Method for constructing arbitrary non-adiabatic and musical quantum logic gate of rare earth ion system

Abstract

The invention discloses a construction method of an arbitrary non-adiabatic sum quantum logic gate of a rare earth ion system, and relates to the technical field of quantum computing. Comprising the following steps: firstly, designing a beveling evolution path with a degree of freedom in a Bloch ball; the degree of freedom is beveled; the evolution path is a random path; converting the evolution path into the amplitude and phase parameters of the optical pulse required for controlling the three-energy-level system through reverse engineering; then generating a group of double-color light pulses by using an arbitrary wave generator and an acousto-optic modulator based on the amplitude and phase parameters; and finally, controlling the quantum state coupled by the light field by using the two-color light pulse so as to construct the non-adiabatic harmony quantum logic gate. The constructed logic gate shows relatively strong robustness to inherent frequency detuning (non-uniform broadening) of an ensemble system and light intensity distribution errors in an experiment, and the accuracy and stability of quantum control in an actual noise environment are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of quantum computing technology, and more specifically to a method, apparatus, device, and readable storage medium for constructing arbitrary non-adiabatic and hybrid quantum logic gates in a rare-earth ion system. Background Technology

[0002] Quantum computing is a cutting-edge research area in the global scientific and technological field. Its core lies in using the principles of quantum mechanics to achieve information processing capabilities that surpass classical computing. One of the key physical foundations for realizing quantum computing is the construction of high-fidelity quantum logic gates. However, the decoherence effect and environmental noise caused by excessively long evolution times have become major bottlenecks restricting the improvement of quantum logic gate fidelity. Harmonious quantum computing has attracted much attention in high-fault-tolerant quantum manipulation due to its strong robustness to environmental noise. This scheme accumulates a geometric phase that is only related to the evolution path by allowing the quantum state to evolve along a closed path in a Hilbert subspace spanned by a set of orthogonal bases. This phase is independent of dynamical details, thus possessing inherent noise resistance. However, traditional harmonious quantum computing is mostly based on adiabatic processes, which require long operation times to meet adiabatic conditions. This exacerbates the decoherence effect, leading to a decrease in the fidelity of quantum logic gates. To address this problem, a non-adiabatic pulse scheme can be used to replace the traditional adiabatic pulse, which significantly shortens the gate operation time while maintaining harmonious conditions, thereby effectively suppressing the effects of decoherence.

[0003] Ensemble rare-earth ion systems are considered one of the most promising physical platforms for realizing quantum computing due to their qubit coherence times of up to 6 hours. However, the non-uniform broadening and interference from other ions in the frequency domain present challenges in constructing high-fidelity quantum logic gates. Taking doped crystals as an example, their optical transition center frequency is located at 579.88 nm, with a large full width at half maximum (FWHM). This requires qubit operations to be highly robust over a large frequency detuning range; simultaneously, low non-resonant excitation of other ions in the frequency domain is also required. Furthermore, the Gaussian beams commonly used in experiments suffer from non-uniform spatial intensity distribution, which further reduces the fidelity of the logic gates. Therefore, the system must also be robust to light intensity errors within a certain range.

[0004] In summary, designing an evolution path capable of precisely manipulating qubits in an ensemble of rare-earth ion systems while simultaneously exhibiting high robustness to frequency detuning and intensity errors is a critical technical problem that urgently needs to be solved in this field. To address this need, this invention proposes a method for constructing arbitrary non-adiabatic harmonic quantum logic gates that are robust to both frequency detuning and intensity errors. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for constructing arbitrary non-adiabatic harmonic quantum logic gates in rare-earth ion systems. By introducing a slanted evolution path with degrees of freedom and combining it with reverse engineering, the optimized geometric path is transformed into a precisely controllable two-color light pulse sequence, thereby realizing fast and high-fidelity non-adiabatic harmonic quantum logic gate operation in ensemble rare-earth ion systems. This method effectively overcomes the shortcomings of traditional adiabatic harmonic schemes, such as long operation time and susceptibility to decoherence. Furthermore, by optimizing the degrees of freedom of the evolution path, the constructed logic gate exhibits strong robustness to the inherent frequency detuning (non-uniform broadening) of the ensemble system and experimental light intensity distribution errors, significantly improving the accuracy and stability of quantum manipulation in real-world noisy environments.

