intelligence and the like in recent years means that the requirement on the speed of information processing is higher and higher, and some phenomena which cannot be explained by classical physics appear, so that the information processing by using a classical computer is more and more difficult, and the finding of a new solution is a urgent need at present. At this time, the twenty-century quantum mechanics appears to describe the field where physics cannot describe the microscopic world. At present, with the gradual perfection and development of the quantum mechanics field, the superiority of quantum computing is being embodied step by step. They use not the conventional bits consisting of 1 and 0, but qubits representing different values at the same time, i.e. two quantum states |0> and |1> are used to encode information. And the processing of this information is achieved by other methods such as microwave pulses or light pulses. In this way, quantum computation stores an excessively large amount of information, and the computation speed exhibits an exponential rise. Furthermore, due to the complexity of quantum computers, they are made faster in performing certain tasks, enabling them to solve problems that modern machines are almost impossible to solve. Therefore, the method is widely applied to aspects of quantum neural network simulation, artificial intelligence, large-mass factorization, unordered database retrieval and the like. And the wide application in the fields of materials science, biology, informatics and the like promotes the birth of an emerging intersection subject. However, in the implementation process of quantum computing, the quantum state is often vulnerable and sensitive due to the influence of surrounding noise, so that the quantum state is often difficult to control. It would be a great challenge to find a physical system that has excellent coherence properties, is easy to handle, and has sufficient handling fidelity.

Currently, there are many physical systems for carrying qubits, such as trapping ion systems, superconducting qubit systems, rare earth ion systems, diamond nitrogen vacancy centre systems, and the like. Different systems have different characteristics, so that proper light pulses are designed according to the characteristics of the systems where different carriers are positioned to realize high-fidelity quantum state control, and the method has important significance for research and development of quantum computation.

In these systems, diamond nitrogen vacancy centres have attracted much researchers' interest due to their simple stable spin level structure, efficient and convenient optical transitions, and extremely long spin quantum state coherence times at room temperature. The method is characterized in that the method has the greatest characteristic that the spin quantum bit has extremely long coherence time at room temperature, the extremely long spin state coherence time brings extremely high magnetic field detection sensitivity, and the nitrogen vacancy center is of a sub-nanometer structure and stably exists in diamond single crystals and nano particles, so that the method is convenient to couple with other systems (such as an optical cavity and a microwave cavity), and extremely high-efficiency quantum control is realized by an optical method and radio frequency microwave pulse. In the nitrogen vacancy centre experimental system, energy levels are generally separated by the zeeman effect of an externally applied magnetic field, and a two-level or three-level system can be obtained, and in such a system, in order to realize the initialization operation of the qubit, the states of spins in the nitrogen vacancy centre need to be controlled. The spin state of the nitrogen vacancy centre is regulated by using a spin magnetic resonance technology, namely, the interaction of a microwave field and spin is utilized to regulate the evolution of the spin state. The base electron spin state is used for initializing and reading the quantum state through optical transition, and the microwave is used for controlling the quantum state to form any superposition state. In the system of the nitrogen vacancy centre of the ensemble, spin ensemble occurs, and non-uniform broadening of spin transitions in the ensemble may occur due to random distribution of spin in diamond, and in the nitrogen vacancy centre of the ensemble, the degree of non-uniform broadening strongly depends on the concentration of the nitrogen vacancy centre, and if the nitrogen vacancy centre of the ensemble is handled as a quantum unit, high robustness for non-uniform broadening is required. Therefore, when quantum state manipulation is performed, a main limiting factor is the decoherence effect caused by natural frequency detuning in a certain range. That is, in such a system, quantum manipulation needs to be robust against frequency mismatch present in the ensemble of qubits when creating any superposition of qubits.

Taking first an example of an ensemble of nitrogen vacancy centres, in this system its ground state is due to a relationship between |m _s =0 > and |m _s = ±1>Zero field splitting produces a spin triplet state. An additional zeeman split is then created by applying an external magnetic field along the crystallographic axis of the nitrogen vacancy centre at the sub-level of |m _s = ±1>, creating a three-level system. Typically, one nitrogen vacancy centre is generally considered a spin, and one ensemble nitrogen vacancy centre is considered an ensemble spin. In experiments, to initialize and read the quantum state of the base electron spin state, optical transitions are typically performed with the first excited state |1> _j and the second excited state |2> _j through the ³ a ground state |0> _j, respectively. Since a random distribution of spins in diamond may lead to a non-uniform broadening of spin transitions in the ensemble (about 300 MHz), and the degree of non-uniform broadening is strongly dependent on the concentration of nitrogen vacancy centres (here illustrated by the number of nitrogen vacancy centres being 10 ¹²), quantum manipulation is required to be highly robust to frequency mismatch if these ensemble nitrogen vacancy centres are manipulated as one quantum unit for the ensemble qubits therein. At this time, reasonable design is required for microwave and optical pulses to realize high-fidelity manipulation for the non-uniform broadening occurring in the system.

