A method to construct quantum logic gates of arbitrary geometry for imperfect systems

Abstract

This invention belongs to the field of quantum computing and discloses a method for constructing arbitrary geometric quantum logic gates for imperfect systems. In a three-level system, two optical pulses with degrees of freedom are designed in the forward direction. The amplitude and phase of these two optical pulses are optimized according to the requirements of the three-level system. The corresponding amplitude and phase are then input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding optical pulse. This radio signal is used to drive an acousto-optic modulator in a continuous laser path to obtain a set of two-color optical pulses. The generated two-color optical pulses are located in the range [0, 1 ... t f Manipulating the quantum state of light field detection, in [ t f ,2 t f Manipulating quantum states that cannot be detected by light fields allows the construction of arbitrary geometric logic gates, which can be applied to imperfect systems addressed by frequency.

Description

Technical Field

[0001] The present invention belongs to the field of quantum computing, and in particular relates to a method for constructing arbitrary geometric quantum logic gates of an imperfect system. Background Art

[0002] Quantum computing has become a hot research topic at home and abroad in recent years. Establishing high-fidelity quantum logic gates is a crucial step in quantum computing. The fidelity of quantum logic gates is mainly affected by environmental noise and the evolution time of quantum systems. Among them, geometric quantum logic gates have good application prospects in many highly robust quantum manipulations due to their good anti-interference ability to environmental noise. The so-called geometric logic gate means that the phase angle formed during the entire evolution process is a geometric phase, and the dynamic phase is zero at the moment the pulse terminates. In addition, the long evolution time of the quantum system will lead to decoherence and reduce the fidelity of the logic gate. The solution to this problem is usually to use non-adiabatic pulses instead of traditional adiabatic pulses to shorten the evolution time of the quantum system.

[0003] The realization of high-fidelity quantum logic gates relies on the precise manipulation of quantum states. In particular, in some systems with physical defects, the changes in the qubit addressing frequency and the frequency detuning caused by uneven broadening make high-fidelity gate operations still challenging. For example, in superconducting transmission line quantum states, quantum state parameters (e.g., qubit frequency) may drift or fluctuate over time. In addition, in order to perform error correction, hundreds of physical bits need to be built in the same circuit, and these physical bits are limited by the manufacturing process and will not be exactly the same. For precise control, the addressing frequency of each physical qubit must be measured with high precision, and the control signal must be customized to match each qubit. Another example is the ensemble rare earth ion qubit system. Because the ensemble qubit is in an impure environment in the frequency domain, there are other qubits nearby, and their non-resonant excitation will interfere with the target qubit. However, the rare earth ion qubit system has a qubit coherence time of up to 6 hours, which is currently a very competitive system. With Y doped 2 SiO 5 Pr in crystal 3+ For example, precise manipulation of the quantum bits in this system requires high robustness to frequency detuning in the ±170kHz range and no interference excitation beyond ±3.5MHz.

[0004] The precise control of quantum bits in the above imperfect systems mainly depends on the design of optical pulses. In a resonant system, as long as the above conditions are met, the pulse envelope can have any shape. However, most of the above imperfect systems are non-resonant systems because of the detuning of the optical field driving frequency and the quantum transition frequency due to uneven broadening or Rabi frequency fluctuations. For such systems, in order to maintain the geometric properties of evolution, the Hamiltonian corresponding to any two moments is required to remove the timing operator. Only square wave pulses can meet this condition. However, square wave pulses have the following disadvantages: (1) Square wave pulses cannot be optimized to meet the requirements of the experimental system; (2) The Fourier transform in the pulse frequency domain has multiple frequency components, which may excite unwanted transitions; (3) Gate operations using square pulses are very sensitive to fluctuations in intensity and phase. For this reason, designing optical pulses that can precisely control quantum bits in imperfect systems is a technical challenge. At present, the optical pulse design for such systems can refer to the "Optical pulse design method for creating arbitrary superposition states of three-level system quantum bits" (application number: 201810234933.5). Yan Ying et al. designed and optimized optical pulses containing multiple degree-of-freedom parameters to achieve the initialization of quantum bits in the ensemble rare earth ion quantum bit system. However, this work does not involve the establishment of quantum logic gates. The present invention will aim to achieve high-fidelity quantum logic gate manipulation in imperfect systems.