[0006] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in rare-earth ion systems, the method comprising: Design a slanted evolution path with degrees of freedom in a Bloch sphere; the slanted evolution path is a random path. The evolution path is converted into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system through reverse engineering. Based on amplitude and phase parameters, an arbitrary wave generator and an acousto-optic modulator are used to generate a set of two-color light pulses; By using two-color light pulses to manipulate the quantum state coupled with the light field, non-adiabatic and hybrid quantum logic gates can be constructed.

[0007] In some embodiments, designing a slant evolution path with degrees of freedom in a Bloch sphere includes: An evolutionary path is constructed within the Bloch sphere, consisting of a first path, a second path, and a third path connected end-to-end; the evolutionary time interval corresponding to the first path is... The evolution time interval corresponding to the second path is The evolution time interval corresponding to the third path is ; Time-varying polar angle on the second path segment and time-varying azimuth The following preset relationships must be satisfied: ; in, for The polar angle at any given moment; For the design's degrees of freedom parameters; Based on the starting time of the second path segment With the finish line Using Bloch spherical coordinates, the time-varying polar angles of the first and third path segments are constructed through Hermitian interpolation. and time-varying azimuth The specific design is as follows: For the first path segment: ; ; For the third path segment: ; ; in, These are the starting and ending polar angles of the first path. The starting and ending polar angles of the third path are given. Here are the starting and ending azimuth angles of the first path. These are the starting and ending azimuth angles of the third path. Here, Hermite is used as the interpolation function; the above design allows the first, second, and third paths to be smoothly connected, forming a complete evolution path with continuous first derivatives. , These are the initial polar angle change rate and the final polar angle change rate for the first path. , The initial polar angle change rate and the final polar angle change rate of the third path are given. , These are the initial and final azimuth rate of change for the first path. , These are the initial and final azimuth rate of change for the third path; The evolutionary path satisfies the following presupposed relationship: ; in, It is half of the solid angle enclosed by the evolution path.

[0008] In some embodiments, the evolution path is converted into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system through reverse engineering, including: By substituting the time-varying polar angle and time-varying azimuth angle into a pre-defined reverse engineering mapping model, the time-varying Rabi frequency of the two-color light pulse is calculated. Phase And the need to artificially introduce detuning into the system The mapping model for reverse engineering is: ; ; ; The amplitude and phase parameters of the optical pulse satisfy the mapping model of reverse engineering.

[0009] In some embodiments, a set of two-color light pulses is generated using an arbitrary wave generator and an acousto-optic modulator based on amplitude and phase parameters, including: The amplitude and phase of the converted optical pulse are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding optical pulse; the phase of the radio signal is represented as follows: and The amplitudes of the radio signals are respectively expressed as and ; The radio signal is input into the acousto-optic modulator to obtain a two-color light pulse; amplitude and All of these change over time and are determined by the following relationship: ; in, yes and The transition dipole moment of optical transition; It is the Rabi frequency of two light pulses; It is from the Rabi frequency of the light pulse. to radio signal amplitude The conversion factor, The imaginary unit, It is the reduced Planck constant; Rabi frequency Depends on angle Relative phase ,time The specific formula is as follows: ; ; in, satisfy: , .

[0010] In some embodiments, the quantum state coupled with the optical field is manipulated using two-color light pulses to construct a non-adiabatic and harmonic quantum logic gate, including: Using this two-color pulse to manipulate quantum states Construct any non-adiabatic and harmonic quantum logic gate in the computational space as follows: ; In the formula, , Here is the Pauli matrix, where exist Within the range, exist Within the range.

[0011] In some embodiments, the method further includes: set up , , Construct NOT gates; set up , , Construct the Hadamard gate.

[0012] Secondly, the present invention also provides a device for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in rare-earth ion systems, the device comprising: The path design module is used to design a slant evolution path with degrees of freedom in the Bloch sphere; the degrees of freedom of the slant evolution path are random paths. The parameter determination module is used to convert the evolution path into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system through reverse engineering. The pulse generation module is used to generate a set of two-color light pulses based on amplitude and phase parameters using an arbitrary wave generator and an acousto-optic modulator. The logic gate construction module uses two-color light pulses to manipulate the quantum state coupled with the light field in order to construct non-adiabatic and hybrid quantum logic gates.

