A method and apparatus for constructing quantum entangled logic gates

Abstract

This application discloses a method and apparatus for constructing a quantum entangled logic gate. The method involves performing preset operations on the spin-related shift of each phonon mode of the ions in the segment and the phase of each pair of accumulated two-qubits between segments to obtain a target correlation function. This target correlation function is then converted into a target function containing a preset vector. The introduced preset vector improves the computational speed of the phase-modulated quantum entangled logic gate. After solving for the local optimal solution of the target function, the logic gate is constructed based on the fidelity of the logic gate corresponding to the local optimal solution. This ensures that the constructed logic gate meets the fidelity requirements, thus realizing a quantum entangled logic gate applicable to large-scale ion arrays.

Description

Technical Field

[0001] This application relates to, but is not limited to, quantum computer technology, including a method and apparatus for constructing quantum entangled logic gates. Background Technology

[0002] A quantum computer is a general-purpose computing device that operates based on the principles of quantum mechanics. Utilizing the properties of quantum superposition and quantum entanglement of qubits, it can achieve significant speedups compared to traditional computers when solving certain problems. Quantum computers have broad application prospects in future basic scientific research, materials and drug development, artificial intelligence, and financial market simulation, and have therefore attracted widespread attention.

[0003] Ion trap quantum computers utilize arrays of ions trapped in a vacuum as qubits. They have advantages in terms of qubit indistinguishability, coherence time, connectivity, and fidelity of various fundamental quantum operations, making them one of the most promising platforms for realizing quantum computers.

[0004] In ion-trap quantum computers, two-qubit quantum entanglement gates are typically implemented using lasers to generate spin-dependent forces on two target ions. By adjusting the amplitude, frequency, or phase of the laser, the evolution of the spatial vibrational modes (phonon modes) of the target ions can be controlled. This results in the decoupling of the spin state and phonon state of the target ions at the end of the gate, while the phase required for quantum entanglement accumulates between the spin states of the two target ions. Theoretically, amplitude modulation is the simplest method to design, allowing for the creation of high-fidelity two-qubit quantum entanglement gates for large-scale arrays of hundreds of ions. However, achieving accurate laser amplitude modulation experimentally is quite difficult. On the other hand, while laser frequency or phase modulation is relatively easy to implement experimentally, theoretically designing high-fidelity frequency or phase-modulated quantum entanglement gates for large-scale ion arrays is even more challenging. Previously, frequency- or phase-modulated quantum entangled logic gates in ion traps were only designed for arrays with fewer than a few dozen ions. For example, designing phase-modulated quantum entangled logic gates would require more than one hour of computation time for an array of 60 ions, and would not be applicable to large-scale ion arrays as the number of ions increases exponentially (e.g., reference: Sheng-Chen Liu, Lin Cheng, Gui-Zhong Yao, Ying-Xiang Wang, and Liang-You Peng, Efficient numerical approach to high-fidelity phase-modulated gates in longchains of trapped ions, Phys. Rev. E 107, 035304 (2023)).

[0005] In summary, how to reduce the computation of phase-modulated quantum entangled logic gates and realize quantum entangled logic gates applicable to large-scale ion arrays has become a problem to be solved. Summary of the Invention

[0006] The following is an overview of the subject matter described in detail in this application. This overview is not intended to limit the scope of the claims.

[0007] This disclosure provides a method and apparatus for constructing quantum entangled logic gates, which can reduce the computation of phase-modulated quantum entangled logic gates and realize quantum entangled logic gates suitable for large-scale ion arrays.

[0008] This disclosure provides a method for constructing quantum entangled logic gates, including:

[0009] After decomposing the logic gate into n segments with different phases, the spin-related shift of each phonon mode of the ion in the segment and the phase of each pair of accumulated two qubits between the segments are pre-calculated to obtain the target correlation function.

[0010] The obtained target-related function is transformed into a target function containing a preset vector, wherein the preset vector includes: a first vector. and / or the second vector

[0011] Determine the partial derivative expression of the objective function for the parameters to be optimized, where the parameters to be optimized include: the modulation phase of the logic gate decomposed into n different phase segments.

[0012] Solve for the objective function, the partial derivative of the objective function, and the initialized parameters to be optimized to obtain the local optimal solution for the parameters to be optimized;

[0013] Based on the fidelity of the logic gate corresponding to the obtained local optimal solution, determine whether to construct a logic gate based on the obtained local optimal solution;

[0014] When determining to construct logic gates based on the obtained local optimal solution, the logic gates are constructed based on the obtained local optimal solution.

[0015] On the other hand, this disclosure also provides a computer storage medium storing a computer program, which, when executed by a processor, implements the above-described method for constructing quantum entangled logic gates.

[0016] Furthermore, embodiments of this disclosure also provide a terminal, including: a memory and a processor, wherein the memory stores a computer program; wherein,

[0017] The processor is configured to execute computer programs in memory;

[0018] When the computer program is executed by the processor, it implements the method for constructing quantum entangled logic gates as described above.

[0019] Furthermore, this disclosure also provides an apparatus for constructing quantum entangled logic gates, comprising: an arithmetic unit, a transformation unit, a partial derivative unit, a solution unit, a processing unit, and a construction unit; wherein,

[0020] The operation unit is set up as follows: after decomposing the logic gate into n segments with different phases, the spin correlation shift of each phonon mode of the ion in the segment and the phase of each pair of accumulated two qubits between the segments are preset to obtain the target correlation function.