[0005] Quantum logic gates are divided into two types: arbitrary and non-arbitrary. The types of gate operations performed by arbitrary quantum logic gates are more than those of non-arbitrary quantum logic gates. This is also the research direction of domestic and foreign scholars. Both forward design and reverse design can realize the construction of arbitrary quantum logic gates. In particular, many schemes for reverse design based on the target state of system evolution have been proposed in recent years. However, in these reverse design schemes, the amplitude and phase of the light pulse are often required to change with time, which greatly increases the difficulty and accuracy of the experiment. Therefore, the present invention will adopt the forward design method in combination with the above-mentioned light pulse design scheme to construct arbitrary geometric quantum logic gates in imperfect systems. Summary of the invention

[0006] The present invention aims to create arbitrary geometric quantum logic gates in an imperfect experimental system through optimizable two-color light pulses. Any quantum logic gate is a gate that can be used for any initial state |ψ 0 >, the light pulse can be made to rotate around an arbitrary n-axis (determined by the angles θ and Defined by), rotate an arbitrary angle (β) to the final target state |ψ target >. The constructed logic gate is a unitary operator composed of these three parameters in the {|0>,|1>} computation subspace. To express, and |ψ target >=U(t f ,0)|ψ 0 >, where For parameters Function expression of t f is the pulse action time.

[0007] The ensemble rare earth ion quantum bit system Pr 3+ : Y 2 SiO 5 For example, under certain conditions, the scheme has the following characteristics:

[0008] A. The pulse frequency is small, the maximum does not exceed 1.5MHz;

[0009] B. The fidelity of the generated logic gates is not less than 98%;

[0010] C. Be robust to frequency detuning in quantum systems within a range of at least ±170kHz;

[0011] D. It basically does not cause excitation to other ions outside the central frequency of the quantum bit ion 3.5MHz.

[0012] The technical problems solved by the present invention are:

[0013] The traditional adiabatic pulse action time is long, which will make the evolution time of the quantum state longer and cause decoherence; the pulse action process has poor robustness to the frequency detuning amount and has a high non-resonant excitation on other ions near the quantum bit.

[0014] In order to solve the above problems, the present invention seeks a method for constructing an arbitrary geometric quantum logic gate of an imperfect system. The two-color light pulse is vertically incident on a three-level quantum system medium, and the two-color light pulse interacts with the quantum system medium to produce an arbitrary geometric quantum logic gate. The specific technical solution is as follows:

[0015] A method for constructing an arbitrary geometric quantum logic gate for an imperfect system, forward designing two optical pulses with degrees of freedom in a three-level system, optimizing the amplitude and phase of the two optical pulses with degrees of freedom according to the requirements of the three-level system, inputting the corresponding amplitude and phase into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding optical pulse, using the radio signal to drive an acousto-optic modulator in a continuous laser optical path to obtain a group of two-color optical pulses, wherein the generated two-color optical pulses are in the range of [0, t f ] to manipulate the quantum state of the light field detection, in [t f , 2t f ] to manipulate quantum states that cannot be detected by light fields, thereby constructing arbitrary geometric logic gates, where t f is the pulse duration of the two-color light pulse.

[0016] The two-color light pulse is firstly f] manipulates the quantum state detected by the light field, and the manipulated quantum state is the bright state; at [t f , 2t f ]By adjusting the pulse amplitude and phase, the quantum state that cannot be directly detected by the light field is converted into a detectable quantum state and then manipulated. The manipulated quantum state is the dark state. Similar quantum manipulation of the dark state can make it accumulate the same phase as the bright state within the time of gate operation. Only in this way can the robustness of the logic gate control fidelity to frequency detuning be achieved after the introduction of frequency detuning.

[0017] Preferably, the f 1μs~4μs, which is smaller than the t f Will cause higher non-resonant excitation, and the t f This will increase the pulse's action time and cause decoherence.