[0013] The beneficial effects of this invention are as follows: The method for constructing arbitrary non-adiabatic harmonious quantum logic gates in rare-earth ion systems in this invention first designs a slanted evolution path with degrees of freedom in a Bloch sphere; the degrees of freedom of the slanted evolution path are random paths; then, through reverse engineering, the evolution path is transformed into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system; then, based on the amplitude and phase parameters, a set of two-color optical pulses is generated using an arbitrary wave generator and an acousto-optic modulator; finally, the two-color optical pulses are used to manipulate the quantum states coupled to the optical field to construct non-adiabatic harmonious quantum logic gates. By introducing a slanted evolution path with degrees of freedom and combining it with reverse engineering, the optimized geometric path is transformed into a precisely controllable two-color optical pulse sequence, thereby realizing fast and high-fidelity non-adiabatic harmonious quantum logic gate operation in the ensemble rare-earth ion system. This method effectively overcomes the shortcomings of traditional adiabatic and harmonic schemes, such as long time requirements and susceptibility to decoherence. At the same time, by optimizing the degree of freedom of the evolution path, the constructed logic gate exhibits strong robustness to the inherent frequency detuning (non-uniform broadening) of the ensemble system and the light intensity distribution error in the experiment, significantly improving the accuracy and stability of quantum manipulation in actual noisy environments.

[0014] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, the preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system according to an embodiment of the present invention. Figure 2 Eu doping in Y₂SiO₅ crystal as shown in one embodiment of the present invention 3+ Schematic diagram of the relevant energy level structure; Figure 3 This is the evolution path on the Bloch sphere under the path parameters shown in one embodiment of the present invention; Figure 4 The Rabi frequency of the dual-color light pulse corresponding to the path shown in one embodiment of the present invention; Figure 5 This is an embodiment of the present invention showing the evolution of quantum states over time during the interaction between a two-color pulse and a detuned quantum system; Figure 6 The Rabi frequency of the Hadamard gate dual-color light pulse shown in one embodiment of the present invention; Figure 7 This is an embodiment of the present invention showing the evolution of quantum states over time during the interaction between a two-color pulse and a detuned quantum system; Figure 8 This is an example of an evolution path on a Bloch sphere according to an embodiment of the present invention; Figure 9 The Rabi frequency of the dual-color light pulse shown in one embodiment of the present invention; Figure 10 This is an embodiment of the present invention showing the evolution of quantum states over time during the interaction between a two-color pulse and a detuned quantum system; Figure 11 The fidelity of the NOT gate created by the interaction of a two-color pulse with a detuned quantum system, as shown in an embodiment of the present invention. Frequency detuning A graph showing the relationship between changes; Figure 12 The fidelity of the NOT gate created by the interaction of a two-color pulse with a detuned quantum system, as shown in an embodiment of the present invention. With strength error A graph showing the relationship between changes; Figure 13 This invention illustrates the distance-encoded quantum state after the interaction of a two-color pulse with a detuned quantum system, as shown in one embodiment of the invention. Non-orthogonal excitation of other ions in the background ; Figure 14 This is an example of an evolutionary path on a Bloch sphere according to an embodiment of the present invention; Figure 15 The Rabi frequency of the dual-color light pulse shown in one embodiment of the present invention; Figure 16 This is an embodiment of the present invention showing the evolution of the quantum state over time during the interaction between a two-color pulse and a detuned quantum system; Figure 17 The fidelity of the Hadamard gate created by the interaction of a two-color pulse with a detuned quantum system, as shown in an embodiment of the present invention. Frequency detuning A graph showing the relationship between changes; Figure 18 The fidelity of the Hadamard gate created by the interaction of a two-color pulse with a detuned quantum system, as shown in an embodiment of the present invention. With strength error A graph showing the relationship between changes; Figure 19 This invention illustrates the distance-encoded quantum state after the interaction of a two-color pulse with a detuned quantum system, as shown in one embodiment of the invention. Non-orthogonal excitation of other ions in the background ; Figure 20 This is a schematic diagram of a device for constructing arbitrary non-adiabatic and quantum logic gates in a rare earth ion system, according to an embodiment of the present invention. Detailed Implementation

[0016] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] It should be noted that references to "an embodiment," "embodiment," "example embodiment," etc., in this specification refer to the described embodiment including specific features, structures, or characteristics; however, not every embodiment must include these specific features, structures, or characteristics. Furthermore, such expressions do not refer to the same embodiment. Moreover, when describing specific features, structures, or characteristics in conjunction with embodiments, whether or not explicitly described, it is indicated that incorporating such features, structures, or characteristics into other embodiments is within the knowledge of those skilled in the art.