[0021] The transformation unit is configured to: convert the obtained target-related functions into target functions containing preset vectors, wherein the preset vectors include: a first vector. and / or the second vector

[0022] The partial derivative unit is set as follows: it is an expression for the partial derivative of the objective function that determines the partial derivatives of the objective function with respect to the parameters to be optimized. The parameters to be optimized include: the modulation phase, which is decomposed into n different phase segments by the logic gate.

[0023] The solution unit is set up to solve for the objective function, the partial derivative expression of the objective function, and the initialized parameters to be optimized, and obtain the local optimal solution for the parameters to be optimized.

[0024] The processing unit is configured to determine whether to construct a logic gate based on the obtained local optimal solution, according to the fidelity of the logic gate corresponding to the obtained local optimal solution.

[0025] The construction unit is set as follows: when determining to construct a logic gate based on the obtained local optimal solution, the logic gate is constructed based on the obtained local optimal solution.

[0026] The method for constructing a quantum entangled logic gate in this embodiment performs preset operations on the spin-related shift of each phonon mode of the ions in the segment and the phase of each pair of accumulated two-qubits between segments to obtain a target correlation function. The obtained target correlation function is converted into a target function containing a preset vector. The introduced preset vector improves the calculation speed of the phase-modulated quantum entangled logic gate. After solving for the local optimal solution of the target function, the logic gate is constructed based on the fidelity of the logic gate corresponding to the local optimal solution. This ensures that the constructed logic gate can meet the fidelity requirements and realizes a quantum entangled logic gate applicable to large-scale ion arrays.

[0027] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the application. Other advantages of this application can be realized and obtained by means of the solutions described in the description and the accompanying drawings. Attached Figure Description

[0028] The accompanying drawings are used to provide an understanding of the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application and do not constitute a limitation on the technical solutions of this application.

[0029] Figure 1 A flowchart illustrating a method for constructing quantum entangled logic gates according to embodiments of this disclosure;

[0030] Figure 2 Initialize the graph of the change between the parameter to be optimized and the objective function in this embodiment of the disclosure;

[0031] Figure 3 A structural block diagram of an apparatus for constructing quantum entangled logic gates according to embodiments of this disclosure;

[0032] Figure 4 A schematic diagram illustrating the application of this application of constructing a quantum entangled logic gate based on ytterbium-171 ions;

[0033] Figure 5 This is a schematic diagram illustrating the robustness of logic gate fidelity to ion trap frequency drift noise, which is an application example of this application. Detailed Implementation

[0034] This application describes several embodiments, but these descriptions are exemplary and not restrictive, and it will be apparent to those skilled in the art that many more embodiments and implementations are possible within the scope of the embodiments described herein. Although many possible combinations of features are shown in the drawings and discussed in the detailed description, many other combinations of the disclosed features are also possible. Unless specifically limited, any feature or element of any embodiment may be used in combination with, or may replace, any feature or element of any other embodiment.

[0035] This application includes and contemplates combinations of features and elements known to those skilled in the art. The embodiments, features, and elements disclosed in this application may also be combined with any conventional features or elements to form a unique inventive scheme as defined by the claims. Any feature or element of any embodiment may also be combined with features or elements from other inventive schemes to form another unique inventive scheme as defined by the claims. Therefore, it should be understood that any feature shown and / or discussed in this application may be implemented individually or in any suitable combination. Therefore, the embodiments are not limited except by the limitations imposed by the appended claims and their equivalents. Furthermore, various modifications and changes may be made within the scope of the appended claims.

[0036] Furthermore, in describing representative embodiments, the specification may have presented methods and / or processes as a specific sequence of steps. However, the method or process should not be limited to the specific order of steps described herein, to the extent that it does not depend on such a specific order. As will be understood by those skilled in the art, other sequences of steps are also possible. Therefore, the specific order of steps set forth in the specification should not be construed as a limitation of the claims. Moreover, the claims concerning the method and / or process should not be limited to the steps performed in the written order, and those skilled in the art will readily understand that these orders can be varied and still remain within the spirit and scope of the embodiments of this application.

[0037] Figure 1 A flowchart of a method for constructing quantum entangled logic gates according to embodiments of this disclosure is shown below. Figure 1 As shown, it includes:

[0038] Step 101: After decomposing the logic gate into n segments with different phases, perform preset operations on the spin correlation shift of each phonon mode of the ion in the segment and the phase of each pair of accumulated two qubits between segments to obtain the target correlation function.

[0039] The logic gate decomposition into phase segments in this disclosure embodiment may include: during logic gate operation, dividing the phase into multiple segments, each segment's phase can be controlled independently, thereby achieving more precise control of the logic gate's phase. Logic gate phase segmentation can improve the logic gate's fidelity. In this disclosure embodiment, the phonon mode of an ion refers to a quasi-particle in a crystal, representing the normal mode energy quantum of lattice vibration. The smallest unit of energy for each vibration mode is called a phonon. When implementing a logic gate, the interaction between two qubits needs to be considered. The phase accumulation between segments of the two qubits is an important concept in quantum computing. The phase accumulation between segments of the two qubits refers to the change in the phase of the two qubits due to phase differences between different segments during logic gate operation.