[0018] The suppression of non-resonant excitation is achieved on the one hand by appropriately increasing the pulse action time, and on the other hand by optimizing the light pulse containing degrees of freedom.

[0019] The constructed logic gates include: NOT gate, Hadamard gate, and phase gate.

[0020] Compared with the prior art, the present invention has the following significant features:

[0021] (1) The generated two-color optical pulse is suitable for a three-level quantum system, which contains two optical pulses acting simultaneously but with different frequencies, amplitudes and phases. The above parameters of the optical pulses can be fully controlled by the arbitrary wave generator and the acousto-optic modulator.

[0022] (2) Two-color light pulses can create arbitrary geometric quantum logic gates in a three-level system, including arbitrary layout number distribution and arbitrary relative phase control between the two quantum bit energy levels.

[0023] (3) The amplitude of the two-color light pulse changes with time, but the frequency and phase do not change with time.

[0024] (4) The amplitude of the light pulse has multiple degrees of freedom that can be adjusted, and the values ​​of these degrees of freedom parameters can be changed to meet the needs of different experimental systems.

[0025] (5) The created logic gate is a pure geometric logic gate and has good anti-interference performance against environmental noise.

[0026] (6) The created logic gate is an arbitrary logic gate. In theory, different logic gates can be realized by setting the amplitude and phase parameters of the optical pulse. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1It is doped with Y 2 SiO 5 Pr in crystal 3+ Schematic diagram of the relevant energy level structure;

[0028] Figure 2 This is a schematic diagram of the control of the bright state |b1> by a two-color light pulse;

[0029] Figure 3 is the Rabi frequency of the NOT gate two-color light pulse Ω p,s Plot of evolution over time;

[0030] Figure 4 It is the evolution diagram of the layout number of each energy level of the system over time during the interaction between the NOT gate two-color light pulse and the quantum state system;

[0031] Figure 5 is the Rabi frequency of the Hadamard gate two-color light pulse Ω p,s Plot of evolution over time;

[0032] Figure 6 It is the evolution diagram of the layout number of each energy level of the system over time during the interaction between the Hadamard gate two-color light pulse and the quantum state system;

[0033] Figure 7 is the Rabi frequency of the NOT gate two-color light pulse Ω p,s Plot of evolution over time;

[0034] Figure 8 It is the evolution diagram of the layout number of each energy level of the system over time during the interaction between the NOT gate two-color light pulse and the quantum state system;

[0035] Fig. 9 This is a graph showing the change in fidelity with frequency detuning after a NOT gate two-color light pulse interacts with a quantum system with frequency detuning;

[0036] Fig.10 This is a graph showing the change in the number of layouts of each energy level of the system with frequency detuning after the NOT gate two-color light pulse interacts with the quantum system with frequency detuning;

[0037] Fig.11 is the Rabi frequency of the Hadamard gate two-color light pulse Ω p,s Plot of evolution over time;

[0038] Fig.12 It is the evolution diagram of the layout number of each energy level of the system over time during the interaction between the Hadamard gate two-color light pulse and the quantum state system;

[0039] Fig.13This is a graph showing the change in fidelity with frequency detuning after a Hadamard gate two-color light pulse interacts with a quantum system with frequency detuning.

[0040] Fig.14 This is a graph showing the change in the number of layouts of each energy level of the system with frequency detuning after the Hadamard gate two-color light pulse interacts with a quantum system with frequency detuning;

[0041] Among them, Ω p is the Rabi frequency of the optical transition from energy level |1> to energy level |e>; Ω s is the Rabi frequency of the optical transition from energy level |0> to energy level |e>; is the phase of the optical transition from |0> to energy level |e>; is the phase of the optical transition from |1> to energy level |e>; t f is the pulse action time; P m is the probability of the ion being in the |m> state at time t; m = 0, 1, e; F is the fidelity of producing the target state; Δ is the off-resonance frequency detuning. DETAILED DESCRIPTION

[0042] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0043] Embodiment 1:

[0044] A method for constructing an arbitrary geometric quantum logic gate for an imperfect system, forward designing two optical pulses with degrees of freedom in a three-level system, optimizing the amplitude and phase of the two optical pulses with degrees of freedom according to the requirements of the three-level system, inputting the corresponding amplitude and phase into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding optical pulse, using the radio signal to drive an acousto-optic modulator in a continuous laser optical path to obtain a group of two-color optical pulses, wherein the generated two-color optical pulses are in the range of [0, t f ] to manipulate the quantum state of the light field detection, in [t f , 2t f ] to manipulate quantum states that cannot be detected by light fields, thereby constructing arbitrary geometric logic gates, where t f is the pulse duration of the two-color light pulse; 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 state is characterized by two energy levels |0> and |1>, the frequency difference between them is f 0-1 , the frequency of the optical transition of electrons from energy level |1> to energy level |e> is ν p , the frequency of the optical transition of electrons from energy level |0> to energy level |e> is ν s The frequency of the radio signal driving the AOM to generate a light pulse acting on the |1>-|e> transition is fp The frequency of the radio signal driving the AOM to generate a light pulse acting on the |0>-|e> transition is f s , both satisfy f p =f aom , f s =f aom +f 0-1 ;f laser+ f p =v p ;f laser+ f s =v s ; The phase of the two radio signals is expressed as: and The amplitude is expressed as: E p and E s ;

[0045] E p and E s Both vary with time and are determined by the following relationship:

[0046]

[0047] Where μ p,s is the transition dipole moment of the |1>-|e> and |0>-|e> optical transitions; Ω p,s is the Rabi frequency of the two light pulses; C is the Rabi frequency of the light pulse Ω p,s To the radio signal amplitude E p,s The conversion coefficient is determined by the experimental system; Rabi frequency Ω p,s Depends on angle θ, time t and phase β, As shown below:

[0048]

[0049] In the formula, satisfy

[0050]

[0051] Ω(t) is designed as follows:

[0052]

[0053] Where t f is the duration of the pulse, here 4μs; Yes 1 (t), γ 2 (t) Differentiation with respect to time; γ 1 (t), γ 2(t) is a time-dependent parameter, which is composed of a series of Fourier components:

[0054]

[0055] Where a n and a n ' is the coefficient of each Fourier component;

[0056] Using this two-color light pulse to manipulate the quantum bit, we can construct the following arbitrary geometric quantum logic gate in the {|0>, |1>} computational subspace:

[0057] where θ is in the range [0, π], β is in the range [0, 2π].

[0058] a n and a n 'The value is selected under the condition that the boundary conditions are met; in practical applications, the frequency of the sine wave may be limited by the time accuracy of the instruments used, so the maximum value of n considered here is 8.

[0059] Attached Figure 1 It is doped with Y 2 SiO 5 Pr in crystal 3+ The schematic diagram of the related energy level structure is used as an example to illustrate the three-level system applicable to the present technical solution; in the figure, the ground state and the excited state respectively contain three hyperfine energy levels, |e> is an excited state, |0> and |1> are two energy levels representing the quantum state, and the coupling between the two is implemented through two optical transitions |1>-|e> and |1>-|e>. Under the basis vector {|1>,|e>,|0>}, the Hamiltonian of the system can be expressed as:

[0060]

[0061] In [0,t f ]The corresponding time evolution operator in time is

[0062]

[0063] Among them, HC is the Hermitian conjugate term, that is, Through three-level coupled differential equations The bright state |b1> and dark state |d1> are solved as follows:

[0064]

[0065] (1) According to different experimental system requirements, the dual-color light pulse Ω is designed by adjusting the values ​​of the parameters in (5) and (6). p,sThe amplitude and phase of the two-color light pulse are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the light pulse. The radio signal is used to drive the acousto-optic modulator in the continuous laser optical path to obtain +1 or -1 deflected output light, generating a group of two-color light pulses.

[0066] (2) In [0, t f ] time, the bright state |b1> is manipulated in time periods by using this set of two-color light pulses. In the first half of the time, the light pulse pumps the quantum state from |b1> to the excited state |e>; in the second half of the time, the light pulse phase increases by β+π, and this light pulse pumps the quantum state from the excited state |e> back to the original |b1<, but along a different path. After such a cycle, the bright state |b1> obtains an arbitrary geometric phase angle β, that is, |b1(t f )>=e iβ |b1(0)>.

