Universal quantum state optimization preparation method and apparatus based on quantum equivalent gates

Abstract

The application provides a universal quantum state optimization preparation method and device based on a quantum equivalent gate, the method first performs subspace decomposition on an n-dimensional target quantum state, reversely constructs a preparation gate sequence based on a two-dimensional unitary operation, and optimizes the number of required quantum logic gates to a minimum of n-1 by merging and moving a phase gate; in a dynamic evolution stage, the difference caused by the equivalent gate operation is compensated by adjusting a control parameter, evolution equivalence in a closed or open quantum system is ensured, and finally, the target quantum state information is accurately recovered by parameterizing and correcting a state tomography measurement operation. The application provides a universal quantum state preparation method with linear complexity of quantum state dimensions for n-dimensional quantum state preparation in a closed or open quantum system, high-efficiency, universal quantum state preparation is realized with the least quantum gate resources, experimental difficulty is significantly reduced, and preparation efficiency and system adaptability are improved.

Description

Technical Field

[0001] This invention belongs to the field of quantum computing technology, specifically relating to a general quantum state optimization preparation method and apparatus based on quantum equivalent gates. Background Technology

[0002] Quantum state preparation is a core foundation of quantum information technology, and its importance is reflected in multiple aspects. Quantum states are the basic units of quantum information processing; whether it's quantum computing, quantum communication, or quantum sensing, quantum states are required as carriers of information. In particular, the efficiency of quantum state preparation directly affects the performance and reliability of quantum systems. For example, in quantum computing, efficient and high-precision quantum state preparation not only greatly reduces experimental difficulty but also helps maintain the coherence of the quantum system and improve the fidelity of quantum states.

[0003] Generally, to prepare a Universal quantum states often require an exponential number of qubit gate operations. However, as the number of qubits increases, the fabrication of universal quantum states typically requires deep quantum circuits and a large number of quantum gate operations. This is not only severely constrained by the finite coherence time of current noisy quantum hardware, but also greatly increases the complexity and error probability of experiments, posing significant technical challenges to experimental fabrication. Although some optimization methods can reduce the number of qubits, these are generally only simplifications of polynomial complexity.

[0004] In the existing technology, there are various schemes for quantum state preparation, but all of them have certain limitations. For example, Chinese invention patent application CN119338020A (publication date: January 21, 2025) discloses a quantum state preparation method that designs dedicated quantum circuits for a specific type of quantum state (quadratic function quantum state). Although the circuit depth can be reduced through structural optimization, its applicability is limited to specific function forms and lacks universality. Another Chinese invention patent application CN110942151A (publication date: March 31, 2020) discloses a quantum state tomography method, which focuses on the characterization and reconstruction of quantum states and uses quantum state tomography to infer unknown states. However, the technical solution itself has huge measurement overhead and does not solve the fundamental problem of how to efficiently prepare the target state. In addition, Chinese invention patent application CN117642754A (publication date: March 1, 2024) discloses a method for preparing a target quantum state of a quantum system. It uses an iterative evolution method to prepare a stable target state, such as a ground state. By calculating evolution parameters through multiple iterations, the target state is gradually approximated. Although it can avoid some of the problems caused by the variational method, the iterative process still requires multiple quantum measurements and feedback, which is complex and time-consuming, and is quite sensitive to errors in intermediate steps.

[0005] Therefore, optimizing the preparation of quantum states using fewer logic gates is a crucial technical challenge for researchers, aiming to further simplify experimental procedures and improve the fidelity of state preparation. Furthermore, real quantum systems are essentially open quantum systems, making the efficient preparation of quantum states and the real-time reading of the system's dynamic evolution information of open quantum systems of significant practical importance. Current technologies for quantum state preparation in open quantum systems that balance versatility, efficiency, and high precision are still lacking, necessitating a focus on methods specifically designed for open quantum systems. The paper proposes a method for preparing quantum states with linear complexity in terms of quantum state dimensions, requiring only [a certain amount of time / efficiency]. The single-qubit gate operation significantly reduced the difficulty of the experiment. Summary of the Invention

[0006] This invention addresses the aforementioned technical problems by proposing a universal quantum state optimization preparation method and apparatus based on quantum equivalence gates. The method, through the concept of quantum equivalence gates, only requires… A single qubit gate completes the process. The preparation of arbitrary quantum states requires a minimum number of qubit gates, and provides corresponding dynamic control and a final state tomography method, greatly improving the efficiency of quantum state preparation. Furthermore, this method is applicable not only to closed systems but also to open quantum systems.