[0040] Step 102: Convert the obtained target correlation function into a target function containing a preset vector, wherein the preset vector includes: a first vector. and / or the second vector Here, the process of converting the target-related function into a target function containing a preset vector can be performed based on mathematical operations. The target function obtained after the conversion contains a first vector and / or a second vector. By introducing the aforementioned preset vector into the target function, the efficiency of subsequent computational processing can be improved.

[0041] Step 103: Determine the partial derivative expression of the objective function for the parameters to be optimized. The parameters to be optimized include: the modulation phase of the logic gate decomposed into n different phase segments. Here, the partial derivative expression of the objective function is obtained by calculating the partial derivatives of the objective function with respect to the parameters to be optimized using advanced mathematics.

[0042] Step 104: Solve for the objective function, the partial derivative expression of the objective function, and the initialized parameters to be optimized to obtain the local optimal solution for the parameters to be optimized;

[0043] In one exemplary embodiment, the solution can be obtained using well-known computational methods skilled in the art, such as the Quasi-Newton's Method (BFGS), the Conjugate Gradient Method, and the Trusted Nonlinear Conjugate Gradient (NCG) algorithm. The BFGS algorithm is an iterative algorithm for solving unconstrained nonlinear optimization problems and is a type of quasi-Newton's method. It updates the search direction by approximating the inverse of the Hessian matrix, thus avoiding the problem of calculating the inverse of the Hessian matrix in each iteration. The Conjugate Gradient Method is an iterative algorithm between the steepest descent method and Newton's method, used to solve large systems of linear equations. It only requires first-order derivative information, but overcomes the slow convergence of the steepest descent method and avoids the problem of storing and calculating the Hessian matrix in Newton's method. The advantages of the Conjugate Gradient Method are fast convergence speed, small memory footprint, and suitability for solving large-scale systems of linear equations. The core idea of ​​the Conjugate Gradient Method is to set the search direction to a linear combination of the previous search direction in each iteration, ensuring that each search direction is conjugate. The Trusted NCG algorithm is a nonlinear optimization algorithm based on the conjugate gradient method for solving unconstrained nonlinear optimization problems. It updates the search direction by approximating the inverse of the Hessian matrix, thus avoiding the need to calculate the inverse of the Hessian matrix in each iteration. The core idea of ​​the Trusted NCG algorithm is to set the search direction to a linear combination of the previous search direction in each iteration, ensuring that each search direction is conjugate. Unlike the traditional conjugate gradient method, the Trusted NCG algorithm calculates a confidence region in each iteration to guarantee that the search direction does not deviate too far from the optimal solution during the iteration process.

[0044] Step 105: Based on the fidelity of the logic gate corresponding to the obtained local optimal solution, determine whether to construct a logic gate based on the obtained local optimal solution; here, the local optimal solution of the parameter to be optimized is determined, that is, the local optimal solution of the modulation phase of the logic gate decomposed into n different phase segments is obtained. Based on the local optimal solution of the modulation phase of the logic gate decomposed into n different phase segments, those skilled in the art can refer to relevant principles to calculate the fidelity of the corresponding logic gate, that is, the fidelity of the logic gate when the modulation phase of the logic gate decomposed into n different phase segments is determined.

[0045] Step 106: When determining the logic gate to be constructed based on the obtained local optimal solution, construct the logic gate based on the obtained local optimal solution.

[0046] In this disclosure, gate fidelity is an indicator used to describe the precision of quantum gate operations, typically expressed as a percentage. Higher fidelity indicates higher precision and smaller error in the quantum gate operation. Gate fidelity is calculated by comparing the difference between an actual implemented quantum gate operation and a theoretically perfect quantum gate operation. The method for calculating fidelity may vary depending on the experimental conditions and the type of quantum gate operation.

[0047] The method for constructing a quantum entangled logic gate in this disclosure decomposes the entangled logic gate into n segments with different phases, introducing sufficient degrees of freedom to achieve a high-fidelity quantum entangled logic gate. Pre-programmed operations are performed on the spin-related shift of each phonon mode of the ions in each segment and the phase of each pair of accumulated biqubits between segments to obtain a target correlation function. This target correlation function is then converted into a target function containing a pre-programmed vector. The introduced pre-programmed vector improves the computational speed of the phase-modulated quantum entangled logic gate. After solving for the local optimal solution of the target function, the logic gate is constructed based on the fidelity of the logic gate corresponding to the local optimal solution. This ensures that the constructed logic gate meets the fidelity requirements, realizing a quantum entangled logic gate applicable to large-scale ion arrays.

[0048] In one exemplary instance, the number of logic gate segments n in this disclosure embodiment may be selected as a positive integer within several hundred; or a positive integer less than twice the total number of ions N.

[0049] In one exemplary instance, this disclosure embodiment may set: parameters to be optimized The initial phase value can be determined by randomly selecting n real numbers, or it can be selected to satisfy symmetry. The real number. Based on common knowledge in the art, the initial value of the parameter to be optimized is... The parameters can be increased or decreased by the same real number as a whole, or by multiples of 2π individually, without affecting their effect.