[0018] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0019] In some embodiments, such as Figure 1 The diagram illustrates a method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system. The specific method includes: S101, design a slant evolution path with degrees of freedom in the Bloch sphere.

[0020] Among them, the degrees of freedom are oblique evolution paths, which are random paths.

[0021] Optionally, a slant evolution path with degrees of freedom can be designed in the Bloch sphere, including: An evolutionary path is constructed within the Bloch sphere, consisting of a first path, a second path, and a third path connected end-to-end; the evolutionary time interval corresponding to the first path is... The evolution time interval corresponding to the second path is The evolution time interval corresponding to the third path is ; Time-varying polar angle on the second path segment and time-varying azimuth The following preset relationships must be satisfied: ; in, for The polar angle at any given moment; For the design's degrees of freedom parameters; Based on the starting time of the second path segment With the finish line Using Bloch spherical coordinates, the time-varying polar angles of the first and third path segments are constructed through Hermitian interpolation. and time-varying azimuth The specific design is as follows: For the first path segment: ; ; For the third path segment: ; ; in, These are the starting and ending polar angles of the first path. The starting and ending polar angles of the third path are given. Here are the starting and ending azimuth angles of the first path. These are the starting and ending azimuth angles of the third path. Here, Hermite is used as the interpolation function; the above design allows the first, second, and third paths to be smoothly connected, forming a complete evolution path with continuous first derivatives. , These are the initial polar angle change rate and the final polar angle change rate for the first path. , The initial polar angle change rate and the final polar angle change rate of the third path are given. , These are the initial and final azimuth rate of change for the first path. , These are the initial and final azimuth rate of change for the third path; The evolutionary path satisfies the following presupposed relationship: ; in, It is half of the solid angle enclosed by the evolution path.

[0022] For example, design a smooth, obliquely cut semi-orange segment path with degrees of freedom on a Bloch sphere; the total pulse duration is... Divided into three continuous intervals , and ; within the time interval Within, let the time-varying polar angle of the evolutionary path With azimuth The following are the preset geometric constraints: ; in, yes The polar angle at any moment To control Adjustable degrees of freedom parameter for the slope of the path within the interval; within the time interval. and Internally, based on the starting point of the overall evolutionary path The start and end points of the second path segment and the end point of the overall path segment. And its derivative, constructing the first and third path segments using Hermite interpolation. and Overall path and The design is shown in the following formula: ; ; In the formula, For Hermite interpolation functions, , , , ,in, In addition, continuous paths need to satisfy the following preset relationships: ; In the formula, It is half of the solid angle enclosed by the path.

[0023] S102 uses reverse engineering to convert the evolution path into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system.

[0024] Optionally, the evolution path can be reverse engineered to convert the amplitude and phase parameters of the optical pulses required to manipulate the three-level system, including: By substituting the time-varying polar angle and time-varying azimuth angle into a pre-defined reverse engineering mapping model, the time-varying Rabi frequency of the two-color light pulse is calculated. Phase And the need to artificially introduce detuning into the system The mapping model for reverse engineering is: ; ; ; The amplitude and phase parameters of the optical pulse satisfy the mapping model of reverse engineering.

[0025] S103 generates a set of two-color light pulses using an arbitrary wave generator and an acousto-optic modulator, based on amplitude and phase parameters.

[0026] Optionally, based on amplitude and phase parameters, a set of two-color light pulses is generated using an arbitrary wave generator and an acousto-optic modulator, including: The amplitude and phase of the converted optical pulse are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding optical pulse; the phase of the radio signal is represented as follows: and The amplitudes of the radio signals are respectively expressed as and ; The radio signal is input into the acousto-optic modulator to obtain a two-color light pulse; amplitude and All of these change over time and are determined by the following relationship: ; in, yes and The transition dipole moment of optical transition; It is the Rabi frequency of two light pulses; It is from the Rabi frequency of the light pulse. to radio signal amplitude The conversion factor, where i is the imaginary unit. It is the reduced Planck constant; Rabi frequency Depends on angle Relative phase ,time The specific formula is as follows: ; ; in, satisfy: , .