Then taking a rare earth ion system Pr ³⁺:Y₂SiO₅ with doping concentration of 0.05% as an example, in the process of forming doped crystals by substituting micro praseodymium ions for yttrium ions in matrix crystals, matrix lattices are distorted, the non-uniform broadening can reach GHz level, and all narrow transition lines of each praseodymium ion are buried in the matrix lattices. In this system, an optical hole burning technique is first required to create a zero absorption region of about 18MHz width in the non-uniform stretched line; a small portion of the ions with a similar optical transition frequency (line width about 170 kHz) are then selectively pumped back into this region by optical pumping as a qubit. It is characterized by billions of randomly distributed rare earth ions and is therefore referred to as an ensemble of qubits. Wherein the coupling between the two qubit energy levels |0> and |1> is achieved by optical transitions between each and one of the excited states |e >. In such a system, to create any superposition state of qubits with high fidelity, quantum manipulation is required to have not only better robustness to frequency mismatch caused by non-uniform broadening present in the ensemble qubits, but also stronger suppression of non-resonant excitation of other ions near the qubit ion addressing frequency.

In a three-level system like this, therefore, to create an arbitrary qubit stack state quickly and with high robustness, it is necessary to satisfy: (1) in an ensemble nitrogen vacancy centre system: the optical pulse can equally control multiple quantum bits in a 300MHz frequency detuning range within 4ns of a shorter time, namely, high fidelity is required to be generated in a + -300 MHz range. (2) in rare earth ion systems: the optical pulse can equally control the ensemble qubit in the detuning range of +/-170 kHz frequency in a short time of 4 mu s, namely the control fidelity in the interval is as close to 1 as possible; the non-resonant excitation for ions other than about 3.5MHz from the ensemble qubit ions is sufficiently small.

Current methods for designing their light pulses fall broadly into three categories: (1) a simple resonance pulse; (2) quantum adiabatic channel technology; (3) Quantum adiabatic shortcut techniques. The simple resonance pulse speed is fast, but is easily influenced by system parameter variation, and the robustness is poor; the quantum adiabatic channel technology has better robustness to the change of parameters, but needs to meet the adiabatic condition, so that the operation time is longer and is easily influenced by decoherence; in order to meet both the requirements of rapidness and high robustness, quantum adiabatic shortcut techniques are proposed. There are two common quantum adiabatic shortcut techniques, one is a reverse engineering method based on Lewis-Riesenfeld invariants, and the other is a non-transition quantum drive theory. Both methods have proven to perform the quantum bit initialization operation quickly and with high robustness.

At present, high-fidelity control of a three-energy-level system exists, and some works solve the problem of decoherence effect caused by frequency detuning. In the optical pulse design method capable of creating any superposition state of quantum bits of a three-energy-level system (application number: 201810234933.5), yanying et al propose an optical pulse design method for creating any superposition state of quantum bits in a three-energy-level system in a rare earth ion system, and a time-containing Schrodinger equation of the three-energy-level system is solved reversely by adopting an invariant theory to construct a group of bicolor optical pulses capable of generating any superposition state of quantum bits. However, this invariant theory requires first to get the invariant of hamiltonian during use, whereas in most systems the invariant is unknown, so this approach is limited in some cases by the construction invariant. The non-transition quantum drive theory provides an effective method because it does not require the construction of the invariant of hamiltonian, and is not limited by most systems, i.e., the quantum states still evolve precisely along the transient eigenstates of the initial hamiltonian by adding an anti-adiabatic coupling term to the initial hamiltonian. However, in the conventional transition-free quantum driving, a microwave coupling term between two ground state energy levels occurs, and a concise expression analysis formula of the microwave coupling term is difficult to directly construct and difficult to be implemented in experiments. Therefore, the invention is inspired by a transition-free quantum drive theory, and in a nitrogen vacancy central system, microwave coupling items between ground state energy levels are canceled by reasonably designing time evolution operators and combining reverse engineering, so that experimental operation is simplified, quantum bits are controlled, and high robustness can be realized for frequency mismatch quantity in the experiment.

Disclosure of Invention

The light pulses designed in the present invention need to have the following characteristics:

(1) Aiming at the center of the nitrogen vacancy of the ensemble, the pulse action time is not more than 4ns;

(2) For the center of the integrated nitrogen vacancy, the high-fidelity frequency-tuning method has high fidelity to the frequency-tuning quantity of at least 300MHz in the system;

(3) Aiming at a rare earth ion system, the method has robustness to frequency detuning within the range of at least +/-170 kHz in a quantum system under the pulse action time of 4 mu s; the method is suitable for a quantum system which needs to select quantum bits by depending on frequency bands;

The invention solves the technical problems that: in an ensemble nitrogen vacancy central system and a rare earth ion system, the robustness to frequency mismatch in the pulse action process is poor, and other ions near the qubit are excited in a higher non-resonance mode. Therefore, in order to improve the robustness and inhibit the non-resonance excitation, the invention seeks a design method of a bicolor light pulse, wherein the bicolor light pulse consists of two pulses with equal duration and different amplitudes, frequencies and phases, and the two pulses simultaneously act on a three-energy-level quantum system consisting of two quantum bit energy levels and one excitation state energy level, and the quantum system can be controlled to evolve from an initial state |0> to any superposition state of quantum bits under the premise of the initial state and the target state of the known system Wherein alpha, beta andIs three angles, alpha and beta are in the range of [0,2 pi ], and represents the distribution condition of the layout number on three energy levels of |0>, |e > and |1 >; Values in the range of [0,2 pi ] characterize the relative phase between the qubit energy states |0> and |1 >.