[0067] (3) In [t f , 2t f ] time, first adjust the parameters of the light pulse to: θ′=π-θ, This operation transforms the dark state |d1> in (2) into a new bright state |b2<, and the bright state |b1< into a new dark state |d2<; then a light pulse with a pulse area of ​​2π is used to perform a unit transformation on |b2>, namely |b2(t f )<=|b2(0)>, and the operation of the optical pulse pair |b2> is performed along the same path in the first half and the second half.

[0068] Attached Figure 2 is the evolution path of |b1> on the Bloch sphere.

[0069] According to the above implementation, the following arbitrary geometric logic gate is established under the {|b1>,|d1>} basis vector:

[0070]

[0071] Further expanding it to the {|0>,|1>} calculation subspace is:

[0072]

[0073] Each set of parameters θ, β, The value of represents different logic gates. In the embodiment, the NOT gate is used. Right now β=π、 and Hadamard gate, β=π、 This is used as an example to illustrate the shape of the light pulse and its working performance.

[0074] Substitute the aforementioned two-color light pulse into the coupled differential equation describing the interaction between light and the three-level quantum system, and simulate the working performance of the light pulse in the software. The fidelity F of the generated quantum state target state is defined as follows:

[0075] F=|<ψ target |ψ(t f )>| 2

[0076] where |ψ(t f )> is the quantum state obtained by solving the three-level coupled differential equation |ψ(t)> at t=t f The state function at time.

[0077] At the end of the interaction between the light pulse and the quantum system, the non-resonant excitation of the background ions by the light pulse is performed using |ψ(t f )> is in the probability P of |1>, |0> and |e> states m To characterize, its expression is:

[0078] P m =| <m|ψ(t f )>| 2

[0079] Where m=0,1,e.

[0080] Embodiment 2:

[0081] Based on the method for constructing an arbitrary geometric quantum logic gate of an imperfect system in the first embodiment, the amplitude of the light pulse is zero at the beginning, that is, Ω p,s (t=0,t f )=0, then all a in formula (5) (6) n and a′ n The following constraints must be met:

[0082] a 1 +3a 3 +5a 5 +7a 7 =-1,

[0083] a 2 +2a 4 +3a 6 +4a 8 =-0.5,

[0084] a′ 1 +3a′ 3 +5a′ 5 +7a′ 7 =-2,

[0085] a′ 2 +2a′ 4+3a′ 6 +4a ′ 8 =-0.5,

[0086] Specifically: take β=π, construct a NOT gate, and take a 1 =-1, a 2 =-0.5,a′ 1 = -2, a′ 2 =-0.5,a 3,4,5,6,7,8 =0,a′ 3，4,5，67，8 =0.

[0087] Attached Figure 3 is the Rabi frequency Ω of the NOT gate two-color light pulse generated in this embodiment p,s (t=0,t f )=0, If the input state is |1>, then after passing through this gate it is |0>. In this embodiment, the light pulse generates the target quantum state |ψ target > has a fidelity of F = 1, but this NOT gate two-color light pulse is only applicable to quantum systems without frequency detuning and non-resonant excitation.

[0088] Attached Figure 4 This is the evolution of the quantum state over time during the interaction between the NOT gate two-color light pulse generated in this embodiment and the non-detuned quantum system. The initial state of the system is |1>, and the final state after passing through the NOT gate is |0>.

[0089] In this embodiment, the light pulse generates the target quantum state |ψ target > has a fidelity of F = 1, but this two-color light pulse is only applicable to quantum systems without frequency detuning and non-resonant excitation.

[0090] The advantage of the optical pulse generated in this embodiment is that the absolute value of the instantaneous Rabi frequency is less than 1 MHz and the changes at the start and end times are relatively slow, which reduces the requirements on the response time of the AOM.

