A highly robust pulse generation method for performing quantum logic gate manipulation

Abstract

This application proposes a high-robust pulse generation method for performing quantum logic gate manipulation. This method uses the reverse engineering method of creating quantum logic gates, solves the time-dependent Schrödinger equation to obtain the general model of optical pulses, and uses an arbitrary waveform generator to drive the acousto-optic modulator in the continuous laser optical path. The acousto-optic modulator modulates the incident continuous laser, and finally the acousto-optic modulator outputs a first-order (+1 order or -1 order) deflected light beam; the generated set of two-color light pulses is vertically incident on the ensemble rare-earth ion system, and the two are coupled to complete an arbitrary single-bit quantum logic gate operation. The additional degrees of freedom introduced in the field strength of the two-color light pulse are used to optimize the shape of the pulse, making it highly robust to the frequency detuning present in the system, so as to perform quantum logic gate manipulation with high fidelity in a short interaction time.

Description

Technical Field

[0001] The present invention belongs to the field of quantum computing, and in particular relates to a highly robust pulse generation method for performing quantum logic gate manipulation. Background Art

[0002] Quantum computers are an important branch of quantum information processing. They have incomparable computing speeds compared to classical computers in problems such as large prime number factorization, global search, machine learning, and biochemical molecular simulation. Using light pulses to perform a set of quantum logic gate manipulations is a key step in the quantum computing process. However, quantum bit physical systems are usually imperfect, and they inevitably have some interference factors, such as frequency detuning, light field intensity fluctuations, light field phase fluctuations, non-resonant excitation, etc. How to generate a set of light pulses that can perform quantum logic gate manipulations on imperfect quantum bit physical systems with short action time, high fidelity, and excellent robustness to interference factors in the system is an important problem that needs to be solved in the field of quantum computing.

[0003] Among the many physical systems that carry quantum computing, rare earth ions randomly doped in inorganic crystals are a relatively competitive carrier. This is because the coherence time of the quantum bit can be as long as 6 hours, and this type of crystal is cheap and commercialized. In this system, the quantum bit is characterized by a group of ensemble rare earth ions on the inhomogeneous broadening line, with Eu doped in the Y2SiO5 crystal. 3+ Take the case of a qubit as an example. The coupling between the two energy levels of the qubit is implemented through optical transitions, thus forming a three-level system. In such a three-level system, to achieve high-fidelity single-bit quantum logic gate control, the light pulse must meet the following conditions: (1) The light pulse exhibits good robustness to the frequency detuning between the qubit ions in the ensemble, that is, the fidelity is as close as possible to the ideal value of 1 within the range of ±300kHz; (2) The non-resonant excitation of other ions that are more than 8.9MHz away from the qubit ion in the frequency domain is small enough to avoid interfering with the neighboring qubit ions; (3) The pulse action time is as short as possible to reduce the influence of excited state decoherence.

[0004] Currently, the optical pulses for implementing quantum logic gate manipulation are mainly divided into three types. The first type is simple resonant pulses, such as square wave pulses, Gaussian pulses, etc. These pulses have a short action time but are sensitive to the interference factors existing in the system. The second type is adiabatic approximation optical pulses, which have good robustness to the interference factors existing in the system. However, because it is an adiabatic process, the pulse action time is relatively long. The third type is adiabatic shortcut optical pulses based on non-adiabatic processes, which have been proven in some physical systems to achieve quantum state population transfer with high fidelity and strong robustness within a short action time. However, population transfer is only a special case in quantum logic gate manipulation, and for quantum computing, arbitrary quantum logic gate manipulation is essential. Summary of the Invention

[0005] To address the above-mentioned deficiencies, the present application proposes a method for generating highly robust pulses for implementing quantum logic gate manipulation. This method aims to solve the problems of excessive pulse action time, poor robustness to frequency detuning, and interference from non-resonant excitation.

[0006] To achieve the above objectives, the present application adopts the following technical solutions:

[0007] A method for generating highly robust pulses for implementing quantum logic gate manipulation, which includes:

[0008] S1. Construct an initial model of a two-color optical pulse,

[0009]

[0010] where: Ω is the initial model of the two-color optical pulse, both α and β are time-dependent parameters;

[0011] S2. Based on an arbitrary waveform generator, output two columns of radio pulses corresponding to the two-color optical pulse, input the two columns of radio pulses into an acousto-optic modulator, and drive the acousto-optic modulator in the continuous laser optical path to modulate and generate a group of two-color optical pulses;

[0012]

[0013] where Ω s , Ω p are two-color optical pulses; θ, are time-independent constants;

[0014] S3. Vertically incident the generated two-color optical pulse onto an ensemble rare-earth ion crystal, and the two-color optical pulse interacts with the ensemble rare-earth ion crystal to generate single-bit quantum logic gate manipulation.

[0015] Preferably, the step of inputting two columns of radio pulses into the acousto-optic modulator in step S3 includes: driving the acousto-optic modulator in the continuous laser light path based on the two columns of radio pulses to obtain +1 or -1 order deflected output light, generating a group of two-color light pulses; vertically incident the generated two-color light pulses into the ensemble rare-earth ion crystal, and the two-color light pulses interact with the ensemble rare-earth ion crystal to generate single-bit quantum logic gate manipulation.