[0007] A general quantum state preparation method based on quantum equivalent gates, comprising: Step 110, input the material to be prepared We determine the target quantum state and perform quantum state analysis to ensure that the target quantum state satisfies the normalization condition. Step 120: The target quantum state is deduced in reverse to obtain the preparation gate sequence of the target quantum state; the preparation gate sequence contains multiple two-dimensional unitary operations for preparing the quantum state; Step 130, use two-dimensional unitary operation to... The Wiehirbert space is divided into multiple two-dimensional subspaces, and each two-dimensional unitary operation acts on one of the two-dimensional subspaces. Step 140 involves optimizing the preparation gate sequence, including: decomposing each two-dimensional unitary operation into a combination of rotation gates and phase gates, and reducing the actual number of gate operations to be performed by shifting and merging phase gates. Step 150: Construct equivalent gates using an equivalent gate sequence, including: retaining only the core rotation gate operation as the equivalent gate sequence, omitting all global phase gates and mergeable rotation gates. Axial phase gates rewrite the unitary operation that prepares the gate sequence into an equivalent gate operation. Step 160, performing dynamic control, includes: initializing the preparation system to the ground state based on the dynamic evolution process, and applying the equivalent gate operation to the preparation system to obtain the equivalent initial state; adjusting the control parameters according to the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate to obtain the quantum state after dynamic evolution; Step 170: Perform quantum state tomography on the dynamically evolved quantum state using a modified state tomography operation; the modified state tomography operation removes the omitted global phase gate and the surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

[0008] On the other hand, the present invention provides a universal quantum state optimization preparation device based on quantum equivalent gates, comprising: The first module is used to input the material to be prepared. We determine the target quantum state and perform quantum state analysis to ensure that the target quantum state satisfies the normalization condition. The second module is used to reverse-engineer the target quantum state to obtain the preparation gate sequence of the target quantum state; the preparation gate sequence contains multiple two-dimensional unitary operations for preparing the quantum state; The third module is used to utilize two-dimensional unitary operations to... The Wiehirbert space is divided into multiple two-dimensional subspaces, and each two-dimensional unitary operation acts on one of the two-dimensional subspaces. The fourth module is used to optimize the preparation of gate sequences, including: decomposing each two-dimensional unitary operation into a combination of rotation gates and phase gates, and reducing the actual number of gate operations to be performed by shifting and merging phase gates; The fifth module is used to construct equivalent gates using equivalent gate sequences, including: retaining only the core rotation gate operation as the equivalent gate sequence, omitting all global phase gates and mergeable rotation gates. Axial phase gates rewrite the unitary operation that prepares the gate sequence into an equivalent gate operation. The sixth module is used for dynamic control, including: initializing the preparation system to the ground state based on the dynamic evolution process, and applying the equivalent gate operation to the preparation system to obtain the equivalent initial state; adjusting the control parameters according to the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate to obtain the quantum state after dynamic evolution; The seventh module is used to perform quantum state tomography on the dynamically evolved quantum state using a modified state tomography operation; the modified state tomography operation removes the omitted global phase gate and the surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

[0009] Compared with the prior art, the technical effects of the present invention include: (1) A major breakthrough in quantum resource utilization has been achieved: the number of quantum gates has been reduced to the theoretical lower limit. Traditional methods: prepare a Arbitrary quantum states typically require multiple quantum gate operations, usually on the order of 1 / 2 quanta. For example, as is known from existing technology, a three-dimensional state initially requires six gates, while this invention reduces the number of required core quantum logic gates to [number missing] through equivalent gate operations and phase gate shifting and merging. The number of gates required (e.g., only 2 gates for a 3D state and 3 gates for a 4D state) represents not only a reduction in quantity but also the theoretical minimum limit. In quantum computing, each logic gate operation introduces error and consumes coherence time; the drastic reduction in the number of gates directly translates to the ultimate optimization of resource utilization efficiency. Fewer gates mean shorter quantum circuit depth. Shallow circuits are less affected by noise, which greatly improves the feasibility of implementing the scheme on near-term hardware in the current era of Noisy Medium-Scale Quantum (NISQ).