[0091] Embodiment three:

[0092] Based on the method for constructing an arbitrary geometric quantum logic gate of an imperfect system in embodiment 1, β=π, construct the Hadamard gate, and take the parameters in (5) and (6) as a 1 =-1,a 2 =-0.5,a′ 1 =-2,a′ 2 =-0.5,a 3,4,5,6,7,8 =0,a′ 3,4,5,6,7,8 =0.

[0093] The constructed Hadamard gate is If the input state is |1>, then after passing through the gate, it is a superposition state of |0> and |1>. The Rabi frequency is 0 at the start and end time, and the constraint conditions in Example 2 must be met. Take a in Example 2 n and a′ n , the optical pulse shape and working performance of implementing Hadamard gate.

[0094] Attached Figure 6 This is the evolution of the quantum state over time during the interaction between the Hadamard gate two-color light pulse generated in this embodiment and the non-detuned quantum system. The initial state of the system is |1>, and the final state after the Hadamard gate is an equal superposition state of |0> and |1>.

[0095] The advantages of the optical pulses generated in this embodiment are: p,s (t=0,t f )=0, on the one hand, the light pulses in two time periods can be combined to prevent the light pulses from jumping at 4μs; on the other hand, it avoids the multiple Fourier frequency components in the frequency domain caused by the sharp change of field intensity at the endpoints that may affect the quantum state in the quantum system with background ions. 2. The absolute value of the instantaneous Rabi frequency is less than 1MHz, and the change at the start and end time is relatively slow, which reduces the response time requirement of the acousto-optic modulator.

[0096] Embodiment 4:

[0097] Based on the method for constructing an arbitrary geometric quantum logic gate of an imperfect system in the second embodiment, by optimizing a n and a′ n At the end of the interaction between the light pulse and the quantum system, the fidelity of the target state and the non-resonant excitation of the background ions are detected as the frequency detuning changes. The pulse parameters for creating the NOT gate in the ensemble quantum bit system are obtained as follows: 1 =0.1909,a 2 =-1.8666,a 3 =-0.3970,a 4 =0.6833,a′ 1 =-0.1926,a′ 2 =-0.2953,a′ 3 =-0.6025,a′ 4 =-0.1023,a 5,6,7,8 =0,a′ 5,6,7,8 =0.

[0098] Attached Figure 7 is the NOT gate two-color light pulse generated in this embodiment, Ωp,s (t=0,t f )=0. Figure 3 In contrast, the light pulse can interact with a quantum system that has a frequency detuning mechanism to create a NOT gate.

[0099] Attached Figure 8 This is the evolution of the quantum state over time during the interaction between the NOT gate two-color light pulse generated in this embodiment and the non-detuned quantum system. The initial state of the system is |1>, and the final state after passing through the NOT gate is |0>.

[0100] Attached Fig. 9 This is a graph showing the relationship between the fidelity F of the NOT gate created after the two-color light pulse of the NOT gate generated in this embodiment interacts with the quantum system with frequency detuning and the frequency detuning Δ, where Δ is the difference between the center frequency of the light pulse and the corresponding transition frequency of the quantum state ion or background ion, that is, the non-resonant frequency detuning. Within the center frequency ±170kHz, the fidelity of the NOT gate is always above 98%, which has strong robustness. For Pr 3+ :Y 2 SiO 5 The full width at half maximum of the quantum state absorption peak is 170kHz, and the pulses generated in this embodiment are sufficient to achieve the requirements of this system. The behavior of the fidelity between ±340kHz and 3.5MHz is irrelevant, because the quantum state ions are located in a frequency window with zero absorption, and the center frequency of the bit ions is about 3.5MHz away from the boundary of the frequency window. For background ions with a detuning amount exceeding 3.5MHz, the value of the fidelity is meaningless for quantum computing, and its behavior is not considered.