[0016] Preferably, step S1 further includes: using the reverse engineering method for creating a quantum logic gate to solve the time-dependent Schrödinger equation to obtain an optical pulse model, that is, using the reverse engineering method for creating a quantum logic gate to solve the time-dependent Schrödinger equation;

[0017] In a three-level quantum system composed of {|0>, |1>, |e>}, introduce bright and dark states |b>, |d>, and then redefine the state evolution space {|b>, |d>, |e>}; derive the Hamiltonian of the system:

[0018]

[0019] Δ is the frequency detuning determined by the ensemble rare-earth ion system;

[0020] Introduce an auxiliary state according to the characteristics of the dark state |d>:

[0021] Add a phase factor where ξ is the time-dependent phase:

[0022] ξ(t) = n(2α - sin(2α)) (n = 1, 2, 3...),

[0023] Construct a solution of the time-dependent Schrödinger equation

[0024] Preferably, the two-color light pulses in step S1 are determined by the parameter functions α(t) and β(t), and the manipulation time includes two segments,

[0025] The first segment of the pulse is denoted by subscript 1 and performs the manipulation from to

[0026] The second segment of the pulse is denoted by subscript 2 and performs the manipulation from to

[0027] The first segment of the pulse and the second segment of the pulse together complete a cyclic evolution;

[0028] In the construction of the time-dependent parameters α and β, introduce the degree-of-freedom parameters a1, a2, a3, a4, and the specific forms are as follows:

[0029] The first segment of the pulse:

[0030]

[0031]

[0032] The second - stage pulse:

[0033]

[0034]

[0035] γ is a constant, τ is the pulse duration; among them, the degrees - of - freedom parameters a1, a2, a3, a4 satisfy:

[0036] a1 + 2a2 + 3a3 + 4a4 = 0.

[0037] Preferably, in the method for generating a highly robust pulse for performing quantum logic gate manipulation,

[0038] a1 = - 0.0401, a2 = - 1.3837, a3 = 0.4089, a4 = 0.3952.

[0039] Preferably, the interaction between the two - color light pulse and the rare - earth ion crystal to generate single - qubit quantum logic gate manipulation further includes a method for generating a highly robust pulse for performing quantum logic gate manipulation to output a two - color light pulse; making this group of two - color light pulses perpendicularly incident on the ensemble rare - earth ion crystal for interaction to complete single - qubit quantum logic gate operation.

[0040] Preferably, the two - color light pulse includes two light pulses that act simultaneously but have different frequencies, amplitudes, and phases, and the amplitude and phase of the two - color light pulse change with time, but the frequency does not change with time.

[0041] Preferably, the parameter values of the frequency, amplitude, and phase of the light pulse are determined by the specific type of quantum logic gate.

[0042] Preferably, the parameters of the frequency, amplitude, and phase of the light pulse are controlled by an arbitrary waveform generating device and an acousto - optic modulator.

[0043] Preferably, in step S3, the action length of the light pulse does not exceed 4 μs. Such a design is to reduce the occurrence probability of decoherence.

[0044] Beneficial effects:

[0045] In the implementation process of the method proposed in this application, a dark state is introduced, and a set of orthonormal and complete auxiliary state basis vectors is constructed. Combining reverse engineering and parallel transport conditions, the design of any single-bit quantum logic gate pulse is completed; at the same time, during the pulse action process, it can show good robustness to the inhomogeneous broadening problem existing in the imperfect ensemble rare-earth ion system. Compared with the prior art, the present invention has the following remarkable features:

[0046] The generated two-color light pulse is vertically incident on the three-level ensemble rare-earth ion crystal, and the two-color light pulse interacts with the ensemble rare-earth ion crystal to generate any single-bit quantum logic gate manipulation.

[0047] The generated two-color light pulse is applicable to a three-level quantum system, including two light pulses that act simultaneously but have different frequencies, amplitudes, and phases. The above parameter values of the light pulse are determined by the specific type of quantum logic gate, and these parameters can be completely controlled by an arbitrary waveform generator and an acousto-optic modulator. Description of the Drawings

[0048] Figure 1 Simplified energy level diagram of a doped rare-earth ion crystal for the X(σ x ) logic gate.

[0049] Figure 2 Evolution diagram of the Rabi frequency Ω x of the two-color light pulse for the X(σ s，p ) logic gate with time.

[0050] Figure 3 Dependence diagram of the population number of the quantum state of the X(σ x ) logic gate on each energy level on the frequency detuning.

[0051] Figure 4 Dependence diagram of the manipulation fidelity of the X(σ x ) logic gate on the frequency detuning under the operation of the light pulse.

[0052] Figure 5 Dependence diagram of the manipulation fidelity of the X(σ x ) logic gate on the Rabi frequency fluctuation when the light pulse acts on a quantum system without detuning or with small detuning.

[0053] Figure 6 Evolution diagram of the population number of the quantum state on each energy level with time during the manipulation of the X(σ x ) logic gate under the action of the light pulse.

[0054] Figure 7 Dependence diagram of the population number of the quantum state of the Hadamard logic gate on each energy level on the frequency detuning.

[0055] Figure 8 It is a graph showing the dependence relationship between the manipulation fidelity of a logic gate and the frequency detuning under the optical pulse operation of a Hadamard logic gate.