In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:

In an ensemble nitrogen vacancy central system, a time-containing schrodinger equation of a three-energy-level system is solved reversely based on a non-transition quantum driving theory, when the time-containing schrodinger equation of the three-energy-level system is solved, a microwave field between two ground-state energy levels is eliminated as a target on the premise of the initial state and the target state of a known system, and a representation form of a time evolution operator is designed through the introduction of a degree-of-freedom parameter; then, the amplitude and the phase of two light pulses are designed in an integrated nitrogen vacancy central system through the reverse direction of a time evolution operator; inputting the amplitude and the phase into an arbitrary wave generator to generate a radio signal with the same amplitude and the same phase as the optical pulse, and driving an acousto-optic modulator in a continuous laser path by using the radio signal to obtain +1-level or-1-level deflection output light to generate a group of bicolor optical pulses; the generated bicolor light pulse is vertically incident into a three-energy-level quantum system medium, and the bicolor light pulse interacts with the quantum system medium to generate any superposition state of quantum bits.

The design of the time evolution operator relates to the introduction of the degree of freedom parameters, and the microwave coupling term between two ground state energy levels is eliminated by combining reverse engineering, so that the experimental operation is simplified; and in the pulse action process, the method has high robustness to the non-uniform broadening appearing in the ensemble system, and realizes high-fidelity control on the quantum bit.

Description of principle effects: in the implementation process, a direct coupling microwave field between two ground state energy levels is eliminated based on a group of orthonormal and complete auxiliary state basic vectors and combined with reverse engineering, so that the experimental difficulty is reduced; meanwhile, in the pulse action process, the quantum bit initialization operation can be realized with high robustness.

Compared with the prior art, the invention has the following remarkable characteristics:

The generated bicolor light pulse is vertically incident into a three-energy-level quantum system medium, and the bicolor light pulse interacts with the quantum system medium to generate any superposition state of quantum bits.

The generated bicolour light pulse is suitable for a three-level quantum system and comprises two light pulses which are simultaneously applied and have different frequencies, amplitudes and phases, and the parameters of the light pulses can be completely controlled by an arbitrary wave generator and an acoustic light modulator.

The bicolor light pulse can generate any superposition state of one quantum bit in a three-energy-level system, including any distribution of layout numbers between two quantum bit energy levels and any relative phase regulation.

The starting and ending values of the bicolor light pulse are zero, so that interference to a target quantum state is avoided, and any superposition state of quantum bits is generated.

The amplitude of the bi-color light pulses varies with time, but the frequency and phase do not.

In the center of the ensemble nitrogen vacancies, the active length of the optical pulses does not exceed 4ns, avoiding decoherence.

In rare earth ion systems, the action length of the light pulse is not more than 4 mu s, and decoherence is avoided.

In the process of the action of the bicolor light pulse and the quantum bit, no direct microwave coupling exists between two ground state energy levels of the quantum bit, and experimental operation can be simplified in an ensemble nitrogen vacancy center system and a rare earth ion system.

The bi-color light pulse is suitable for quantum systems which need to select quantum bits by means of frequency bands, and non-resonance excitation is restrained.

Drawings

FIG. 1 is a schematic representation of the relative energy level structure of nitrogen-vacancy centres where there is a frequency mismatch;

Wherein Ω _p in the figure is the ratio frequency of the optical transition from level |0> to excited state level |2 >; omega _s is the ratio frequency of the optical transition from level |1> to excited state level |2 >; Is the phase of the optical transition of the |1> to the excited state level |2 >; t is the pulse action time; p _m is the probability that the ion is in the |m > state at time t; m=0, 1, e; f is the fidelity of the resulting target state; delta is the difference in transition frequency between energy levels, the amount of frequency mismatch; a ₄ is one of the degrees of freedom parameters contained in the light pulse design; the |2> state in fig. 1 is the excited state level |e >.

FIG. 2 is a graph of the evolution of the Rate frequency Ω _p,s of an optical pulse over time;

FIG. 3 is a graph of the number of layouts of the energy levels of a system over time when light pulses act on a quantum system without detuning;

FIG. 4 is a graph of the evolution of the Rate frequency Ω _p,s of an optical pulse over time;

FIG. 5 is a graph of the number of layouts of the energy levels of the system over time as light pulses act on a quantum system without detuning;

FIG. 6 is a graph of the dependence of the fidelity of the system evolution to a given target state under the action of light pulses on the amount of frequency mismatch;

FIG. 7 is a graph of the dependence of the system evolution to a given target state in terms of fidelity versus frequency mismatch and degree of freedom parameter a ₄ under the action of light pulses;

FIG. 8 is a schematic diagram of the energy level structure of Pr ions ³H₄-¹D₂ randomly doped in Y ₂SiO₅ crystals;

FIG. 9 is a plot of the evolution over time of the Rate frequency Ω _p,s of the light pulses;

FIG. 10 is a graph of the number of layouts of the energy levels of the system over time as light pulses act on a quantum system without detuning;

FIG. 11 is a graph of the dependence of the fidelity of the system evolution to a given target state under the action of light pulses on frequency mismatch in a rare earth ion system;

FIG. 12 is a graph showing the dependence of the number of layouts of the energy levels of a three-level system on the amount of frequency mismatch when an optical pulse is applied to the system,

Wherein Ω _p in the figure is the ratio frequency of the optical transitions from level |1> to level |e >; omega _s is the ratio frequency of the optical transition from level |0> to level |e >; Is the phase of the optical transition of |0> to energy level |e >; t is the pulse action time; p _m is the probability that the ion is in the |m > state at time t; m=0, 1, e; f is the fidelity of the resulting target state; delta is the amount of non-resonant frequency mismatch; a ₄ is a degree of freedom parameter in the light pulse.