[0101] Attached Fig.10 It is the non-resonant excitation of the background ions ΔMHz away from the quantum state ions after the NOT gate two-color light pulse generated in this embodiment interacts with the frequency-detuned quantum system, which is reflected in the distribution rate P of the ions in the three energy states at the time of pulse termination. m . Pr 3+ :Y 2 SiO 5 The system requires no excitation for ions with |Δ|≥3.5MHz. In this embodiment, the input state of the system is |1>. When Δ=±3.5MHz, there is a 0.85% probability that the ions are transferred from the initial state |1> to the |0> state, and the probability of being in the |e> state is zero. Considering that the background ion density at this frequency detuning amount is only 1 / 6 of the quantum state ion density, the 1.9% transfer probability is small enough to ignore the interference caused to the quantum state ions.

[0102] Embodiment five:

[0103] Based on the method for constructing an arbitrary geometric quantum logic gate of an imperfect system in the second embodiment, by optimizing a n and a′ n At the end of the interaction between the light pulse and the quantum system, the fidelity of the target state and the non-resonant excitation of the background ions are detected as the frequency detuning changes. It is concluded that a Hadamard gate is created in the ensemble quantum bit system. The initial state is |1> and after the Hadamard gate, it changes to (|0>-|1>),a n The value of is optimized to get a 1 =0.4108,a 2 =-1.7610,a 3 =-0.4703,a 4 =0.6305,a′ 1 =-0.0216,a′ 2 =-0.1669,a′ 3 =-0.6595,a′ 4 =-0.1665,a 5,6,7,8 =0,a′ 5,6,7,8 =0.

[0104] Attached Fig.11 is the Hadamard gate two-color light pulse generated in this embodiment, Ω p,s (t=0,t f )=0. Figure 5 In contrast, the light pulse can interact with a quantum system that has a frequency detuning mechanism to create a Hadamard gate.

[0105] Attached Fig.12 This is the evolution of the quantum state over time during the interaction between the Hadamard gate two-color light pulse generated in this embodiment and the non-detuned quantum system. The initial state of the system is |1>, and the probability of the final state being at |0> and |1> after the Hadamard gate is 50%.

[0106] Attached Fig.13 4 is a graph showing the relationship between the fidelity F of the Hadamard gate created after the Hadamard gate two-color light pulse generated in this embodiment interacts with a quantum system with frequency detuning and the frequency detuning Δ.

[0107] Attached Fig.14 It is the non-resonant excitation of the background ions ΔMHz away from the quantum state ions after the Hadamard gate two-color light pulse generated in this embodiment interacts with the frequency-detuned quantum system, which is reflected in the distribution rate P of the ions in the three energy states at the time of pulse termination. mIn this embodiment, the input state of the system is |1>. When Δ=±3.5MHz, there is a 0.24% probability that the ions are transferred from the initial state |1> to the |0> state. The probability of being in the |e> state is zero, and the interference to the quantum state ions can be ignored.

[0108] The advantages of this embodiment are: 1. The instantaneous absolute value of the Rabi frequency is not greater than 1.5 MHz. 2. 3+ :Y 2 SiO 5 The fidelity of the optical pulses to the created logic gates is as high as 98% within the frequency detuning range of ±170kHz, while the off-resonance excitation is less than 3% outside the frequency detuning range of ±3.5MHz.

[0109] The above technical solution can construct an arbitrary geometric quantum logic gate system for imperfect systems. On the one hand, it solves the problem that the traditional adiabatic pulse has a long action time and is prone to decoherence. On the other hand, it improves the robustness of quantum manipulation within a specific frequency detuning range for imperfect systems, suppresses non-resonant excitation outside the specific frequency detuning range, and provides a technical reference for quantum manipulation in imperfect systems.

[0110] The above technical solution can construct an ensemble rare earth ion quantum state system. Arbitrary geometric logic gates can be used to prepare quantum chips or quantum memories, and applied to quantum computing systems based on frequency addressing.

[0111] The parts of this technical solution that are not described in detail belong to the common knowledge of those skilled in the art.