[0027] For example, the driving frequency of the acousto-optic modulator is In a continuous laser optical path, the laser frequency is A quantum state consists of two energy levels and To characterize, the frequency difference between them is Electrons from energy levels to energy level The optical transition frequency is Electrons from energy levels to energy level The optical transition frequency is The driving acousto-optic modulator generates an effect on - The frequency of the radio signal of the transition light pulse is The driving acousto-optic modulator generates an effect on - The frequency of the radio signal of the transition light pulse is Both satisfy , ; ; The phase of two radio signals is represented as: and The amplitude is expressed as: and ; and Both change over time and are determined by the following relationship: ; In the formula yes - and - The transition dipole moment of optical transition; It is the Rabi frequency of two light pulses; It is from the Rabi frequency of the light pulse. to radio signal amplitude The conversion factor, The imaginary unit is the Rabi frequency. Depends on angle Relative phase ,time As shown in the following formula: ; ; satisfy: , .

[0028] S104 utilizes two-color light pulses to manipulate the quantum state coupled with the light field in order to construct a non-adiabatic and hybrid quantum logic gate.

[0029] Optionally, the quantum states coupled with the light field can be manipulated using two-color light pulses to construct non-adiabatic and harmonic quantum logic gates, including: Using this two-color pulse to manipulate quantum states Construct any non-adiabatic and harmonic quantum logic gate in the computational space as follows: ; In the formula, , Here is the Pauli matrix, where exist Within the range, exist Within the range.

[0030] In another embodiment, such as Figure 2 As shown, Figure 2 Eu doping in Y2SiO5 crystal 3+ The diagram shows the relevant energy level structure, which is used as an example to illustrate the three-level system to which this invention applies; the ground state and excited state in the diagram both contain three hyperfine levels. It is an excited state. and The two energy levels that encode the quantum state are coupled through... and This is achieved through two optical transitions. Under the basis vectors, the Hamiltonian of the system can be expressed as: ; By introducing basis vectors Rewrite equation (11) as follows In the formula This represents the conjugate term. Under this transformation, it can be driven by applying a two-color pulse. The state evolves on the Bloch sphere according to the path designed in equations (2) and (3) and accumulates a global phase. To construct arbitrary non-adiabatic and eurythmic quantum logic gates.

[0031] With initial state In the NOT gate, ,Right now , , And Hadamard Gate, ,Right now , , Taking the evolution of the path as an example, we can illustrate the shape of the path and its performance.

[0032] The system's Hamiltonian is substituted into the Lindblad quantum master equation, and the performance of the scheme is numerically simulated in Matlab. The fidelity between the target state and the ideal state is described. The definition is as follows: ; in, The initial state is obtained by solving the Lindblad quantum master equation. exist The state evolved at a given time. 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 used in... At this moment Number of state layouts To indicate: .

[0033] In another embodiment, the start and end times of the light pulse amplitude are 0, i.e. In equations (2) and (3) , , , The derivative of the time step and the corresponding time step must be 0.

[0034] Based on this, take , , Construct a NOT gate and retrieve... , , , , , Appendix Figure 3 The evolution path on the Bloch sphere is given by the path parameters. The state starts from the North Pole, rotates a certain angle along the equator, and returns to the North Pole, accumulating a geometric phase of π during its evolution. (Appendix) Figure 4 This refers to the pull ratio frequency of the dual-color light pulse corresponding to the path in this embodiment. The maximum pull ratio frequency of the dual-color light pulse does not exceed [a certain value]. Appendix Figure 5 This describes the evolution of the quantum state over time during the interaction between the two-color pulse and the detuned quantum system in this embodiment. The initial state of the system... After NOT gate operation, the result is obtained State. Evolved state. With the target state The fidelity is 99.89%. However, this NOT gate evolution path is only applicable to quantum systems without frequency detuning.

[0035] The advantage of the path generated in this embodiment is that the path is smooth and unsloping, resulting in a smaller... The instantaneous Rabi frequency reduces the requirements for the response time of the acousto-optic modulator.

[0036] In another embodiment, take , , Construct the Hadamard door and retrieve... , , , , , Appendix Figure 3 This represents the evolution path on the Bloch sphere under path parameters. (Appendix) Figure 6 This refers to the Rabi frequency of the Hadamard gate dual-color light pulses generated in this embodiment. The maximum Rabi frequency of the dual-color light pulses does not exceed [a certain value]. Appendix Figure 7 This describes the evolution of the quantum state over time during the interaction between the two-color pulse and the detuned quantum system in this embodiment. Initial input state. After passing through the Hadamard gate, a superposition state is obtained. The evolved state in this embodiment With the target state The fidelity is 99.96%, but this Hadamard gate evolution path is only applicable to quantum systems without frequency detuning.