Detailed Description

The invention is further described below with reference to the drawings and examples.

Embodiment one:

Optical pulse generation method for performing high-fidelity control on ensemble qubits according to initial state |0> and target state of system Wherein alpha, beta andIs three angles, alpha and beta are in the range of [0,2 pi ], and represents the distribution condition of the layout number on three energy levels of |0>, |e > and |1 >; i is an imaginary unit; Taking values in the range of [0,2 pi ], and representing the relative phase between the quantum bit energy states |0> and |1 >;

The time-containing Schrodinger equation of the three-energy-level system is solved reversely based on the non-transition quantum driving theory, but the method is different from the non-transition quantum driving theory, mainly aims at a microwave field between two ground-state energy levels, utilizes ingenious design of a time evolution operator, is based on a group of orthogonal normalized and complete auxiliary state basic vectors, and eliminates a microwave coupling term between the two ground-state energy levels by combining reverse engineering, so that experimental operation is simplified, initialization operation of quantum bits is realized, and Hamiltonian quantity of the system is obtained; the key point is to introduce an additional time-containing parameter into the time evolution operator, and the parameter provides an additional degree of freedom for regulating and controlling the interaction between light and substances; in the experimental system, the arbitrary waveform generator directly generates microwave pulses. The first order deflected beam of the acousto-optic modulator produces a pulse of light, and the typical rise time of the first order deflected beam is tens of nanoseconds when the focal diameter is 100 μm. The acousto-optic modulator is driven by two radio frequency signals generated by the arbitrary waveform generator; specifically, under the premise of the known initial state and target state of the system, the amplitude and phase of two optical pulses are designed, the amplitude and phase are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the optical pulses, an acousto-optic modulator in a continuous laser path is driven by the radio signal to obtain +1 level or-1 level deflection output light, and a group of bicolor optical pulses are generated;

Wherein: the driving frequency of the acousto-optic modulator is f _aom, the laser frequency in the continuous laser light path is f _laser, the quantum bit is characterized by two energy levels |0> and |1>, the frequency difference between them is f _0-1, the optical transition frequency of electrons from the energy level |1> to the energy level |e > is v _p, the optical transition frequency of electrons from the energy level |0> to the energy level |e > is v _s, the frequency of a radio signal driving the acousto-optic modulator to generate an optical pulse acting on the transition of |1> - |e > is f _p, the frequency of a radio signal driving the acousto-optic modulator to generate an optical pulse acting on the transition of |0> - |e > is f _s, and the phase of two radio signals satisfying f_p＝f_aom,f_s＝f_aom+f_0-1;f_laser+f_p＝ν_p;f_laser+f_s＝ν_s; is expressed as: And The amplitude is expressed as: e _p and E _s;

then the following is satisfied: both E _p and E _s change over time, as determined by the following relationship:

Wherein μ _p,s is the transition dipole moment of the optical transitions of |1> - |e > and |0> - |e >; omega _p,s is the ratio frequency of the two light pulses; c is the conversion coefficient from the rad frequency Ω _p,s of the light pulse to the radio signal amplitude E _p,s, determined by the experimental system; the ratio frequency Ω _p,s is shown by the following equation depending on the time t:

wherein alpha (t) and beta (t) are time dependent AndIs the differentiation of the functions α (t) and β (t) with respect to time;

furthermore, considering the limitations of the light pulses in the experiment and the manipulation goals for any quantum states, the following α (t) and β (t) are proposed:

Wherein a _k is a coefficient of each Fourier component, C is a constant, and the value of the coefficient is selected under the condition that alpha (t) is met; consider here the simplest case, i.e., the Hamiltonian drive system evolves from an initial state |0> to a target superimposed state along |φ ₁ (t) > Then there is a defined boundary condition for α (t) and β (t) according to |φ ₁ (t) >, where C is taken as 0, based on the constraints of the boundary condition for α (t).

In the invention, in order to solve the problem that a microwave field between two ground state energy levels is difficult to operate in certain experiments, a quantum state is evolved from an initial moment to a termination moment by introducing a time evolution operator; one method involved is to introduce a time-dependent parameter into the design of the time evolution operator, thus expanding the operable space when light interacts with the substance; before designing the time evolution operators, a group of orthonormal and complete auxiliary state base vectors needs to be constructed firstly:

the design of the time evolution operator is then as follows:

U(t)＝|φ₁(t)><φ₁(0)|+∑_m,n＝2,3γ_mn(t)|φ_m(t)><φ_n(0)| (4),

Wherein, |phi ₁ (t) > is the evolution state and gamma _mn (t) is an introduced time-dependent parameter; m, n are time independent constants; because of the normalized nature of the time evolution operator Then gamma _mn (t) needs to satisfy the following relationship:

∑_j＝1γ_mj(t)γ_nj(t)＝δ_mn,(m,n＝2,3) (5)，

Under the constraint of the above formula, γ _mn (t) is expressed by means of another time-dependent variable l (t), so that the time evolution operator is expressed in another form:

U(t)＝|φ₁(t)><φ₁(0)|+cosl(t)|φ₂(t)><φ₂(0)|+sinl(t)|φ₂(t)><φ₃(0)|-

sinl(t)|φ₃(t)><φ₂(0)|+cosl(t)|φ₃(t)><φ₃(0)| (6)，

Then, in conjunction with reverse engineering, hamiltonian is expressed as:

Substituting |phi _n (t) > into formula (7) to obtain a new Hamiltonian expression form under the basis vector, and eliminating microwave coupling items in two ground state energy levels by using the degree of freedom parameters cited in formula (3); and further, comparing the Hamiltonian quantity with the initial Hamiltonian quantity to obtain an expression form of the light pulse; the light pulse obtained in the above manner is used for an initializing operation in a quantum system; at the center of the nitrogen vacancy of the ensemble, the arbitrary waveform generator directly generates microwave pulses; the first-order deflected beam of the acousto-optic modulator generates an optical pulse, and the typical rise time of the first-order deflected beam is tens of nanoseconds when the focusing diameter is 100 μm; the acousto-optic modulator is driven by two radio frequency signals generated by the arbitrary waveform generator; wherein: the driving frequency of the acousto-optic modulator is f _aom, the laser frequency in the continuous laser light path is f _laser, the quantum bit is characterized by two energy levels |0> and |1>, the frequency difference between them is f _0-1, the optical transition frequency of electrons from the energy level |1> to the energy level |e > is v _p, the optical transition frequency of electrons from the energy level |0> to the energy level |e > is v _s, the frequency of a radio signal driving the acousto-optic modulator to generate an optical pulse acting on the transition of |1> - |e > is f _p, the frequency of a radio signal driving the acousto-optic modulator to generate an optical pulse acting on the transition of |0> - |e > is f _s, and the phase of two radio signals satisfying f_p＝f_aom,f_s＝f_aom+f_0-1;f_laser+f_p＝ν_p;f_laser+f_s＝ν_s; is expressed as: And The amplitude is expressed as: e _p and E _s;

Wherein μ _p,s is the transition dipole moment of the optical transitions of |1> - |e > and |0> - |e >; omega _p,s is the ratio frequency of the two light pulses; c is the conversion coefficient from the rad frequency Ω _p,s of the light pulse to the radio signal amplitude E _p,s; the ratio frequency Ω _p,s is shown by the following equation depending on the time t:

Wherein a _k is a coefficient of each Fourier component, C is a constant, and the value of the coefficient is selected under the condition that alpha (t) is met; consider here the simplest case, i.e., the Hamiltonian drive system evolves from an initial state |0> to a target superimposed state along |φ ₁ (t) > Then α (t) and β (t) have defined boundary conditions, i.e., C is taken to be 0, based on the constraints of the boundary conditions for α (t).

The amplitude of the bicolor light pulse generated by the technical scheme comprises a plurality of degrees of freedom (a _k, k=1, 2,3 … infinity), the feasibility of the scheme is illustrated by taking the maximum value 4 of k as an example, the value of a _k is regulated in the real number range, and the light pulses with different performances are designed;

Fig. 1 is: there is a schematic representation of the relevant energy level structure of the frequency-detuned nitrogen-vacancy centre. The nitrogen vacancy defect center of diamond is composed of substituted nitrogen atoms and vacancies of adjacent lattice sites; its ground state is also a spin triplet state, defined by the space between the ground state subenergy levels Is generated by applying an external magnetic field along the crystallographic axis of the nitrogen vacancy centre at the sublevel of |m _s = ±1 >; here the initialization and readout of the quantum states is achieved by optical transitions between energy levels.

In an embodiment in a linear superposition stateFor example, the shape, the working performance and the robustness of quantum manipulation of the light pulse are illustrated; at the end of the light pulse and quantum system interaction, the quantum state of the qubit at the pulse termination time is represented by |phi (t _f) >, and the probability of the quantum bit in the |0> state, |e > state and |1> state is represented by P _m, where the expression is:

P_m＝|<m|φ(t_f)>|²

Where m=0, e,1.

The parameter a ₁,a₂,a₃,a₄ contained in the amplitude of the light pulse is reasonably valued within the range of [0,1], and the frequency mismatch quantity is introduced by utilizing a coupling differential equation describing the action of light and a three-energy quantum system, so that the shape, the working performance and the robustness of the light pulse are simulated in software; how to measure the robustness of an optical pulse is generally measured in terms of the fidelity F of the target state of the resulting qubit. The definition is as follows:

F＝|<φ_target|φ(t_f)>|²

Where |φ (t _f) > is the state function of the quantum state |φ (t) > at the time t=t _f obtained by solving the three-level coupling differential equation, and |φ _target > is the target quantum state.

Embodiment two:

Based on the optical pulse generation method for performing high-fidelity manipulation on the ensemble qubits in the embodiment one, in the formula (11), all values of a _k are taken, taking k=4 as an example, and the values of a ₁,a₂,a₃,a₄ are respectively assigned, wherein in the formula (12), c=0; at this time:

a₁+2a₂+3a₃+4a₄＝0， (13),

Selecting diamond materials in an ensemble nitrogen vacancy center system to construct a spin environment of an ensemble nitrogen vacancy center; by scanning the value of a _k, the termination moment of the action of the optical pulse and the quantum system is detected, and the non-uniform broadening of spin transitions in the ensemble is caused by the random distribution of spin in diamond in the center of the nitrogen vacancy of the ensemble, so that the fidelity condition of a _k in the target state is influenced, and the optimal value of a _k in the formula (11) is obtained.