[0050] In one exemplary instance, the initial parameters to be optimized in this embodiment of the disclosure are: Where θ0 can be a random real number.

[0051] In one exemplary instance, the initialized parameters to be optimized are: Furthermore, the method in this embodiment of the disclosure also includes:

[0052] Scan the objective function as θ0 changes, and determine the global minimum point θ0 in the range of 0 to 2π.m θ, the global minimum point m Assign the value θ0.

[0053] The selection of the random real numbers in this embodiment can be efficiently solved as a single-variable optimization problem by optimizing the optimal value of the objective function under the proposed assumption, or by constructing a new objective function to characterize the degree of deviation from the extreme point position of the objective function. The θ in the initialized parameters to be optimized in this embodiment... i =iθ0,θ i For modulating phase The i-th modulation phase in the equation; by initializing appropriate parameters to be optimized, the design of quantum entangled logic gates can be accelerated; see [link to relevant documentation]. Figure 2 This embodiment of the disclosure finds the global minimum point θ in the range of 0 to 2π by scanning the objective function as θ0 changes. m , and thus Using the initial values ​​of the parameters to be optimized, the global minimum point θ of the constructed objective function can be found. m ,based on Figure 2 For example, θ can be obtained. m ≈0.773π; This embodiment of the present disclosure can scan the objective function using numerical calculation software or other methods known to those skilled in the art; in related technologies, the initial phase value is set to a random real number, and the obtained local optimal solution can only probabilistically reach or approach the global optimal solution depending on the selection of the random initial value. Typically, multiple calculations are required to obtain a high-fidelity quantum entangled logic gate design that meets the requirements. This embodiment of the present disclosure initializes the parameters to be optimized. It can deterministically reach or approach the global optimum. Based on common knowledge in the art, the initial values ​​of the parameters to be optimized... The parameters can be increased or decreased by the same real number as a whole, or by multiples of 2π individually, without affecting their effect.

[0054] In one exemplary instance, the target-related function in this disclosure embodiment includes a function obtained by computation through one of the following methods;

[0055] The function for calculating the fidelity of logic gates is reorganized into a function calculated using spin-dependent shifts and two-qubit phases;

[0056] The function for calculating the fidelity of logic gates is rearranged into a function calculated using spin-dependent shift and two-qubit phase. The partial derivative of this function with respect to a preset factor is then obtained to obtain the fidelity partial derivative function.

[0057] The integral function is obtained by integrating the spin-dependent shift and the phase of the two qubits.

[0058] In one exemplary embodiment, this disclosure calculates the spin-related shift α of each phonon mode of the segmented ions based on the relevant parameters of the ion trap containing the quantum entanglement logic gate and the laser used. jkp and the phase γ of the two qubits accumulated between each pair of segments pq In this disclosure, the subscript j describes the target ion, the subscript k describes the phonon mode, and the subscripts p and q describe the segments from 1 to n. The embodiments of this disclosure can include spin-related shift α. ikp and the phase γ of the two qubits pq It is expressed in matrix form. When determining the spin-related displacement α... ikp and the phase γ of the two qubits pq Subsequently, based on the determined spin-dependent displacement α ikp and the phase γ of the two qubits pq How to obtain the function of logic gate fidelity calculated by spin-dependent shift and two-qubit phase, the fidelity partial derivative function, and the above-mentioned integral function are common knowledge to those skilled in the art, and this disclosure does not limit this; after obtaining the above-mentioned function of logic gate fidelity, fidelity partial derivative function, and integral function, this disclosure uses one of the obtained functions as the above-mentioned target correlation function.

[0059] In one exemplary instance, the preset factor in the embodiments of this disclosure may include parameters that are susceptible to noise and can improve their robustness in the design, such as laser frequency or ion trap frequency.

[0060] In one exemplary instance, this embodiment of the disclosure determines whether to construct a logic gate based on the obtained local optimal solution according to the logic gate fidelity corresponding to the obtained local optimal solution, including:

[0061] When the fidelity of the logic gate corresponding to the local optimal solution is greater than or equal to a pre-set fidelity threshold, the logic gate is constructed based on the obtained local optimal solution;

[0062] When the fidelity of the logic gate corresponding to the local optimal solution is less than the fidelity threshold, one or more parameters of the laser used by the logic gate are adjusted according to the preset strategy until the fidelity of the logic gate corresponding to the local optimal solution is greater than or equal to the fidelity threshold after adjusting one or more parameters of the laser used by the logic gate. Then, the logic gate is constructed based on the newly obtained local optimal solution.

[0063] The parameters of the laser used in the logic gate include one or any combination of the following: logic gate time T, laser detuning μ, number of phase segments n, and time t for each segment. p .

[0064] In one exemplary instance, the fidelity threshold in this disclosure embodiment can be 1-∈, where ∈ represents the quantum precision error target of a single logic gate. The quantum precision error target ∈ of a single logic gate in this disclosure embodiment can be set to a real number between 0 and 1, for example, it can be selected as 10. -5 Up to 10 -2 The real numbers between. In embodiments of this disclosure, a person skilled in the art can adjust the parameters of the laser used in the logic gate based on experience, referring to the value of the logic gate fidelity; for example, extending the logic gate time T, increasing the number of phase segments n.