[0037] The advantage of the path generated in this embodiment is that the path is smooth and unsloping, resulting in a smaller... The instantaneous Rabi frequency reduces the requirements for the response time of the acousto-optic modulator.

[0038] In another embodiment, based on the method of constructing NOT gates, by optimizing... and The value of this value is used to detect the fidelity under frequency detuning and intensity error at the final moment of system evolution. Based on the relationship between the non-resonant excitation of background ions and the frequency detuning, the path parameters for creating a NOT gate in the rare-earth ion quantum system are derived as follows: , , , , , .

[0039] Appendix Figure 8 This is the evolution path on the Bloch sphere under the parameters in this embodiment. The state starts from the North Pole, evolves along the tilted surface of the Bloch sphere, and returns to the North Pole, accumulating a geometric phase of π during the evolution process.

[0040] Appendix Figure 9 This refers to the pull ratio frequency of the dual-color light pulse corresponding to the path in this embodiment. The maximum pull ratio frequency of the dual-color light pulse does not exceed [a certain value]. .

[0041] Appendix Figure 10 This describes the evolution of the quantum state over time during the interaction between the two-color pulse and the detuned quantum system in this embodiment. The initial state in this embodiment... The state after evolution through the NOT gate With the target state The fidelity is 99.94%.

[0042] Appendix Figure 11 This refers to the fidelity of the NOT gate created by the interaction of the two-color pulse and the detuned quantum system in this embodiment. Frequency detuning The relationship between the changes at the center frequency. Within the range, the average fidelity of the NOT gate is The high-fidelity (99.5%) window is [-52.5, 40] MHz. This satisfies... For ensemble rare earth ion systems, the central transition frequency Robustness requirements within the scope.

[0043] Appendix Figure 12 This refers to the fidelity of the NOT gate created by the interaction of the two-color pulse and the detuned quantum system in this embodiment. With strength error The graph showing the relationship between light intensity and its variation. Within the error range, the average fidelity of the NOT gate is The high-fidelity (99.5%) window is [-0.07, 0.07], which solves the problem of decreased robustness of logic gates caused by uneven light intensity distribution of the light spot generated by the Gaussian beam used in the experiment.

[0044] Appendix Figure 13 In this example, the interaction between a two-color pulse and a detuned quantum system results in a distance-encoded quantum state. Non-orthogonal excitation of other ions in the background . Ensemble rare earth ion system requirements Ions outside this region were not excited; approximately 4.92% of them were in this range. The state was transferred to In terms of state, and shifted to The number of configurations in the state is approximately 0, which satisfies the system's requirement for non-resonant excitation.

[0045] The advantages of this embodiment are: (1) This scheme has a center frequency Within the frequency detuning range, the average fidelity can still reach In light intensity Within the error range, the average fidelity is as high as This satisfies the high robustness requirement of the ensemble rare earth ion system for frequency detuning and effectively solves the problem of reduced robustness caused by uneven intensity distribution of Gaussian beams in experiments. (2) For In the frequency domain, the proportion of background ions and non-resonant excitation is only 4.92%, which meets the stringent requirements of ensemble rare earth ions for suppressing background ion interference and significantly reduces the risk of crosstalk. (3) The path design brings about less than The instantaneous Rabi frequency reduces the requirements for the response time of the acousto-optic modulator.

[0046] In another embodiment, based on the method of constructing Hadamard gates, by optimizing... and The value of this value is used to detect the fidelity under frequency detuning and intensity error at the final moment of system evolution. Based on the relationship between the non-resonant excitation of the background example and the frequency detuning, the path parameters for creating a Hadamard gate in the rare-earth ion quantum system are derived as follows: , , , , , .

[0047] Appendix Figure 14 The evolution path on the Bloch sphere under the given parameters in this embodiment. The state starts from the North Pole, evolves along the tilted surface of the Bloch sphere, and returns to the North Pole, accumulating a geometric phase of π during the evolution process.

[0048] Appendix Figure 15 This refers to the pull ratio frequency of the dual-color light pulse corresponding to the path in this embodiment. The maximum pull ratio frequency of the dual-color light pulse does not exceed [a certain value]. .