[0056] Figure 9 It is a graph showing the dependence relationship between the manipulation fidelity of a logic gate and the Rabi frequency fluctuation when the optical pulse of a Hadamard logic gate acts on a quantum system with no detuning or small detuning.

[0057] Figure 10 It is a graph showing the evolution of the population number of a quantum state at each energy level with the manipulation time under the action of the optical pulse of a Hadamard logic gate.

[0058] Figure 11 It is a graph showing the evolution of the population number of a quantum state at each energy level with the manipulation time under the action of a pulse in the embodiment of the present application.

[0059] Figure 12 It is the relationship between the population number of a qubit state and the evolution time under the action of a pulse in the embodiment of the present application.

[0060] Figure 13 It is the dependence relationship between the population number of a quantum state and the frequency detuning under the action of a pulse in the embodiment of the present application.

[0061] Figure 14 It is the dependence relationship between the fidelity of a quantum logic gate and the frequency detuning under the action of a pulse in the embodiment of the present application. Detailed implementation manners

[0062] The above solution will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are for illustrating the present application and not for limiting the scope of the present application. The implementation conditions adopted in the embodiments can be further adjusted according to the conditions of specific manufacturers, and the implementation conditions not specified are usually the conditions in conventional experiments.

[0063] The present application proposes a high-robust pulse generation method for performing quantum logic gate manipulation. This method uses the reverse engineering method of creating a quantum logic gate, solves the time-dependent Schrödinger equation to obtain a general model of the optical pulse, and uses an arbitrary waveform generator to drive the acousto-optic modulator in a continuous laser light path, and uses the acousto-optic modulator to modulate the incident continuous laser. Finally, the acousto-optic modulator outputs a first-order (+1 order or -1 order) deflected light beam; the generated group of two-color light pulses is vertically incident on the ensemble rare-earth ion system, and the two are coupled to complete an arbitrary single-qubit quantum logic gate operation. The additional degrees of freedom introduced in the field strength of the two-color light pulse are used to optimize the shape of the pulse, making it highly robust to the frequency detuning existing in the system, so as to perform quantum logic gate manipulation with high fidelity in a short action time and improve the manipulation fidelity of the quantum state in the ensemble rare-earth ion system.

[0064] In one embodiment, the method includes:

[0065] In a three-level qubit system, starting from the initial qubit state |0> (in principle, the initial state can be any superposition state of |0> and |1>), a quantum logic gate optical pulse with reverse design is used to act on the ensemble rare-earth ion crystal, and the quantum state can evolve from the initial state |0> to the target quantum state Thus, a quantum logic gate manipulation is completed, where θ, and γ are three angles, all determined by the optical pulse parameters. θ, within the range of [0, 2π], characterizes the distribution of the population number on the |0> and |1> energy levels; γ takes values within the range of [0, π], characterizing the relative geometric phase between the qubit energy states |0> and |1>, represents any single-qubit quantum logic gate. The specific technical solution details are as follows:

[0066] (1). Using the reverse engineering method to create a quantum logic gate to solve the time-dependent Schrödinger equation;

[0067] In a three-level quantum system composed of {|0>, |1>, |e>}, bright and dark states |b>, |d> are introduced, and then the state evolution space {|b>, |d>, |e>} is redefined; and according to the semi-classical theory of the interaction between light and matter, the Hamiltonian of the system is derived:

[0068] where Ω s , Ω p are two-color optical pulses; Δ is the frequency detuning determined by the ensemble rare-earth ion system;

[0069] According to the characteristics of the dark state |d>, an auxiliary state is introduced:

[0070]

[0071] where α, β are two time-dependent parameters;

[0072] Add a phase factor where ξ is the time-dependent phase:

[0073] ξ(t) = n(2α - sin(2α)) (n = 1, 2, 3,...)

[0074] Construct a solution of the time-dependent Schrödinger equation

[0075] Solve the following Schrödinger equation:

[0076]

[0077] (2). Construct the original model of the optical pulse

[0078]

[0079] Wherein:

[0080] (3). Use an arbitrary waveform generator to output two radio pulses corresponding to the two-color optical pulse,

[0081]

[0082]

[0083] where θ is a parameter determined by specific quantum logic gate operations; is the phase of the two-color optical pulse, satisfying:

[0084] (4). Input the two radio pulses into an acousto-optic modulator, and use this radio signal to drive the acousto-optic modulator in the continuous laser optical path to obtain a +1 or -1 order deflected output light, generating a group of two-color optical pulses; Vertically incident the generated two-color optical pulses on the ensemble rare-earth ion crystal, and the two-color optical pulses interact with the ensemble rare-earth ion crystal to generate single-bit quantum logic gate manipulation.

[0085] Based on the original model (2), design time-dependent parameters α, β, and introduce degrees of freedom parameters a1, a2, a3, a4, and the specific form is as follows:

[0086] The first pulse:

[0087]

[0088]

[0089] The second pulse:

[0090]

[0091]

[0092] The first pulse performs the manipulation from The second pulse performs the manipulation from to complete a cyclic evolution together; τ is the pulse duration; where the degrees of freedom parameters a1, a2, a3, a4 satisfy the following conditions:

[0093] a1 + 2a2 + 3a3 + 4a4 = 0

[0094] Based on this condition, a set of values of the degrees of freedom parameters is derived:

[0095] a1 = -0.0401, a2 = -1.3837, a3 = 0.4089, a4 = 0.3952.