[0010] (2) The method of the present invention significantly improves the preparation efficiency and fidelity: fewer operations mean shorter state preparation time, which can significantly shorten the overall running time and improve the computational efficiency for computational tasks or quantum algorithms that require frequent initialization of quantum states; in quantum hardware, each gate operation has a certain error rate. Reducing the number of gates directly reduces the probability of errors, thus making it possible to eventually prepare target quantum states with higher fidelity.

[0011] (3) The method has greater applicability: it is applicable to both closed and open quantum systems, through the control parameters in subsequent dynamic parameters (such as the control parameters in the Hamiltonian). The method of this invention coordinates the adjustment of the measurement operation (state tomography) to compensate for the effects caused by the gate operation omitted in the equivalent gate step. This "front-end simplification and back-end compensation" approach makes the method of this invention also applicable to open quantum systems with dissipation and decoherence, greatly expanding its application scope and usage scenarios. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0013] Figure 1This is a flowchart illustrating the steps of a general quantum state optimization preparation method based on quantum equivalent gates in one embodiment of the present invention. Figure 2 This is a schematic diagram of the quantum state preparation and readout process in one embodiment of the present invention; Figure 3 This is a schematic diagram of the basic process of an optimization method for constructing equal school gates in one embodiment of the present invention. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. 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.

[0015] In one embodiment, such as Figure 1 As shown, this invention provides a general quantum state optimization preparation method based on quantum equivalent gates, comprising: Step 110, input the material to be prepared We determine the target quantum state and perform quantum state analysis to ensure that the target quantum state satisfies the normalization condition. Step 120: The target quantum state is deduced in reverse to obtain the preparation gate sequence of the target quantum state; the preparation gate sequence contains multiple two-dimensional unitary operations for preparing the quantum state; Step 130, use two-dimensional unitary operation to... The Wiehirbert space is divided into multiple two-dimensional subspaces, and each two-dimensional unitary operation acts on one of the two-dimensional subspaces. Step 140 involves optimizing the preparation gate sequence, including: decomposing each two-dimensional unitary operation into a combination of rotation gates and phase gates, and reducing the actual number of gate operations to be performed by shifting and merging phase gates. Step 150: Construct equivalent gates using an equivalent gate sequence, including: retaining only the core rotation gate operation as the equivalent gate sequence, omitting all global phase gates and mergeable rotation gates. Axial phase gates rewrite the unitary operation that prepares the gate sequence into an equivalent gate operation. Step 160, performing dynamic control, includes: initializing the preparation system to the ground state based on the dynamic evolution process, and applying the equivalent gate operation to the preparation system to obtain the equivalent initial state; adjusting the control parameters according to the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate to obtain the quantum state after dynamic evolution; Step 170: Perform quantum state tomography on the dynamically evolved quantum state using a modified state tomography operation; the modified state tomography operation removes the omitted global phase gate and the surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

[0016] The main technical idea of ​​this invention is to design gate sequence operations based on quantum equivalent gates, which will target general... The number of qubit gates (gate operations) required for the preparation of 3D quantum states, from the general... The number of orders of magnitude decreased to This invention significantly improves the efficiency of quantum state preparation. Furthermore, the universal preparation method provided by this invention is applicable not only to closed systems but also to the optimized preparation of quantum states in open quantum systems. It also provides universally applicable, operational-level kinetic control and state tomography methods during the preparation and experimental processes, such as… Figure 2 As shown.

[0017] Specifically, in step 110, let... The target quantum state of dimension is represented as , , It is a positive integer; the target quantum state satisfies at least the following normalization condition: .

[0018] The Taking values ​​in the complex field, it represents the probability amplitude of the target quantum state, describing the core information of the quantum state. This indicates that when the system is measured, the quantum state collapses to the first... The probability of each ground state (energy level); .

[0019] Furthermore, in step 120, the target quantum state is... By performing reverse derivation, the preparation gate sequence of the target quantum state is obtained.

[0020] Due to the existence of unitary operation This allows the target quantum state to return to its ground state. ,that is: ; This means It can be done Inverse operation (Hermitian conjugate, corresponding matrix form satisfies) , (It is the identity matrix), from the ground state The inverse operation is obtained through evolution. It is still a monotonous operation, and ,in, yes The reverse operation, The above evolutionary process can be represented as: ; Among them, the ground state each It is a two-dimensional unitary operation. ( ) constitutes the preparation gate sequence of the target quantum state.