Claims

1. A method for constructing arbitrary geometric quantum logic gates for imperfect systems, characterized by: In a three-level system, two optical pulses with degrees of freedom are forward designed. The amplitude and phase of the two optical pulses with degrees of freedom are optimized according to the requirements of the three-level system. The corresponding amplitude and phase are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding optical pulse. The radio signal is used to drive an acousto-optic modulator in a continuous laser optical path to obtain a group of two-color optical pulses. The generated two-color optical pulses are in [0, t f ] to manipulate the quantum state of the light field detection, in [0, 2t f ] to manipulate quantum states that cannot be detected by light fields, thereby constructing arbitrary geometric logic gates, where t f is the pulse duration of the two-color light pulse; The amplitude and phase of the two-color light pulse are input into the arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding light pulse. The phase of the radio signal is expressed as: and The amplitude of the radio signal is expressed as: E p and E s ; E p and E s Both vary with time and are determined by the following relationship: Where μ p，s is the transition dipole moment of the |1>-|e> and |0>-|e> optical transitions; Ω p，s is the Rabi frequency of the two light pulses; C is the Rabi frequency of the light pulse Ω p，s To the radio signal amplitude E p，s The conversion coefficient, i is the imaginary unit, Rabi frequency Ω p，s Depends on angle θ, time t and phase β, As shown below: In the formula, satisfy: Ω(t) is designed as follows: In the formula is the time differential of γ1(t) and γ2(t); γ1(t) and γ2(t) are time-dependent parameters, which are formed by the superposition of Fourier components: where a n and a′ n are the coefficients of each Fourier component; This two-color light pulse is used to manipulate the quantum state to construct the following arbitrary geometric quantum logic gate in the {|0>,|1>} computational subspace: where θ is in the range [0, π], β is in the range [0, 2π].

2. The method for constructing an arbitrary geometric quantum logic gate of an imperfect system according to claim 1, characterized in that: The amplitude of the optical pulse is zero at the start time, and the parameters in equations (5) and (6) should satisfy the following conditions: a1+3a3+5a5+7a7=-1, a2+2a4+3a6+4a8=-0.5, a′1+3a′3+5a′5+7a′7=-2, a′2+2a′4+3a′6+4a′8=-0.

5.

3. The method for constructing an arbitrary geometric quantum logic gate of an imperfect system according to claim 2, characterized in that: Pick β=π, construct a NOT gate, and take a1=-1, a2=-0.5, a′1=-2, a′2=-0.5, a 3,4,5,6,7,8 =0,a′ 3,4,5,6,7,8 =0.

4. The method for constructing an arbitrary geometric quantum logic gate of an imperfect system according to claim 2, characterized in that: Pick β=π, construct the Hadamard gate, and take the parameters in (5)(6) as a1=-1, a2=-0.5, a′1=-2, a′2=-0.5, a 3,4,5,6,7,8 =0,a′ 3,4,5,6,7,8 =0.

5. The method for constructing an arbitrary geometric quantum logic gate of an imperfect system according to claim 2, characterized in that: By optimizing a n and a′ n At the termination moment of the interaction between the light pulse and the quantum system, the fidelity of the target state and the non-resonant excitation of the background ions are detected as the frequency detuning changes. It is found that the pulse parameters for creating the NOT gate in the ensemble quantum state system are a1=0.1909, a2=-1.8666, a3=-0.3970, a4=0.6833, a′1=-0.1926, a′2=-0.2953, a′3=-0.6025, a′4=-0.1023, a 5,6,7,8 =0,a′ 5,6,7,8 =0.

6. The method for constructing an arbitrary geometric quantum logic gate of an imperfect system according to claim 2, characterized in that: By optimizing a n and a′ n At the termination moment of the interaction between the light pulse and the quantum system, the fidelity of the target state and the non-resonant excitation of the background ions are detected as the frequency detuning changes. It is found that the pulse parameters for creating the Hadamard gate in the ensemble quantum state system are a1=0.4108, a2=-1.7610, a3=-0.4703, a4=0.6305, a′1=-0.0216, a′2=-0.1669, a′3=-0.6595, a′4=-0.1665, a 5,6,7,8 =0,a′ 5,6,7,8 =0.

7. A quantum logic gate generated by the method for constructing an arbitrary geometric quantum logic gate of an imperfect system as claimed in any one of claims 1 to 6.

8. A quantum chip made using the quantum logic gate described in claim 7.

9. A quantum memory made using the quantum logic gate according to claim 7.

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