[0096] Substitute this set of parameters into the parameters α and β to derive a specific set of two-color optical pulses; through this set of optical pulses Ω s = Ω s (α i , β i ), (i = 1, 2), Ω p = Ω p (α i , β i ), (i = 1, 2). Input this amplitude and phase into an arbitrary waveform generator to generate a radio signal with the same amplitude and phase as the optical pulse. Use this radio signal to drive the acousto-optic modulator in the continuous laser optical path to obtain a +1 or -1 order deflected output light, generating a set of two-color optical pulses; Vertically incident the generated two-color optical pulses onto the ensemble rare-earth ion crystal, and the two-color optical pulses interact with the ensemble rare-earth ion crystal to generate single-bit quantum logic gate manipulation.

[0097] Among them, the design of the arbitrary quantum logic gate pulse involves the introduction of degrees of freedom parameters, and combined with the parallel transport condition, the dynamic phase is eliminated; and during the pulse action process, it has high robustness to the inhomogeneous broadening that appears in the ensemble system, realizing high-fidelity manipulation of qubits.

[0098] In the implementation process of this scheme, a dark state is introduced, and a set of orthonormal and complete auxiliary state basis vectors is constructed. Combining reverse engineering and parallel transport conditions, the design of an arbitrary single-bit quantum logic gate pulse is completed; at the same time, during the pulse action process, it can show good robustness to the inhomogeneous broadening problem existing in the imperfect ensemble rare-earth ion system. Compared with the prior art, the present invention has the following remarkable features:

[0099] Vertically incident the generated two-color optical pulses onto the three-level ensemble rare-earth ion crystal, and the two-color optical pulses interact with the ensemble rare-earth ion crystal to generate arbitrary single-bit quantum logic gate manipulation.

[0100] The generated two-color optical pulses are applicable to a three-level quantum system, including two optical pulses that act simultaneously but have different frequencies, amplitudes, and phases. The above parameter values of the optical pulses are determined by the specific type of quantum logic gate, and these parameters can be completely controlled by an arbitrary waveform generator and an acousto-optic modulator.

[0101] The two-color optical pulses can generate a universal arbitrary single-bit quantum logic gate in a three-level system, including the Hadamard logic gate, the X logic gate, the Pauli logic gate (σ x , σy , and σ z ), phase logic gates, etc. The starting and ending values of the Rabi frequency of the two-color optical pulse are both zero, avoiding interference with the quantum state and thus enabling high-fidelity quantum logic gate manipulation.

[0102] The amplitude and phase of the two-color optical pulse vary with time, but the frequency does not change with time.

[0103] In the ensemble rare-earth ion system, the action length of the optical pulse does not exceed 4 μs, reducing the occurrence probability of decoherence.

[0104] During the interaction between the two-color optical pulse and the qubit system, due to the non-adiabatic and geometric quantum scheme, the system evolves rapidly and has a certain robustness to local noise.

[0105] The two-color optical pulse is applicable to all qubit systems relying on frequency addressing. The introduction of the pulse degree of freedom makes this pulse have good robustness to the frequency detuning of the ensemble qubit system relying on frequency addressing.

[0106] Example 1

[0107] A high-robustness pulse generation method for performing quantum logic gate manipulation:

[0108] (1). Using the reverse engineering method of creating quantum logic gates to solve the time-dependent Schrödinger equation; in a three-level quantum system composed of {|0>, |1>, |e>}, introducing bright and dark states |b>, |d>, and then redefining the state evolution space {|b>, |d>, |e>}; and according to the semi-classical theory of the interaction between light and matter, deriving the Hamiltonian of the system:

[0109]

[0110] where Ω s , Ω p is the two-color optical pulse; Δ is the frequency detuning amount determined by the ensemble rare-earth ion system;

[0111] Introducing an auxiliary state according to the characteristics of the dark state |d>:

[0112]

[0113] where α and β are two time-dependent parameters;

[0114] Adding a phase factor where ξ is the time-dependent phase:

[0115] ξ(t) = n(2α - sin(2α)) (n = 1, 2, 3,...)

[0116] Construct the solution of the time-dependent Schrödinger equation

[0117] Solve the following Schrödinger equation:

[0118]

[0119] (2). Construct the original model of the optical pulse

[0120]

[0121] Where:

[0122] (3). Use an arbitrary waveform generator to output two radio pulses corresponding to the two-color optical pulse,

[0123]

[0124]

[0125] where θ is a parameter determined by specific quantum logic gate operations; is the phase of the two-color optical pulse, satisfying:

[0126]

[0127] (4). Input the two radio pulses into an acousto-optic modulator, and use this radio signal to drive the acousto-optic modulator in the continuous laser optical path to obtain a +1-level or -1-level deflected output light, generating a set of two-color optical pulses; Vertically incident the generated two-color optical pulses into the medium of the three-level rare-earth ion system, and perform quantum gate manipulation in the ensemble rare-earth ion system. The two-color optical pulses interact with the ensemble rare-earth ion crystal to generate single-bit quantum logic gate manipulation.