[0021] The physical significance of two-dimensional unitary operations lies in the fact that by using a series of precisely controlled qubit gate operations, the probability amplitude is transferred between two states and the phase is adjusted, thereby realizing the construction of a specific quantum state (target quantum state). It can only change the energy level (quantum state) to and The probability amplitude above, and precisely reduce a portion of the probability amplitude from Transferred to Above, and set at the same time and The relative phase between states. In quantum mechanics, phase determines the interference mode. By controlling the relative phase, the amplitude of a specific state can be enhanced or suppressed, thereby achieving amplification or suppression effects in the preparation of quantum states.

[0022] Furthermore, in step 130, the following will be performed: Wichbert space Divided into multiple two-dimensional subspaces ,in: ; For ease of explanation, the two-dimensional subspace will be used. Abbreviated as Then the two-dimensional unitary operation Acting on the corresponding two-dimensional subspace superior, And keep other energy levels unchanged. This "function" is a highly complex, "well-encapsulated" macroscopic operational instruction, which is still defined as a whole... Transformations on Wichlbert space, rather than a single, fundamental quantum gate. Based on Because of its high-dimensionality, it cannot be directly realized experimentally and needs to be further decomposed into a sequence of gates.

[0023] In theory, any action on a two-dimensional subspace Two-dimensional unitary operations (unitary matrices) on [a surface]. It can utilize the core operations that produce the effect to Represented in matrix form: ; in, , , and Represents matrix elements in the complex field, used to characterize For two-dimensional subspace The key role played (acting in the ground state) and (Core operations on the platform).

[0024] The It can be broken down into the following gate operations (logic gates): ; in, , , and These are real-number parameters used to construct the decomposition of unitary operations into gate operations; specifically, It is the global phase factor; This is the first step of the door operation, indicating that it involves going around... Axis rotation The revolving door It is the initial phase provided by the first gate operation; This is the second step of the door operation, indicating that you need to go around. Axis rotation The revolving door It is the angular parameter used to control the probability amplitude transfer in the second-step gate operation, changing the dimension of the quantum state on the Bloch sphere; This is the third step of the door operation, indicating that you need to go around. Axis rotation The revolving door It is the relative phase of the third gate operation. , , and They are given by the following formulas respectively: ; ; ; ; In the above formula, the function Used to determine the argument (phase angle) of a complex number. This indicates the calculation of the modulus of a complex number.

[0025] In fact, around the coordinate axes , or Rotation Revolving doors at angles are defined by the following formulas: ; ; .

[0026] As can be seen from the definition, around A rotating door with a rotating axis It only changes the relative phase, not the probability amplitude between quantum states, and is therefore also called a phase gate; The decomposition requires three gate operations, which can be regarded as a combination of a rotation gate and a phase gate.

[0027] Based on the gate operation decomposition theory of the two-dimensional unitary operation described above, in step 140, the preparation gate sequence of the target quantum state is optimized, including: Each two-dimensional unitary operation in the preparation gate sequence It can be broken down into a combination of revolving door and phase door operations: ; in, , , and These are the real-number parameters used to construct the decomposition backdoor operation; at this point, It is the global phase factor; This is the first step of the door operation. It is the initial phase provided by the first gate operation; This is the second step of the door operation. It is the angle parameter used to control the probability amplitude shift in the second step of the gate operation; This is the third step of the door operation. It is the relative phase of the third-step gate operation; and Indicates phase gate, It's a pure revolving door; , and They are given by the following formulas respectively: ; ; .

[0028] Phase gate The first gate operation is moved to the next step and merged with the second and third gate operations, reducing the number of required gate operations and resulting in an optimized two-dimensional unitary operation. Specifically: ; Among them, the merged revolving door operation , defined by the following formula: ; In this embodiment, , .