[0065] In one exemplary instance, after constructing the logic gate, the method of this disclosure embodiment further includes:

[0066] A pre-determined regularization parameter is added to the objective function to adjust the laser intensity used by the logic gate.

[0067] In one exemplary instance, this disclosure embodiment adds a predetermined regularization parameter to the objective function, including: adding the product of ξ and the laser intensity to the objective function; where ξ is a regularization parameter.

[0068] This embodiment of the disclosure introduces a regularization parameter ξ, which reduces the laser intensity requirement of the logic gate while meeting the high fidelity requirement. Increasing the regularization parameter ξ in this embodiment can reduce the required laser intensity, but it may also increase the error of the logic gate. Therefore, the regularization parameter ξ needs to be selected by comprehensively considering the set logic gate error target ∈.

[0069] In one exemplary instance, after the logic gates are constructed, the method of this disclosure embodiment further includes:

[0070] The phase sequence in the local optimal solution of the logic gate is combined with the spin echo to adjust the constructed logic gate.

[0071] This embodiment combines the phase sequence in the local optimal solution of a logic gate with a spin echo, which can be implemented with reference to related technologies, for example, by reducing the designed laser Rabi frequency Ω to [missing information]. Simultaneously, the phase sequence obtained through the local optimal solution is repeated once, with a spin echo added in the middle to reduce the influence of low-frequency noise. In this embodiment, the phase sequence obtained by the solution can also be repeated several times, adjusting the laser Rabi frequency during each repetition to ensure the total two-qubit phase reaches a set value, and adding spin echoes of arbitrary order between each repetition, which can also reduce the influence of low-frequency noise. The type of spin echo used in the above processing of this embodiment can be selected by those skilled in the art with reference to relevant technologies; this embodiment does not limit this selection.

[0072] Figure 3A structural block diagram of the apparatus for constructing quantum entangled logic gates according to embodiments of this disclosure is shown below. Figure 3 As shown, it includes: an arithmetic unit, a transformation unit, a partial derivative unit, a solution unit, and a processing unit; wherein,

[0073] The operation unit is set up as follows: after decomposing the logic gate into n segments with different phases, the spin correlation shift of each phonon mode of the ion in the segment and the phase of each pair of accumulated two qubits between the segments are preset to obtain the target correlation function.

[0074] The transformation unit is configured to: convert the obtained target-related functions into target functions containing preset vectors, wherein the preset vectors include: a first vector. and / or the second vector

[0075] The partial derivative unit is set as follows: it is an expression for the partial derivative of the objective function that determines the partial derivatives of the objective function with respect to the parameters to be optimized. The parameters to be optimized include: the modulation phase, which is decomposed into n different phase segments by the logic gate.

[0076] The solution unit is set up to solve for the objective function, the partial derivative expression of the objective function, and the initialized parameters to be optimized, and obtain the local optimal solution for the parameters to be optimized.

[0077] The processing unit is configured to determine whether to construct a logic gate based on the obtained local optimal solution, according to the fidelity of the logic gate corresponding to the obtained local optimal solution.

[0078] In one exemplary instance, the initial parameters to be optimized in this embodiment of the disclosure are:

[0079] Where θ0 is a random real number.

[0080] In one exemplary instance, the apparatus of this disclosure further includes a scanning unit, configured as follows:

[0081] Scan the objective function as θ0 changes, and determine the global minimum point θ0 in the range of 0 to 2π. m θ, the global minimum point m Assign the value θ0.

[0082] In one exemplary instance, the computation unit of this disclosure embodiment is configured to include obtaining the target-related function by performing computation through one of the following methods:

[0083] The function for calculating the fidelity of logic gates is reorganized into a function calculated using spin-dependent shifts and two-qubit phases;

[0084] The function for calculating the fidelity of logic gates is rearranged into a function calculated using spin-dependent shift and two-qubit phase. The partial derivative of this function with respect to a preset factor is then obtained to obtain the fidelity partial derivative function.

[0085] The integral function is obtained by integrating the spin-dependent shift and the phase of the two qubits.

[0086] In one exemplary instance, the processing unit of this disclosure embodiment is configured as follows:

[0087] When the fidelity of the logic gate corresponding to the local optimal solution is greater than or equal to a pre-set fidelity threshold, the logic gate is constructed based on the obtained local optimal solution;

[0088] When the fidelity of the logic gate corresponding to the local optimal solution is less than the fidelity threshold, one or more parameters of the laser used in the logic gate are adjusted according to the preset strategy until the fidelity of the logic gate corresponding to the local optimal solution obtained after parameter adjustment is greater than or equal to the fidelity threshold. Then, the logic gate is constructed based on the local optimal solution obtained after parameter adjustment.

[0089] The parameters of the laser used in the logic gate include one or any combination of the following: logic gate time T, laser detuning μ, number of phase segments n, and time t for each segment. p .

[0090] In one exemplary instance, the apparatus of this disclosure embodiment further includes a first adjustment unit, configured to:

[0091] A pre-determined regularization parameter is added to the objective function to adjust the laser intensity used by the logic gate.

[0092] In one exemplary instance, the regularization parameter in this disclosure includes: the product of ξ and the laser intensity added to the objective function; where ξ is a regularization parameter.