The value of the bicolor pulse at the initial and final moments is equal to 0, namely the extra degree of freedom in omega _p,s(t＝0,t_f)＝0;a_k is arbitrarily selected in the real number range [0,1], the optical pulse is constructed under the constraint of the conditions, the quantum system can be rapidly controlled with high fidelity, and the established target state |phi _target > is created; the shape and handling properties of the light pulses will be described here by way of example in the simplest case a _1,2＝0,a₃＝-0.8,a₄ =0.6.

FIG. 2 is a graph showing the evolution of the ratio frequency of the two-color pulses generated by this embodiment over time; the pulse duration is 4ns, and the values of the ratio frequency are 0 at the initial and final moments, so that interference of multiple redundant frequency components brought by sharp pulse edges in a frequency domain to quantum state control is avoided.

FIG. 3 shows the evolution of the number of energy levels of the system over time under the pulse without frequency mismatch; all the layout numbers of the quantum system start from the ground state |0> and finally are distributed equally over the energy levels |0> and |1>, which are consistent with the expected initial and target states.

The light pulse energy produced by this embodiment creates a quantum superposition state |phi _target > that is only suitable for quantum systems where no frequency mismatch exists.

The advantage of the light pulse in this embodiment is that the value of the ratio frequency at the initial and final instants is 0 when the light pulse acts on the quantum system. Because if the light pulse amplitude changes rapidly in the time domain, it must bring multiple redundant components in the frequency domain, potentially interfering with the target quantum state. The disadvantage is that the implementation is ideal, and does not introduce interference of frequency mismatch and other factors, and the application range is limited.

Embodiment III:

Based on the optical pulse generating method for performing high-fidelity control on the ensemble spin in the center of the nitrogen vacancy of the ensemble in the first embodiment, in the formula (11), values of a _k are taken as an example, k=4, and values of a ₁,a₂,a₃,a₄ are respectively assigned again. At this time:

a₁+2a₂+3a₃+4a₄＝0，

The value of a _k ensures that under the condition that the value of the bicolor pulse at the initial and final moments is equal to 0, namely omega _p,s(t＝0,t_f) =0, the extra degree of freedom in a _k is arbitrarily selected within the range of [0,1], and the quantum system can be controlled rapidly and with high fidelity by constructing the light pulse under the constraint of the conditions, and a set target state is created; here, the shape and the manipulation performance of the light pulse will be described by taking a ₁＝-0.4357,a₂＝0.8439,a₃＝0,a₄ = -0.313 as an example.

FIG. 4 is a graph showing the evolution of the ratio frequency of the two-color pulses generated by this embodiment over time. The pulse duration is 4ns, and the values of the ratio frequency are 0 at the initial and final moments, so that interference of a plurality of redundant frequency components brought by sharp edges in a frequency domain to quantum state control is avoided.

FIG. 5 is a graph of the evolution of the number of energy levels of a system over time, with light pulses acting on a quantum system without detuning. The layout numbers are all distributed at the energy level |0> at the initial time and are distributed at the energy levels |0> and |1> nearly equally at the final time.

FIG. 6 is a graph of the dependence of the fidelity of the system evolution between the final state and the given target state at the termination time of the light pulse on the frequency mismatch present in the ensemble. At a frequency of 300MHz, the fidelity has reached 99.39%, guaranteeing high fidelity to the non-uniform stretching that occurs in the spin ensemble in the ensemble nitrogen vacancy centre system.

Fig. 7 is a scan of the fidelity of the light pulse at the termination time, between the final state of the system evolution and the given target state, the frequency mismatch present in the ensemble, and the dependence on the effective range of a ₄. The effect of a ₄ on fidelity in the frequency mismatch range of + -300 MHz is emphasized by letting a ₃＝0,a₄ be in the effective range of [ -0.488,0.488 ]. From the graph, it was found that fidelity was not affected when Δ=0. With greater precision control, the robustness is significantly reduced, which means that the arbitrary waveform generator provides more precision control to some extent. The parameter a _k for this detuning range is further optimized in a system that takes into account frequency detuning.

The optical pulse generated in the embodiment has the advantages that the values of the ratio frequency at the initial and final moments are all 0, so that the requirement on the response speed of the acousto-optic modulator is reduced; and when quantum state control is performed in a system with nonuniform stretching of about 300MHz, high fidelity (99.39%) is ensured; and the degree of freedom parameters contained in the light pulse have a large space to optimize, so that the light pulse has a larger application space.

The optical pulse generation method for performing high-fidelity manipulation on the ensemble qubit can be further applied to quantum state manipulation based on an ensemble nitrogen vacancy central system.

Embodiment four:

Based on the optical pulse generation method for performing high-fidelity manipulation on the ensemble qubits in the first embodiment, the value a _k in the formula (11) is reasonably assigned to design that the optical pulse is applied to a qubit system relying on frequency band screening, such as a rare earth ion system. The degree of freedom parameter in the light pulse at this time satisfies (for example k=4):

a₁+2a₂+3a₃+4a₄＝0，

Under the condition that the value of a _k at the initial and final moments of the bicolor pulse is guaranteed to be equal to 0, namely omega _p,s(t＝0,t_f) =0, the extra degree of freedom in a _k is arbitrarily selected within the real number range [0,1], the optical pulse is constructed under the constraint of the above elements, the quantum system can be controlled rapidly and with high fidelity, and the established target state |phi _target > is created. Here, the following is the case A _3,4 =0 is an example to describe the shape and handling properties of the light pulse.