[0029] Specifically, in step 150, an equivalent gate is constructed using an equivalent gate sequence, including: retaining only the core rotation gate operation, omitting all global phase gates and mergeable z-axis phase gates, resulting in... One core gate, as an equivalent gate sequence; Two adjacent two-dimensional subspaces and The optimized two-dimensional unitary operations obtained above are combined as shown in the following equation: ; in, , It can be seen that originally It requires 6 door operations, but after moving and merging, it only requires 4 door operations; Using the same approach, phase gates for all optimized two-dimensional unitary operations in the preparation gate sequence (including...) The operation and global phase are shifted and merged, and the resulting adjustments are all made through the rotating door operation. The parameters in the data are used to restore it; exist A unitary operation consisting of two-dimensional unitary operations In the middle, only retain A core rotary gate operation, omitting all global phase gates and mergeable z-axis phase gates. ,Will Rewritten in tensor product form as an equivalent gate sequence: ; in, , For phase gate; It is a tensor product; It is an equivalent gate.

[0030] The core of the technological innovation of this invention lies in the fact that it does not require complete implementation. Instead of performing all departmental operations, only the equivalent gate needs to be executed. middle The equivalent gate sequence corresponds to a rotating gate operation. The differences caused by the equivalent gates can be completely recovered by adjusting the system parameters and state tomography operations in the subsequent dynamics process, thus obtaining the exact same dynamics and state readout information.

[0031] Furthermore, in step 160, dynamic regulation is performed, including: Step 161: Based on the dynamic evolution process, initialize the preparation system to the ground state, and apply the equivalent gate operation to the preparation system to obtain the equivalent initial state, such as... Figure 3 As shown.

[0032] For open quantum systems, the master equation is dynamically satisfied: ; in, For Liu Weier's superoperator, It is the density matrix of the quantum system. It is the derivative with respect to time, representing the rate of change of the state of a quantum system with time; It is the unitary evolution of a quantum system, which is the part governed by the Schrödinger equation; It is the imaginary unit; The Hamiltonian is a function of the control parameters that govern the transitions between quantum energy levels. To describe from energy level arrive Dissipation operators between states.

[0033] The aforementioned master equation can be expressed in Liouville space (i.e., the tensor product of two Hilbert spaces). The vectorization is performed in the resulting high-dimensional space, thus giving the matrix form of the Liouville hyperoperator: ; in, yes Dimensional unit operator, This indicates taking the conjugate complex number. This indicates the matrix transpose.

[0034] In the quantum system After time elapses, the state of the quantum system becomes: .

[0035] Will Substituting the equivalent gate into the state of the quantum system, we get: ; The initial state prepared by the equivalent gate Defined as the equivalent initial state, it can be expressed as: ; The equivalent initial state It is identical to the target quantum state in probability amplitude, but differs in relative phase, such as Figure 3 As shown.

[0036] Step 162: Based on the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate, adjust the control parameters to obtain the dynamically evolved quantum state, including: Representing the state of a quantum system using an equivalent initial state: .

[0037] Assume the Hamiltonian of the quantum system is ,in: ; ; ; ; In the above formula, and Hamiltonian and The control parameters that control the transitions between quantum energy levels.

[0038] The dissipation term of the Liouville superoperator has no effect on the shift of the phase gate operation. Therefore, the phase gate operation in the state of the quantum system can be further shifted after the dynamical manipulation, resulting in: ; in: ; .

[0039] In actual initial state preparation operations, the phase gate operation at the beginning of the above equation... No need to perform this, then the control parameters will be used during the dynamic process. The corresponding adjustment is as follows: This allows us to obtain the final equivalent solution that guarantees dynamic equivalence.

[0040] It should be noted that for closed quantum systems, since the quantum state evolution process is unitary, the omitted phase gate can be directly adjusted and compensated through the control parameters of the Hamiltonian; however, for open quantum systems with dissipation or decoherence, the definition of the Liouville superoperator still allows for adjustment of the operator. The parameters in (from) and This is used to compensate for the gate operations omitted in the early stages. This compensation does not depend on whether the system is coupled with the environment, and only requires that the dynamics be linear (whether unitary or non-unitary). It does not require the actual execution of all the initial gate operations. The preparation and evolution of the target quantum state can be realized in closed or open systems simply by constructing equivalent gates, adjusting parameters, and measuring compensation (state tomography).

[0041] Furthermore, in step 170, information is read, that is, the state is... Perform state chromatography. Since initially, the prepared state is... Instead , The true state of a quantum system at any given moment is: .

[0042] Therefore, it is necessary to use state tomography to remove the steps omitted in step 150 when obtaining the equivalent gate. The impact of the operation will be compensated for. The specific operation needs to be adjusted according to the dimension of the quantum state, which will be elaborated in subsequent embodiments.