[0093] In one exemplary instance, the apparatus of this disclosure embodiment further includes a second adjustment unit, configured to:

[0094] The phase sequence in the local optimal solution of the logic gate is combined with the spin echo to adjust the constructed logic gate.

[0095] This disclosure also provides a computer storage medium storing a computer program, which, when executed by a processor, implements the above-described method for constructing a quantum entanglement logic gate.

[0096] This disclosure also provides a terminal, including: a memory and a processor, wherein the memory stores a computer program;

[0097] in,

[0098] The processor is configured to execute computer programs in memory;

[0099] When a computer program is executed by a processor, it implements the method described above for constructing quantum entangled logic gates.

[0100] The following application examples briefly illustrate the embodiments of this disclosure. These application examples are only used to illustrate the embodiments of this disclosure and are not intended to limit the scope of protection of the embodiments of this disclosure.

[0101] Application Examples

[0102] This disclosure proposes a method for constructing a phase-modulated quantum entanglement gate. Given the number of ions in an ion array, the frequencies and normal modes of each phonon mode, the average number of phonons in each phonon mode, the wavelength and spatial direction of the laser used to implement the gate, and two target ions, the method allows for the following: For multi-ion arrays, the gate time T can be set to tens to hundreds of microseconds, the laser detuning μ can be set to tens to hundreds of kilohertz (kHz) near the phonon mode frequencies, and the gate is decomposed into multiple segments with different phases; the time t of each segment with different phases... p The following methods can be used to select t: uniform selection p =T / n; randomly selected as any condition satisfying... The non-negative number; when randomly selected, any number satisfies Based on non-negative numbers, the time of the p-th phase segment and the time of the (n-p+1)-th phase segment satisfy the symmetry t. p =t n-p+1 (p = 1, 2, ..., n). The phase and segmentation of the laser applied to the two target ions can be the same or different: if the phase and segmentation of the laser applied to the two target ions are the same, the total number of optimization parameters is n; if the phase and segmentation of the laser applied to the two target ions are different, the number of segments n1 and n2 of the two target ions, as well as the time of each segment, can be independently selected according to the above method, and the total number of parameters to be optimized is n = n1 + n2. Compared with the related technology, the number of segments of the logic gate can theoretically only be selected as a dozen or so, in the embodiments of this disclosure, the number of segments n of the logic gate can be selected as a positive integer within several hundred or set as a positive integer less than twice the total number of ions N. For ease of illustration, the laser phase and segmentation of the two target ions are selected to be the same, and the values ​​of the initialized optimization parameters are... You can randomly select n real numbers, or randomly select numbers that satisfy symmetry. The values ​​are real numbers, or hypotheses of the form [θ0, 2θ0, ..., nθ0], where θ0 can be random real numbers. Given the above parameters, the spin-dependent shift α of each phonon mode of the ion corresponding to each segment is...ikp and the phase γ of the two qubits accumulated between each pair of segments pq All of these can be calculated using methods known to those skilled in the art, where the subscript i describes the target ion, the subscript k describes the phonon mode, and the subscripts p and q describe the segments from 1 to n. α ikp and γ pq The design of logic gates in this disclosure embodiment can be expressed as parameters to be optimized, in matrix form. Make the objective function Minimize (or maximize the objective function by negating the objective function). This objective function... α can be used ikp and γ pq The error of a logic gate can be directly described by the robustness of the logic gate to noise (using α). ikp and γ pq Optimization of partial derivatives with respect to noise-sensitive parameters or with respect to laser power (with the addition of a regularization parameter ξ). Utilizing α ikp and γ pq The matrix form employs logic gate fidelity known to those skilled in the art, where the partial derivative of the logic gate fidelity with respect to the ion trap frequency or laser frequency, or α... ikp and γ pq The formula for calculating the integral of the objective function can be used to calculate the objective function. Represented as including the first vector and / or the second vector The relevant matrix form. Given the objective function. The parameters to be optimized can be calculated using methods known to those skilled in the art. The analytical expression for the partial derivatives. Given the above objective function. The parameters to be optimized The partial derivatives, the selected initial parameters to be optimized Then, numerical optimization algorithms known to those skilled in the art, such as the BFGS algorithm, conjugate gradient method, and trust NCG algorithm, can be used to solve the local minimum (local optimal solution) of the optimization problem. It should be noted that, given the above formulation of the optimization problem, the obtained local optimal solution does not significantly depend on the optimization algorithm used; therefore, the specific optimization algorithm used should not be considered a limitation of this application. For the found local optimal solution, it can be checked whether the fidelity of its corresponding logic gate satisfies the requirement of being higher than 1-∈. If it satisfies the requirement of being higher than 1-∈, the required logic gate design is obtained; if it does not satisfy the requirement of being higher than 1-∈, the logic gate time T, laser detuning μ, the number of phase modulation segments n, and the time t of each segment can be fine-tuned. pBy adjusting one or more parameters, such as extending the logic gate time T and / or increasing the number of phase modulation segments n, the above process of calculating the local optimal solution and constructing the logic gate is repeated.