FIG. 8 is a schematic diagram of the energy level structure of Pr ion ³H₄-¹D₂ randomly doped in Y ₂SiO₅ crystal, which is a typical three-level system with non-uniform broadening, and is taken as an example to illustrate the technical scheme; in the figure, the ground state and the excited state both comprise 3 hyperfine energy levels, and the interval between the three energy levels is between 4.6 and 17.3 MHz. The qubit energy level is composed of a |0> state and a |1> state, and |e > is an excited state. The coupling between qubit energy levels is achieved by optical transitions |0> - |e > and |1> - |e >.

FIG. 9 is a graph showing the evolution of the Rate frequency of the bi-color pulses generated by this embodiment. The pulse duration is4 mu s, and the values of the ratio frequency are 0 at the initial and final moments, so that interference of multiple redundant frequency components brought by sharp pulse edges in a frequency domain to quantum state control is avoided.

FIG. 10 is a graph of the evolution of the number of energy levels of a system over time, with light pulses acting on a quantum system without detuning. The layout numbers are all distributed at the energy level |0> at the initial time and are distributed at the energy levels |0> and |1> nearly equally at the final time.

FIG. 11 is a graph of the dependence of the fidelity of the system evolution between the final state and the given target state at the termination time of the light pulse on the frequency mismatch present in the ensemble. Wherein frequency mismatch is the difference between the optical pulse center frequency and the actual optical transition frequency of the qubit ion. Within the range of + -140 kHz, the fidelity is always maintained above 99.1%, i.e. the frequency detuning of the range is better robust. Between hundreds of kHz and 3.5MHz, there are no ions, so fidelity in this interval is insignificant; when the frequency is detuned by more than +/-3.5 MHz, the fidelity is between 50% -50.27%, and the deviation from the ideal value is 50%, which shows that the bicolor pulse has certain non-resonance excitation for ions in the range.

FIG. 12 is a graph of the dependence of the number of layouts on levels |0>, |e >, and |1> on the amount of frequency mismatch when light pulses are applied to a three-level system, which better illustrates the non-resonant excitation of background ions by the light pulses. For rare earth ion systems, the number of layouts in the 1> state is about 1.13% below 3% outside the range of + -3.5 MHz from the center frequency, which means that off-resonance excitation is very effectively suppressed, which is within an acceptable range for rare earth ion ensemble qubits.

The advantage of the light pulses generated in this embodiment is that the light pulses have a better robustness to frequency mismatch present in the ensemble subsystem, low enough to non-resonant excitation of background ions, and suitable for use in qubit systems relying on frequency band screening. Therefore, the light pulse in the embodiment has the characteristics of high robustness and low resonance excitation, and ensures the realization of high-fidelity quantum control.

The optical pulse generation method for performing high-fidelity control on the ensemble qubit can be further applied to performing quantum state control in a rare earth ion system. In rare earth ion systems, there are two features: the optical transitions of the ensemble of qubit ions have a certain frequency width due to non-uniform broadening; the target ensemble qubit is in an impure environment in the frequency domain, and other qubits exist nearby, and their non-resonance excitation can cause interference to the target qubit. When the optimal value of a _k is solved, the robustness in the preset small frequency domain range is required to meet the requirement, and the interference excitation is not caused in the preset large frequency domain. The preset small frequency domain and the preset large frequency domain are two frequency range values set according to an actual experimental device.

On the basis of solving the decoherence problem caused by frequency detuning, the invention further solves the problem of microwave field between two ground state energy levels, simplifies experimental operation, and performs rapid and high-robustness quantum state initialization control. Meanwhile, the light pulse for solving the two problems has better application prospect. Can be used for an integrated nitrogen vacancy center system, even a rare earth ion system, a superconducting qubit system and the like. In addition, although the technical scheme is developed for a three-energy-level system, under specific conditions, the three-energy-level system is collapsed into a two-energy-level system by controlling the light pulse, so that the two-energy-level system is constructed to carry out layout number transfer and create the superimposed light pulse; furthermore, the method herein is mainly directed to the design of time evolution operators, and then any single-qubit logic gate is implemented by reasonable changes to its form (such as the time-containing degree of freedom parameters). Such minor variations or modifications in the art are still within the scope of the present invention.

The technical solutions, which are not described in detail, belong to the known technology of the person skilled in the art.

Claims

1. The optical pulse generation method for performing high-fidelity control on the ensemble qubits is characterized by comprising the following steps of: in an integrated nitrogen vacancy center system, adopting a time-containing Schrodinger equation which is reversely solved based on a non-transition quantum drive theory, when the time-containing Schrodinger equation of the three-energy system is solved, taking a microwave field between two ground state energy levels as a target on the premise of the initial state and the target state of the known system, and designing a representation form of a time evolution operator through the introduction of a degree-of-freedom parameter; then reversely designing the amplitude and the phase of two light pulses in an integrated nitrogen vacancy central system through a time evolution operator; inputting the amplitude and the phase into an arbitrary wave generator to generate a radio signal with the same amplitude and the same phase as the optical pulse, and driving an acousto-optic modulator in a continuous laser path by using the radio signal to obtain +1-level or-1-level deflection output light to generate a group of bicolor optical pulses; the generated bicolor light pulse is vertically incident into a three-energy-level quantum system medium, and the bicolor light pulse interacts with the quantum system medium to generate any superposition state of quantum bits;