[0128] As Figure 1 shown, the figure takes the X(σ x ) logic gate as an example, and shows the simplified energy level diagram of the doped rare-earth ion crystal (such as Eu 3+ :Y2SiO5), which is a three-level system composed of two ground states |0>, |1> and an excited state |e>. After introducing the bright state |b> and the dark state |d>, it is equivalent to a new three-level system. Since the dark state does not participate in the evolution, it can be ignored during the pulse action.

[0129] An arbitrary waveform generator here outputs two radio signals, which are transmitted to an acousto-optic modulator. They have the same duration, different amplitudes, frequencies and phases, and the amplitudes all change with time; the light output by the laser is incident on the acousto-optic modulator driven by the arbitrary waveform generator; a rare-earth ion crystal is placed in the +1st or -1st order optical path of the acousto-optic modulator; the arbitrary waveform generator outputs a third square wave signal whose frequency changes linearly with time; a photodetector is placed on the optical path transmitted from the rare-earth ion crystal; the photodetector detects the optical signal transmitted from the rare-earth ion crystal and transmits it to an oscilloscope and a computer.

[0130] Based on the above method, a group of two-color optical pulses for performing arbitrary single-bit quantum logic gate manipulation can be created. According to the initial state |ψ in > = |0> and the target state where θ, and γ are three angles, θ, in the range of [0, 2π], characterizing the distribution of the population numbers at the |0> and |1> energy levels; γ takes values in the range of [0, π], characterizing the relative geometric phase between the quantum bit energy states |0> and |1>; thus, a group of two-color optical pulses is obtained, and their Rabi frequencies Ω p，s depend on time t as shown in the following formula:

[0131]

[0132]

[0133] where θ, are constants independent of time, taking values in the range of [0, 2π], and satisfying: Ω(t) is a function dependent on time, as follows:

[0134]

[0135] The two-color optical pulses are determined by the parametric functions α(t) and β(t). The manipulation time is divided into two segments. The first segment of the pulse is denoted by subscript 1 and performs the manipulation from The second segment of the pulse is denoted by subscript 2 and performs the manipulation from The first segment of the pulse and the second segment of the pulse together complete a cyclic evolution; design α i , β i , (i = 1, 2) the functions are in the following form:

[0136]

[0137]

[0138]

[0139]

[0140] The pulse contains 4 degrees of freedom, namely a1, a2, a3, and a4; they are the coefficients of the Fourier components in the above formula, and γ is a constant whose value is determined by the specific type of single-bit quantum logic gate; for example, for an X logic gate, that is, the initial state |ψ in >=|0〉 is driven to the target state |Ψ target 〉=|1〉, then the parameters in the time evolution operator U(θ, Φ, γ) are Φ=0,γ=π.

[0141] The parameters of the two-color light pulse generated by the above technical solution include multiple degrees of freedom (a k , k = 1, 2, 3, 4) adjust a within the real number range k The value of can be used to design light pulses with different performances, but they can all achieve the same quantum logic gate control;

[0142] Figure 1 It is a simplified schematic diagram of the energy level structure of a rare earth ion-doped crystal, consisting of two ground states |0〉, |1〉 and one excited state |e〉 (see Figure 1 a) is a three-level system. After the introduction of the bright state |b> and the dark state |d>, it is equivalent to a new three-level system consisting of |b>, |d>, and |e> (see Figure 1 In b), the dark state does not evolve under the action of the light field and can be ignored.

[0143] In this embodiment, X logic gates are used to illustrate the shape of the corresponding light pulse, the working performance and the robustness of quantum manipulation. When the light pulse and the quantum system are finished, the quantum state of the quantum bit is represented by |Ψ(τ)>, and its layout number in the |0> state, |e> state and |1> state is represented by P m To represent, the expression is:

[0144] P m =|<m|Ψ(τ)> | 2 , (8)

[0145] Where m = 0, e, 1

[0146] The coefficients a1, a2, a3, and a4 contained in the parameters of the optical pulse are taken in the range of [-3, 3]. The frequency detuning amount is introduced into the coupled differential equations describing the interaction between light and the three-level quantum system, and the shape of the optical pulse is examined in the software to simulate its working performance and robustness. In order to measure the robustness of the optical pulse, it is generally measured by the square of the modulus of the inner product between the quantum state of the quantum system and the target quantum state at the end of the logic gate operation, that is, the fidelity F. It is defined as follows:

[0147] F = |〈Ψ target |Ψ(τ)〉| 2 , (9)

[0148] where |Ψ(τ)> is the state function of the quantum state |Ψ(t)> at time t = τ obtained by solving the three-level coupled differential equation, and |ψ target > is the target quantum state.

[0149] A method for generating a quantum gate optical pulse for high-fidelity manipulation of qubits based on an embodiment, obtaining the conditions satisfied by the coefficients a1, a2, a3, a4:

[0150] a1 + 2a2 + 3a3 + 4a4 = 0, (10)

[0151] This condition ensures that the values of the two-color optical pulse at the initial and termination times are equal to zero, i.e., Ω p，s (t = 0, τ) = 0; a k (k = 1, 2, 3, 4) are arbitrarily selected within the real number range [-3, 3]. Under the above condition constraints, constructing an optical pulse for quantum logic gate manipulation can quickly and with high fidelity complete the quantum logic gate operation to reach the established target state U(θ, φ, γ)|0〉, and can also exhibit relatively high robustness to frequency detuning; here, taking a simple case of a1 = -0.0401, a2 = -1.3837, a3 = 0.4089, a4 = 0.3952 as an example, the shape and manipulation performance of the optical pulse are described.