[0103] The construction of the quantum entangled logic gate in this embodiment may include: 1. Selecting the logic gate time T, laser detuning μ, the number n of segments n into which the logic gate is decomposed into segments with different phases, and the time t of each phase segment of the logic gate. p The parameters to be optimized are set as follows: the logic gate is decomposed into a modulation phase of n different phase segments. Select the initial value of the parameter to be optimized. The optimization objective for logic gates is set to a fidelity greater than 1 - ∈, where 0 < ∈ < 1 is a parameter describing the quantum precision error target of a single logic gate. 2. Calculate the spin-dependent shift α for each phonon mode corresponding to each segment. ikp and the phase γ of the two qubits accumulated between each pair of segments pq This is expressed in matrix form. 3. Using spin-dependent displacement α ikp and the phase γ of the two qubits pq Describe the objective function of the optimization problem Write it as containing the first vector and / or the second vector 4. Calculate the matrix form. Parameters to be optimized 5. Analytical expression for the partial derivatives of the objective function. The parameters to be optimized The partial derivatives, the selected initial parameters to be optimized Solve the optimization problem to obtain the local optimal solution for the parameters to be optimized. 6. Check whether the fidelity of the logic gate corresponding to the obtained local optimal solution is higher than the target of 1-∈. If the fidelity of the logic gate corresponding to the local optimal solution satisfies the target of 1-∈, then the required logic gate design is obtained based on the local optimal solution; if the fidelity of the logic gate corresponding to the local optimal solution does not satisfy the target of 1-∈, change the logic gate time T, laser detuning μ, the number of segments n with different phases in the logic gate decomposition, and the time t of each segment. p One or more of the above processes are repeated. In this embodiment, the logic gate design problem is formulated as an optimization problem of the spin-dependent shift of the target ion and the phase of the two qubits (an optimization problem is the problem of finding the optimal solution from all feasible solutions under certain constraints. This process can be described by a mathematical model, usually involving an objective function and some constraints). The objective function of this optimization problem is... Represented as the first vector and / or the second vector The relevant matrix form is used to analytically solve the objective function. Phase of the parameter to be optimized on each segment The partial derivatives are used to efficiently solve this optimization problem.

[0104] See Figure 4 With target ions as 171 Yb + Taking ions as an example, the vertical axis in the figure represents the phase of each segment of the logic gate, and the p-th segment on the horizontal axis corresponds to the phase θ of that segment on the vertical axis. p In this embodiment of the disclosure, one consists of N=100 171 Yb + Ions arranged at equal intervals of 5 micrometers, in ω x A one-dimensional ion array with a radial trap frequency of 2π × 2.5 MHz in the x-direction is cooled to approximately one phonon per normal mode in the x-direction. A pair of 355 nm Raman lasers propagating in opposite directions along the x-direction are used to realize a phase-modulated quantum entangled logic gate. For the two target ions at the center of the ion array, the target error of the logic gate is set to ∈ = 10. -5 The logic gate time T = 180 μs can be selected, divided into n = 150 segments, and Raman laser detuning can be set to centroid mode ω. x The above δ = 2π × 25kHz, i.e., μ = ω x +δ. Using the above design method, the attached value can be obtained within tens of seconds. Figure 4 The phase modulation sequence has a theoretical error of 5 × 10⁻⁶ for the logic gates. -6 The design requirements are met, and the required laser intensity is calculated to be the Rabi frequency Ω = 2π × 121.5 kHz. A pre-determined regularization parameter is added to the objective function to adjust the laser intensity used by the logic gate. For example, by adding a regularization parameter ξ = 10, the required laser intensity can be reduced from the Rabi frequency Ω = 2π × 121.5 kHz to the Rabi frequency Ω = 2π × 112.2 kHz. It should be noted that the phase sequence of the parameters to be optimized in this embodiment is... The parameters can be increased or decreased by the same real number as a whole, or by multiples of 2π individually, without affecting the effect.

[0105] In addition to using the fidelity of the quantum entangled logic gate as an optimization objective, this disclosure also incorporates the robustness of the quantum entangled logic gate to parameter drift as an optimization objective, thus designing a noise-insensitive quantum entangled logic gate. This disclosure expresses the objective function as the integral of the spin-dependent shift and the phase of the two qubits over time, and expresses it as the parameters to be optimized. The function, further expressed as containing the first vector, is... and / or the second vector Related matrix forms; such as Figure 5 As shown, the vertical axis represents the value δF of the logic gate's fidelity deviating from 1, where δF = 1 - F, and F is the logic gate's fidelity. The embodiments of this disclosure demonstrate robustness to parameter drift; a change in the ion trap frequency Δω corresponds to a change in fidelity δF. The designed quantum entangled logic gate can resist the main noise source of the ion trap system, namely, the error caused by the shift in the ion trap frequency. The logic gate is relatively insensitive to ion trap frequency shifts; ideally, the error is less than 10. -5 The error is less than 10 when the frequency shifts by ±2kHz. -3 The error is less than 10 when the frequency shifts by ±4kHz. -2 In comparison, if robustness is not used as the optimization objective, but only logic gate fidelity is used, the error will typically exceed 10 when the frequency shifts by ±1kHz. -3 .

[0106] The embodiments disclosed herein can efficiently design high-fidelity quantum entangled logic gates for large-scale ion arrays, and the phase modulation method used is easy to implement in current ion trap systems; therefore, it has important scientific research value and broad industrial application prospects in realizing scalable ion trap quantum computers.