[0049] Appendix Figure 16 This describes the evolution of the quantum state over time during the interaction between the two-color pulse and the detuned quantum system in this embodiment. The evolved state in this embodiment... With the target state The fidelity is 99.97%.

[0050] Appendix Figure 17 This refers to the fidelity of the Hadamard gate created by the interaction of the two-color pulse and the detuned quantum system in this embodiment. Frequency detuning The relationship between the changes at the center frequency. Within the range, the average fidelity of the Hadamard door is The high-fidelity (99.5%) window is [-77.5, 57.5] MHz. This satisfies... For ensemble rare earth ion systems, the central transition frequency Robustness requirements within the scope.

[0051] Appendix Figure 18 This refers to the fidelity of the Hadamard gate created by the interaction of the two-color pulse and the detuned quantum system in this embodiment. With strength error The graph showing the relationship between light intensity and its variation. Within the error range, the average fidelity of the Hadamard gate is The high-fidelity (99.5%) window is [-0.1, 0.1], which solves the problem of decreased robustness of logic gates caused by uneven light intensity distribution of the light spot generated by the Gaussian beam in the experiment.

[0052] Appendix Figure 19 In this example, the interaction between a two-color pulse and a detuned quantum system results in a distance-encoded quantum state. Non-orthogonal excitation of other ions in the background . Ensemble rare earth ion system requirements Ions outside this region were not excited; approximately 3.19% of them were in this range. The state was transferred to In terms of state, and shifted to The number of configurations in the state is approximately 0, which satisfies the system's requirement for non-resonant excitation.

[0053] The advantages of this embodiment are: (1) This scheme has a center frequency Within the frequency detuning range, the average fidelity can still reach In light intensity Within the error range, the average fidelity is as high as This satisfies the high robustness requirement of the ensemble rare earth ion system for frequency detuning and effectively solves the problem of reduced robustness caused by uneven intensity distribution of Gaussian beams in experiments. (2) For The background ions in the frequency domain, with non-resonant excitation accounting for only 3.19%, meet the stringent requirements of ensemble rare earth ions for suppressing background ion interference, significantly reducing the risk of crosstalk. (3) The path design brings about less than The instantaneous Rabi frequency reduces the requirements for the response time of the acousto-optic modulator.

[0054] Based on the same inventive concept, this application also provides a device for constructing arbitrary non-adiabatic and harmonic quantum logic gates in rare-earth ion systems, for implementing the above-described method for constructing such gates. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations in one or more embodiments of the device for constructing arbitrary non-adiabatic and harmonic quantum logic gates in rare-earth ion systems provided below can be found in the limitations of the method for constructing such gates in rare-earth ion systems described above, and will not be repeated here.

[0055] In one embodiment, such as Figure 20 As shown, a device for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system is provided. The device includes: The path design module 30 is used to design a slant evolution path with degrees of freedom in the Bloch sphere; the degrees of freedom of the slant evolution path are random paths. The parameter determination module 31 is used to convert the evolution path into the amplitude and phase parameters of the optical pulse required to manipulate the three-level system through reverse engineering. The pulse generation module 32 is used to generate a set of two-color light pulses based on amplitude and phase parameters using an arbitrary wave generator and an acousto-optic modulator. The logic gate construction module 33 uses two-color light pulses to manipulate the quantum state coupled with the light field in order to construct a non-adiabatic and hybrid quantum logic gate.

[0056] Obviously, those skilled in the art should understand that the modules or steps of this application described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device, or fabricating them separately as individual integrated circuit modules, or fabricating multiple modules or steps as a single integrated circuit module. Thus, this application is not limited to any particular combination of hardware and software.

[0057] The technical features of the above embodiments can be arbitrarily integrated. For the sake of brevity, not all possible integrations of the technical features in the above embodiments are described. However, as long as the integration of these technical features does not contradict each other, they should be considered to be within the scope of this specification.

[0058] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system, characterized in that, The method includes: Design a slant evolution path with degrees of freedom in a Bloch sphere; the degrees of freedom are defined by the slant evolution path being a random path. The evolution path is converted into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system through reverse engineering. Based on the amplitude and phase parameters, a set of two-color light pulses are generated using an arbitrary wave generator and an acousto-optic modulator. The quantum state coupled with the light field is manipulated using the two-color light pulses to construct the non-adiabatic and harmonic quantum logic gate.