[0152] Figure 2 , which is the evolution diagram of the Rabi frequency Ω of the corresponding two-color optical pulse when this embodiment performs the X logic gate manipulation; the pulse duration is 4 μs, and at the initial and termination times, the values of the Rabi frequency are both zero, avoiding the interference of multiple redundant frequency components brought by the sharp pulse edges in the frequency domain to the quantum state manipulation. s，p The advantage of this optical pulse is that when the optical pulse acts on the quantum system, the values of the Rabi frequency at the initial and termination times are both zero. Because if the amplitude of the optical pulse changes rapidly in the time domain, then it will inevitably bring multiple redundant components in the frequency domain, which may interfere with the target quantum state.

[0153] Then, the degree-of-freedom parameters a1, a2, a3, a4 in equation (10) are assigned values again., where a

[0154] The value of k ensures that the values of the two-color optical pulse at the initial and termination times are always equal to zero, i.e., Ω p，s (t = 0, τ) = 0. Under the condition that k ​​(where \(k = 1, 2, 3, 4\)), the additional degrees of freedom are arbitrarily selected within the real number range \([-3, 3]\). Under the above-mentioned conditional constraints, an optical pulse is constructed, and a single-bit and happy quantum logic gate can be created quickly and with high fidelity. Here, taking \(a_1=-0.0401\), \(a_2 = -1.3837\), \(a_3 = 0.4089\), \(a_4 = 0.3952\) as an example, the shape and manipulation performance of the optical pulse are described.

[0155] Figure 3 , which is the evolution diagram of the population number of the quantum state at each energy level with the manipulation time under the action of the optical pulse. Here is the case of the X logic gate. It can be seen that the evolution time of the quantum gate has been shortened to 4 μs.

[0156] Figure 4 , which is the dependence relationship between the fidelity of the logic gate and the frequency detuning under the action of the optical pulse. Here is the manipulation of the X logic gate. It can be seen that the quantum logic gate executed by such an optical pulse has a very high fidelity and has good robustness to the frequency detuning within the range of \([-300, 300]\) kHz. The action effects of other quantum logic gates are similar.

[0157] Figure 5 , which is the dependence relationship between the fidelity of the logic gate and the Rabi frequency fluctuation when the optical pulse acts on a quantum system without detuning or with small detuning. This is the case of the X logic gate. The quantum gate under this pulse operation also has good robustness to frequency detuning and light intensity fluctuation, and the fidelity of the logic gate is as high as 99.83%.

[0158] Figure 6 , which shows the dependence relationship between the population number of the quantum state and the frequency detuning under this pulse operation. Here, only the X logic gate is taken as an example for illustration. It can be seen that within the frequency detuning range of \([-300, 300]\) kHz, the change of the population number of the quantum state is gentle, which is very beneficial to the manipulation of the ensemble quantum system.

[0159] Example 2

[0160] Using this pulse generation method, a group of two-color optical pulses for performing quantum logic gate manipulation is obtained; the manipulation of the quantum gate is performed in the diamond ensemble nitrogen-vacancy color center system. The energy level schematic diagram of this system is as Figure 7As shown. The combination includes hardware devices such as a laser, an acousto-optic modulator, an arbitrary waveform generator, an oscilloscope, a photodetector, etc. Here, the arbitrary waveform generator outputs two radio signals, and the two radio signals are transmitted to the acousto-optic modulator. They have the same duration, different amplitudes, frequencies and phases, and the amplitudes all change with time; the light output by the laser is incident on the acousto-optic modulator driven by the arbitrary waveform generator; a rare-earth ion crystal is placed in the +1st or -1st order optical path of the acousto-optic modulator; the arbitrary waveform generator outputs a third square wave signal whose frequency changes linearly with time; the photodetector is placed on the optical path of the light transmitted from the diamond crystal; the photodetector detects the light signal transmitted from the diamond crystal and transmits it to the oscilloscope.

[0161] Based on the above device, a set of two-color light pulses for performing arbitrary single-bit quantum logic gate operations can be created. Let the initial state of the quantum system be |ψ in >(here, |ψ in > = |0> is taken as an example) and the target state where θ, and γ are three angles, θ, in the range of [0, 2π], characterizing the distribution of the population numbers on the |0〉 and |1〉 energy levels; γ takes values in the range of [0, π], characterizing the relative geometric phase between the quantum bit energy states |0> and |1>; thus, a set of two-color light pulses is obtained, whose Rabi frequencies Ω p，s depend on time t, and the functional form is consistent with equations (1) and (2) in Embodiment 1. This set of two-color light pulses is determined by the parameter functions α(t) and β(t), and adopts the forms of equations (4), (5), (6), and (7) in Embodiment 1. Each of the two pulse parameters contains 4 degrees of freedom, namely, adjusting the values of a k (k = 1, 2, 3, 4) in the real number range to find the light pulses that meet the requirements, but they can all achieve the same quantum gate operation;

[0162] Figure 7 is the energy level schematic diagram of the ensemble nitrogen-vacancy color center, which is a three-level system composed of two ground states |m s = 0>, |m s = 1> and an excited state |m s = -1> (see Figure 7 a). After introducing the bright state |b> and the dark state |d> (see Figure 7 b), a three-level system composed of {|b>, |d>, |e>} is formed.