[0107] It will be understood by those skilled in the art that all or some of the steps, systems, or apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all components may be implemented as software executed by a processor, such as a digital signal processor or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software may be distributed on a computer-readable medium, which may include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

Claims

1. A method of constructing a quantum entanglement logic gate, characterized by, The method comprises the following steps: After the logical gate is decomposed into n segments with different phases, preset operations are performed on the spin-dependent displacement of each phonon mode of the ions in the segments and the accumulated two-qubit phase between each pair of segments to obtain a target correlation function; The obtained target correlation function is converted into a target function containing preset vectors, wherein the preset vectors include: a first vector and / or a second vector determining a target function partial derivative expression of the target function with respect to an optimization parameter, wherein the optimization parameter comprises a modulation phase of a logical gate decomposition into n different phase segments Solving the target function, the partial derivative expression of the target function and the initialized to-be-optimized parameters obtains a local optimal solution of the to-be-optimized parameters; According to the logical gate fidelity corresponding to the obtained local optimal solution, it is determined whether to construct the logical gate according to the obtained local optimal solution; When it is determined to construct the logical gate according to the obtained local optimal solution, the logical gate is constructed according to the obtained local optimal solution.

2. The method of claim 1, wherein, The initialized parameter to be optimized is Wherein, θ0 is a random real number.

3. The method of claim 2, wherein, The initialized parameter to be optimized is When the parameter to be optimized is a parameter of a neural network, the method further comprises: scanning the objective function for changes in θ0determines the global minimum point θ0in the range 0 to 2π m assigns the global minimum point θ0 m assigns θ0.

4. The method of claim 1, wherein, The target correlation function comprises a function obtained by performing one of the following operations: The function for calculating the logical gate fidelity is arranged to be a function calculated based on the spin-dependent displacement and the two-qubit phase; After the function for calculating the logical gate fidelity is arranged to be a function calculated based on the spin-dependent displacement and the two-qubit phase, the partial derivative of the obtained function with respect to a preset factor is obtained to obtain a fidelity partial derivative function; The spin-dependent displacement and the two-qubit phase are integrated to obtain an integral function.

5. The method according to any one of claims 1 to 4, characterized in that, The method further comprises the following steps: When the logical gate fidelity corresponding to the local optimal solution is greater than or equal to a preset fidelity threshold, it is determined to construct the logical gate according to the obtained local optimal solution; When the logical gate fidelity corresponding to the local optimal solution is less than the fidelity threshold, one or more parameters of the laser used for the logical gate are adjusted according to a preset strategy until the logical gate fidelity corresponding to the local optimal solution obtained after the parameter adjustment is greater than or equal to the fidelity threshold, and then it is determined to construct the logical gate according to the local optimal solution obtained after the parameter adjustment; The parameters of the laser used by the logic gate include one or any combination of the following: logic gate time T, laser detuning μ, number of phase segments n, and time t of each segment p .

6. The method according to any one of claims 1 to 4, characterized in that, After the logical gate is constructed, the method further comprises the following steps: A predetermined regularization parameter term is added to the target function to adjust the laser intensity of the laser used for the logical gate.

7. The method of claim 6, wherein, The method further comprises the following steps: The product of ξ and the laser intensity is added to the target function. Wherein, ξ is the regularization parameter.

8. The method according to any one of claims 1 to 4, wherein after the logical gate is constructed, the method further comprises the following steps: The phase sequence in the local optimal solution of the logical gate is combined with a spin echo to adjust the constructed logical gate.

9. A computer storage medium, wherein a computer program is stored in the computer storage medium, and the computer program is executed by a processor to implement the method for constructing a quantum entangled logical gate according to any one of claims 1 to 8.

10. A terminal comprising: A memory and a processor, wherein the memory stores a computer program; The processor is configured to execute the computer program in the memory; The computer program is executed by the processor to implement the method for constructing a quantum entangled logical gate according to any one of claims 1 to 8.

11. An apparatus for constructing a quantum entanglement logic gate, comprising: The method comprises the following steps: An operation unit, a conversion unit, a partial derivative unit, a solving unit, a processing unit and a construction unit; wherein The operation unit is configured to: after decomposing the logical gate into n segments with different phases, performing preset operations on the spin-dependent displacement of each phonon mode of the ion in the segment and the accumulated two-qubit phase between each pair of segments, to obtain a target correlation function; The conversion unit is configured to convert the obtained target correlation function into a target function containing preset vectors, wherein the preset vectors include: a first vector and / or a second vector The partial derivative unit is configured to determine a target function partial derivative expression of a target function with respect to an optimization parameter, wherein the optimization parameter comprises a modulation phase of a logical gate decomposition into n different phase segments The solving unit is configured to: solve the target function, the partial derivative expression of the target function, and the initialized to-be-optimized parameters, to obtain a local optimal solution of the to-be-optimized parameters; The processing unit is configured to: determine whether to construct the logical gate according to the local optimal solution obtained according to the logical gate fidelity corresponding to the local optimal solution obtained; The constructing unit is configured to: when it is determined to construct the logical gate according to the local optimal solution obtained, construct the logical gate according to the local optimal solution obtained.

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