2. The method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system as described in claim 1, characterized in that, Design a slant evolution path with degrees of freedom in a Bloch sphere, including: An evolutionary path is constructed within the Bloch sphere, consisting of a first path, a second path, and a third path connected end-to-end; the evolutionary time interval corresponding to the first path is... The evolution time interval corresponding to the second path is The evolution time interval corresponding to the third path is: ; Time-varying polar angle on the second path segment and time-varying azimuth The following preset relationships must be satisfied: ； in, for The polar angle at any given moment; For the design's degrees of freedom parameters; Based on the start time of the second path segment With the finish line Using Bloch spherical coordinates, the time-varying polar angles of the first and third path segments are constructed through Hermitian interpolation. and time-varying azimuth The specific design is as follows: For the first path segment: ； ； For the third path segment: ； ； in, These are the starting and ending polar angles of the first path. The starting and ending polar angles of the third path are given. Here are the starting and ending azimuth angles of the first path. These are the starting and ending azimuth angles of the third path. Here, Hermite is used as the interpolation function; the above design allows the first, second, and third paths to be smoothly connected, forming a complete evolution path with continuous first derivatives. , These are the initial polar angle change rate and the final polar angle change rate for the first path. , The initial polar angle change rate and the final polar angle change rate of the third path are given. , These are the initial and final azimuth rate of change for the first path. , These are the initial and final azimuth rate of change for the third path; The evolution path satisfies the following preset relationship: ； in, It is half of the solid angle enclosed by the evolution path.

3. The method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system as described in claim 2, characterized in that, The evolution path is converted into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system through reverse engineering, including: By substituting the time-varying polar angle and the time-varying azimuth angle into a preset reverse engineering mapping model, the time-varying Rabi frequency of the two-color light pulse is calculated. Phase And the need to artificially introduce detuning into the system The mapping model for the reverse engineering is as follows: ； ； ； The amplitude and phase parameters of the optical pulse satisfy the mapping model of the reverse engineering.

4. The method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system as described in claim 3, characterized in that, Based on the amplitude and phase parameters, a set of two-color light pulses is generated using an arbitrary wave generator and an acousto-optic modulator, including: The amplitude and phase of the converted optical pulse are input into an arbitrary wave generator to generate a radio signal with the same amplitude and phase as the corresponding optical pulse; the phase of the radio signal is represented as follows: and The amplitudes of the radio signals are respectively expressed as and ; The radio signal is input into the acousto-optic modulator to obtain a two-color light pulse; The amplitude and All of these change over time and are determined by the following relationship: ； in, yes and The transition dipole moment of optical transition; It is the Rabi frequency of two light pulses; It is from the Rabi frequency of the light pulse. to radio signal amplitude The conversion factor, The imaginary unit, It is the reduced Planck constant; the Rabi frequency Depends on angle Phase ,time The specific formula is as follows: ； ； in, satisfy: , .

5. The method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system as described in claim 4, characterized in that, Manipulating the quantum state coupled with the light field using the dual-color light pulses to construct the non-adiabatic and harmonic quantum logic gate includes: Using this two-color pulse to manipulate quantum states Construct any non-adiabatic and harmonic quantum logic gate in the computational space as follows: ； In the formula, , Here is the Pauli matrix, where exist Within the range, exist Within the range.

6. The method for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system as described in claim 5, characterized in that, The method further includes: set up , , Construct NOT gates; set up , , Construct the Hadamard gate.

7. A device for constructing arbitrary non-adiabatic and homogeneous quantum logic gates in a rare-earth ion system, characterized in that, The device includes: The path design module is used to design a slant evolution path with degrees of freedom in the Bloch sphere; the degrees of freedom are that the slant evolution path is a random path; The parameter determination module is used to convert the evolution path into the amplitude and phase parameters of the optical pulses required to manipulate the three-level system through reverse engineering. A pulse generation module is used to generate a set of dual-color light pulses based on the amplitude and phase parameters using an arbitrary wave generator and an acousto-optic modulator. The logic gate construction module uses the two-color light pulses to manipulate the quantum state coupled with the light field in order to construct the non-adiabatic and homogeneous quantum logic gate.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the method for constructing any non-adiabatic and quantum logic gate of the rare earth ion system as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the method for constructing any non-adiabatic and quantum logic gate of the rare-earth ion system according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the method for constructing arbitrary non-adiabatic and hybrid quantum logic gates for the rare-earth ion system as described in any one of claims 1 to 6.

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