[0163] In the embodiment, the operation of the Hadamard logic gate is taken as an example to illustrate the shape of the corresponding optical pulse, its working performance, and the robustness of quantum manipulation. At the end of the interaction between the optical pulse and the quantum system, the quantum state of the quantum system is represented by |Ψ(τ)>, and the populations in the |0>, |e>, and |1> states are characterized by P m as shown in Equation (8) in Embodiment 1.

[0164] The coefficients a1, a2, a3, and a4 included in the parameters of the optical pulse are taken within the range of [-3, 3]. By introducing the frequency detuning in the coupled differential equations describing the interaction between light and the three-level quantum system, and by examining the shape of the optical pulse in software, its working performance and robustness are simulated. To measure the robustness of the optical pulse, generally, the square of the modulus of the inner product of the quantum state of the quantum system at the end of the logic gate operation and the target quantum state is used as the measure, that is, the fidelity F. Its definition is shown in Equation (9) in Embodiment 1; where |Ψ(τ)> is the state function of the quantum state |Ψ(t)> obtained by solving the three-level coupled differential equation at the moment t = τ, and |ψ target > is the target quantum state.

[0165] A method for generating an optical pulse of a quantum logic gate for high-fidelity manipulation of qubits based on Embodiment 1. According to the condition of the degree-of-freedom constraint in Equation (10), this condition ensures that the values of the two-color optical pulse at the initial and termination moments are always equal to zero, that is, Ω p，s (t = 0, τ) = 0; a k (k = 1, 2, 3, 4) The additional degrees of freedom are arbitrarily selected within the real number range [-3, 3]. Under the above condition constraints, an optical pulse for quantum logic gate manipulation is constructed, and the quantum logic gate operation can be completed quickly and with high fidelity to reach the established target state U(θ, φ, γ)|ψ in >, and it can also show high robustness to frequency detuning. Here, taking a simple case of a1 = -0.0401, a2 = -1.3837, a3 = 0.4089, and a4 = 0.3952 as an example, the shape and manipulation performance of the optical pulse are illustrated.

[0166] Figure 8 Shows the dependence relationship between the population of the quantum state and the frequency detuning under this pulse operation. Here, only the Hadamard logic gate is taken as an example for illustration. It can be seen that within the frequency detuning range [-300, 300] kHz, the change in the population of the quantum state is gentle, which is very beneficial for the manipulation of the ensemble quantum system.

[0167] Figure 9It shows the dependence of the fidelity of the logic gate on the frequency detuning under this pulsed operation. Taking the performance of the Hadamard logic gate as an example only, it can be seen that the fidelity of the quantum logic gate implemented by such optical pulses is higher than 99.72%, and it has good robustness to frequency detuning in the range of [-300, 300] kHz.

[0168] Figure 10 It shows the dependence of the manipulation fidelity of the logic gate on the Rabi frequency fluctuation when this pulse acts on a quantum system without detuning or with small detuning (|Δ|≤10 kHz). Taking the Hadamard logic gate as an example only for illustration, it can be seen that the quantum gate under this pulsed operation also has good robustness to frequency detuning and light intensity fluctuation, and the fidelity of the logic gate is as high as 99%.

[0169] Figure 11 It shows the evolution diagram of the population number of the quantum state at each energy level with the manipulation time under this pulse. Taking the implementation of the Hadamard logic gate in the ensemble nitrogen vacancy color center system as an example, it can be seen that the manipulation time of the quantum logic gate has been shortened to 500 ns.

[0170] Example 3

[0171] Using the pulse design method in Example 1, a set of two-color optical pulses for implementing the σy gate manipulation is found to complete the σ y manipulation in a three-level system. The degree-of-freedom parameters a1, a2, a3, a4 satisfy the constraint conditions of Equation (10) in Example 1. Similarly, a set of values a1 = -0.0401, a2 = -1.3837, a3 = 0.4089, a4 = 0.3952 is selected to illustrate the performance of this pulse.

[0172] Figure 12 It is the relationship between the population number of the qubit state and the evolution time under the action of this pulse.

[0173] Figure 13 It is the dependence of the population number of the quantum state on the frequency detuning under the action of this pulse.

[0174] Figure 14 It is the dependence of the fidelity of the quantum logic gate on the frequency detuning under the action of this pulse. It can be seen that within the frequency detuning range of [-300, 300] KHz, the fidelity of the quantum gate is as high as 99.72%, which has stronger robustness compared with the previous optical pulse manipulation.