[0043] Preferably, in one embodiment, The matrix form can be set as: ; that is, , , and ; in, yes The conjugate of complex numbers; It is the cumulative amplitude, defined by the following formula: ; The above In the definition of a matrix, " The '' sign guarantees the unitarity of the operation, while all other energy levels are in this operation. The following remains unchanged.

[0044] In one embodiment, the dimension of a quantum state For any two dimensions ( quantum state By employing an optimized quantum state preparation method based on quantum equivalent gates, the number of qubit gate operations required for quantum state preparation is reduced from three in conventional methods to [number missing]. It provides corresponding dynamic control and final state tomography methods to improve the efficiency of quantum state preparation.

[0045] Specifically, in this embodiment, the steps of the quantum state optimization preparation method based on quantum equivalent gates include: Step 210, Two-dimensional target quantum state It satisfies the normalization condition: ; Step 220, for any two-dimensional target quantum state ,according to For the target quantum state By reverse derivation, we can see that: ; At this point, the preparation gate sequence contains only one two-dimensional unitary operation. ,that is, .

[0046] Step 230: Initialize the system in a quantum state. ,at this time, Hilbert space of vid It is itself a two-dimensional subspace Two-dimensional unitary operation Directly acting on two-dimensional Hilbert space superior.

[0047] Then a two-dimensional unitary operation is performed on the quantum system. , The specific matrix expression is as follows: ; Step 240: Decompose the two-dimensional unitary operation into the following gate operations: ; Step 250, perform the phase gate operation from step one. Move it to the right and merge it to get: ; The revolving door operation This is the equivalent gate constructed (the equivalent gate sequence contains only one rotating gate operation).

[0048] Step 260, perform dynamic regulation, including: After the quantum system evolves at time t, the state of the quantum system can be represented as follows: ; Will Substituting the equivalent gate into the state of the quantum system, we get: ; The equivalent initial state prepared using the equivalent gate is: .

[0049] Using the equivalent initial state to represent the state of the quantum system, we obtain: .

[0050] Assume the Hamiltonian of the quantum system is ,according to: , get: ; in, , .

[0051] In actual initial state preparation operations, the phase gate operation at the very beginning of the quantum system's state is... No need to perform this, then the control parameters will be used during the dynamic process. The corresponding adjustment is as follows: This allows us to obtain the final equivalent solution that guarantees dynamic equivalence.

[0052] Step 270: Read information and check the status. Perform state tomography to remove the omitted global phase gate and surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

[0053] Since initially, the prepared state is Instead , The true state of a quantum system at any given moment is Therefore, it is necessary to use state tomography to remove the previously omitted... The impact of the operation was made up for.

[0054] In general, that is, without considering the construction of equivalent gates based on translation (shift and merge) operations, a total of 4 tomography operations are required for a two-dimensional quantum state, namely: ; However, regarding the quantum states in the equivalent scheme When performing state tomography, considering the influence of translation operations, in order to ensure that the state tomography results are consistent with the expected state of the dynamic system... To be equal, the aforementioned state tomography operation needs to be modified as follows: ; ; .

[0055] In one embodiment, the dimension of a quantum state For any three-dimensional target quantum state By employing a quantum state preparation method based on quantum equivalent gates, the number of qubit gates required for quantum state preparation is reduced from the general optimization of 6 to [number missing]. It provides corresponding dynamic control and final state tomography methods to improve the efficiency of quantum state preparation.

[0056] The specific methods and steps include: Step 310, Three-dimensional target quantum state It satisfies the normalization condition: ; Step 320, for any three-dimensional target quantum state ,according to For the target quantum state By reverse derivation, we can see that: ; At this point, the preparation gate sequence contains only two two-dimensional unitary operations. and ,that is, .

[0057] Step 330: Initialize the system in a quantum state. ,at this time, Hilbert space of vid Divided into two-dimensional subspaces and Two-dimensional unitary operation and Acting on two-dimensional subspaces respectively and superior.

[0058] The and The specific matrix expression is as follows: ; ; Will and Press in two-dimensional subspace and The actual effects produced above are expressed as follows: ; .