Based on the initial state |0> and the target state of the system Wherein alpha, beta andIs three angles, alpha and beta are in the range of [0,2 pi ], and represents the distribution condition of the layout number on three energy levels of |0>, |e > and |1 >; i is the unit of an imaginary number,Taking values in the range of [0,2 pi ], and representing the relative phase between the quantum bit energy states |0> and |1 >;

First, assuming that the time variable is expressed as t, two temporal variables α (t) and β (t), a set of orthonormal and complete auxiliary state basis vectors are constructed:

the time evolution operators of the system are assumed to be:

U(t)＝|φ₁(t)><φ₁(0)|+∑_m,n＝2,3γ_mn(t)|φ_m(t)><φ_n(0)| (4),

Where m, n is a constant independent of time, i.e. the system will evolve along the initial state |φ ₁ (t) > of the qubit, due to the normalization of the time evolution operators, the parameter γ _mn (t) needs to satisfy:

∑_j≠1γ_mj(t)γ_nj(t)＝δ_mn(m,n＝2,3) (5)，

Where δ _mn is a Kronecker Delta function, γ _mn (t) is expressed by means of another time-dependent parameter l (t) under the constraint of equation (5), and equation (4) is then expressed in another form:

U(t)＝

|φ₁(t)><φ₁(0)|+cosl(t)|φ₂(t)><φ₂(0)|+sinl(t)|φ₂(t)><φ₃(0)|-sinl(t)|φ₃(t)><φ₂(0)|+cosl(t)|φ₃(t)><φ₃(0)| (6),

Then, in conjunction with reverse engineering, hamiltonian is expressed as:

substituting |phi _n (t) > into formula (7) to obtain a novel Hamiltonian expression form under the basis vector; and further, comparing the Hamiltonian quantity with the initial Hamiltonian quantity to obtain an expression form of the light pulse;

Using the obtained light pulse for initializing operation in the quantum system; at the center of the nitrogen vacancy of the ensemble, the arbitrary waveform generator directly generates microwave pulses; the first-order deflected beam of the acousto-optic modulator generates an optical pulse, and the typical rise time of the first-order deflected beam is tens of nanoseconds when the focusing diameter is 100 μm; the acousto-optic modulator is driven by two radio frequency signals generated by the arbitrary waveform generator; wherein: the driving frequency of the acousto-optic modulator is f _aom, the laser frequency in the continuous laser light path is f _laser, the quantum bit is characterized by two energy levels |0> and |1>, the frequency difference between them is f _0-1, the optical transition frequency of electrons from the energy level |1> to the energy level |e > is v _p, the optical transition frequency of electrons from the energy level |0> to the energy level |e > is v _s, the frequency of a radio signal driving the acousto-optic modulator to generate an optical pulse acting on the transition of |1> - |e > is f _p, the frequency of a radio signal driving the acousto-optic modulator to generate an optical pulse acting on the transition of |0> - |e > is f _s, and the phase of two radio signals satisfying f_p＝f_aom,f_s＝f_aom+f_0-1;f_laser+f_p＝ν_p;f_laser+f_s＝ν_s; is expressed as: And The amplitude is expressed as: e _p and E _s;

Where alpha (t) and beta (t) are time dependent, AndIs the differentiation of the functions α (t) and β (t) with respect to time.

2. The method of generating optical pulses for high fidelity manipulation of ensemble qubits according to claim 1, wherein:

Where a _k is a coefficient of each fourier component, C is a constant, and its value is selected under the boundary condition that α (t) is satisfied.

3. The method of generating optical pulses for high fidelity manipulation of ensemble qubits according to claim 2, wherein: hamiltonian drive system evolves from an initial state |0> to a target superimposed state along |phi ₁ (t) > According to formula (1), the boundary conditions of α (t) and β (t) are determined, where C is 0.

4. The method of generating optical pulses for high fidelity manipulation of ensemble qubits according to claim 1, wherein: when k=4 in formula (11), the value of a _k needs to satisfy the following condition

a₁+2a₂+3a₃+4a₄＝0 (13)，

5. The method of generating optical pulses for high fidelity manipulation of ensemble qubits according to claim 1, wherein: selecting diamond materials in an ensemble nitrogen vacancy center system to construct a spin environment of an ensemble nitrogen vacancy center; by scanning the value of a _k, the termination moment of the action of the optical pulse and the quantum system is detected, and the non-uniform broadening of spin transitions in the ensemble is caused by the random distribution of spin in diamond in the center of the nitrogen vacancy of the ensemble, so that the fidelity condition of a _k in the target state is influenced, and the optimal value of a _k in the formula (11) is obtained.

6. The method of generating optical pulses for high fidelity manipulation of ensemble qubits as set forth in claim 4, wherein: the optimal value of a _k is: a ₁＝-0.4357,a₂＝0.8439,a₃＝0,a₄ = -0.313.

7. A rare earth ion system, characterized in that: use of the optical pulse generation method of any one of claims 1 to 6 for high fidelity manipulation of ensemble qubits.

8. The rare earth ion system of claim 7, wherein: when the optimal value of a _k is solved, the robustness in the preset small frequency domain range is required to meet the requirement, and the interference excitation is not caused in the preset large frequency domain.