[0175] The method for generating two-color optical pulses proposed in the above technical solution can be used for quantum gate manipulation or qubit initialization in an ensemble nitrogen-vacancy center and a rare-earth ion system. That is to say, it has great application value in future quantum computers or quantum memories. The components of these two devices include: a laser with continuous laser output, the optical pulse generation system described above, including an arbitrary waveform generator and an acousto-optic modulator; this ensemble rare-earth ion system can provide an extremely long coherence time; it is worth pointing out that although this technical solution is developed for a three-level system, under specific conditions, this three-level system can be extended to a four-level system by simply disassembling the four-level system into two three-level systems, so as to design optical pulses for quantum state initialization and quantum gate operations. This solution can also be applied to all three-level quantum systems relying on frequency addressing, such as an ensemble nitrogen-vacancy center system, a superconducting qubit system, and a molecular qubit system, etc.

[0176] The above is only the preferred embodiment of this application. Of course, this application can also have many other embodiments. Without departing from the spirit and essence of this application, those skilled in the art can make various corresponding changes and deformations according to this application, such as changing the size, shape or material, etc. However, these corresponding changes and deformations should all fall within the protection scope of this application.

Claims

1. A highly robust pulse generation method for performing quantum logic gate manipulation, characterized in that Including: S1. Construct an initial model of a two-color optical pulse. where: Ω is the initial model of the two-color optical pulse, both α and β are time-dependent parameters; S2. Based on an arbitrary waveform generator, output two radio frequency pulses corresponding to the two-color optical pulse, input the two radio frequency pulses into an acousto-optic modulator, and drive the acousto-optic modulator in the continuous laser optical path to modulate to generate a set of two-color optical pulses. where Ω s , Ω p is a two-color optical pulse; θ, is a time-independent constant; S3. Vertically incident the generated two-color optical pulse into an ensemble rare-earth ion crystal, and the two-color optical pulse interacts with the ensemble rare-earth ion crystal to generate single-bit quantum logic gate manipulation. The step of inputting the two radio frequency pulses into the acousto-optic modulator in step S3 includes: driving the acousto-optic modulator in the continuous laser optical path based on the two radio frequency pulses to obtain a +1 or -1 order deflected output light, generating a set of two-color optical pulses; vertically incident the generated two-color optical pulse into the ensemble rare-earth ion crystal, and the two-color optical pulse interacts with the ensemble rare-earth ion crystal to generate single-bit quantum logic gate manipulation. Step S1 also includes: using the reverse engineering method of creating a quantum logic gate to solve the time-dependent Schrödinger equation to obtain an optical pulse model, that is, using the reverse engineering method of creating a quantum logic gate to solve the time-dependent Schrödinger equation. In a three-level quantum system composed of {|0>, |1>, |e>}, introduce bright and dark states |b>, |d>, and then redefine the state evolution space {|b>, |d>, |e>}; derive the Hamiltonian of the system: Δ is the frequency detuning determined by the ensemble rare-earth ion system. Introduce an auxiliary state according to the characteristics of the dark state |d>: Adding a phase factor where ξ is the time-dependent phase: ξ(t) = n(2α - sin(2α)) (n = 1, 2, 3...). Construct a solution to the time-dependent Schrödinger equation 2. The high-robustness pulse generation method for performing quantum logic gate manipulation according to claim 1, characterized in that In step S1, the two-color optical pulse is determined by parameter functions α(t) and β(t), and the manipulation time includes two segments. The first pulse is denoted by the subscript 1 and performs the operation starting from ​ The second pulse is represented by the subscript 2 and performs the operation starting from ​ The first segment pulse and the second segment pulse together complete a cyclic evolution. In the construction of time-dependent parameters α and β, introduce degrees of freedom parameters a1, a2, a3, a4, and the specific forms are as follows: The first segment pulse: The second segment pulse: γ is a constant, and τ is the pulse duration; where the degrees of freedom parameters a1, a2, a3, a4 satisfy: a1 + 2a2 + 3a3 + 4a4 = 0.

3. The high-robust pulse generation method for performing quantum logic gate manipulation according to claim 2, wherein a1 = -0.0401, a2 = -1.3837, a3 = 0.4089, a4 = 0.3952.

4. The high-robustness pulse generation method for performing quantum logic gate manipulation according to claim 1, characterized in that The interaction between the two-color optical pulse and the rare-earth ion crystal to generate single-bit quantum logic gate manipulation further includes that the high-robustness pulse generation method for performing quantum logic gate manipulation outputs a two-color optical pulse; vertically incident this set of two-color optical pulses into the ensemble rare-earth ion crystal to interact and complete the single-bit quantum logic gate operation.

5. The high-robustness pulse generation method for performing quantum logic gate manipulation according to claim 4, characterized in that The two-color optical pulse includes two optical pulses that act simultaneously but have different frequencies, amplitudes, and phases, and the amplitude and phase of the two-color optical pulse change with time, but the frequency does not change with time.

6. The high-robust pulse generation method for performing quantum logic gate manipulation as described in claim 5, wherein: The parameter values of the frequency, amplitude, and phase of the optical pulse are determined by the specific type of quantum logic gate.

7. The high-robust pulse generation method for performing quantum logic gate manipulation as described in claim 5, wherein: The parameters of the frequency, amplitude, and phase of the optical pulse are controlled by an arbitrary waveform generator and an acousto-optic modulator.

8. The high-robust pulse generation method for performing quantum logic gate manipulation as described in claim 1, wherein: In step S3, the action length of the optical pulse does not exceed 4 μs.

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