[0059] Step 340, will and These can be broken down into the following gate operations: ; ; The two decompositions described above require a total of 6 gate operations and 2 global phase gate operations; the subscripts 0,1 or 0,2 represent operations on the subspace. or The (qubit) gate operation performed.

[0060] Step 350 optimizes the operation for preparing the gate sequence, including: Will and The first step in decomposition is the phase gate operation. Move it to the right and merge it to get: ; ; The unitary operation formed by two two-dimensional unitary operations Only two core rotary gate operations are retained, omitting all global phase gates and mergeable z-axis phase gates. ,Will Rewritten as the (tensor) product form of the equivalent gate sequence: ; in ,

[0061] make: It is a global phase gate. It is a mergeable phase gate around the z-axis. and Construct an equivalent gate sequence, The equivalent gate that constitutes a quantum system. The core value of the quantum state preparation method designed in this invention lies in the fact that it only requires performing two rotation gate operations. .

[0062] Step 360, perform dynamic regulation, including: Step 361: Based on the dynamic evolution process, initialize the preparation system to the ground state and apply the equivalent gate operation to the preparation system to obtain the equivalent initial state.

[0063] In the quantum system After the time evolution, refer to In the dynamical analysis of the 3D case, the state of the quantum system is represented as: .

[0064] Will Substituting the equivalent gate sequence into the state of the quantum system, we get: ; The equivalent initial state prepared by the equivalent gate can be expressed as: .

[0065] Step 362: Based on the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate, adjust the control parameters to obtain the dynamically evolved quantum state, including: Representing the state of a quantum system using equivalent initial states: .

[0066] Assume the Hamiltonian of the quantum system is ,according to: ; in, and These are the control parameters for the Hamiltonian. and These are the control parameters after Hamiltonian adjustment; Furthermore, by moving the phase gate operation in the state of the quantum system further back to after the dynamical manipulation, we can obtain: ; in: ; ; .

[0067] In actual initial state preparation operations, phase gate operations are not required. Then, the parameters are changed during the dynamic process. The corresponding adjustment is as follows: This allows us to obtain the final equivalent scheme for preparing the target quantum state that guarantees dynamic equivalence.

[0068] Step 370: Read information and check the state. Perform state tomography to remove the omitted global phase gate and surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

[0069] Similarly, state tomography is needed to resolve the previously omitted steps. The impact of the operation was made up for.

[0070] Without considering translation operations, there are a total of 9 tomographic operations for a three-dimensional quantum state: , , ; However, regarding the state of a quantum system based on equivalent gates When performing state tomography, considering the influence of translation operations, in order to ensure that the state tomography results are consistent with the expected dynamic system states... Equal to the above, the state tomography is modified as follows: , , , , , , , .

[0071] In one embodiment, the quantum state dimension For any four-dimensional quantum state By using the concept of quantum equivalent gates, the number of two-dimensional quantum logic gates required to prepare quantum states is reduced to three, and corresponding dynamic control and final state tomography methods are provided, which greatly improves the efficiency of quantum state preparation.

[0072] The specific methods and steps mainly include: Step 410, Four-dimensional target quantum state ,satisfy: ; Step 420, for any four-dimensional target quantum state ,according to For the target quantum state By reverse derivation, we can see that: ; At this point, the preparation gate sequence contains only three two-dimensional unitary operations. , and ,that is, .

[0073] Step 430: Initialize the system in a quantum state. ,at this time, Hilbert space of vid Divided into two-dimensional subspaces , and Two-dimensional unitary operation , and Acting on two-dimensional subspaces respectively , and superior.

[0074] The specific expressions for the three two-dimensional unitary operations in the preparation gate sequence are as follows: ; ; ; Step 440, will , and These can be broken down into the following gate operations: ; ; ; thereby A total of 9 two-dimensional gate operations and 3 global phase operations are required. (Subscript) Represents a two-dimensional subspace Two-dimensional unitary operation performed.

[0075] Step 450, optimize the above-mentioned gate sequence preparation, including: Will , and The first step in decomposition is the phase gate operation. Move it to the right and merge it to get: ; ; ; The unitary operation is composed of three two-dimensional unitary operations. Only 3 core rotary gate operations are retained, omitting all global phase gates and mergeable rotation gates. Axis phase gate ,Will Rewritten as the (tensor) product form of the equivalent gate sequence: ; in: ; ; ; Thus far, a general optimized gate decomposition of unitary operations for arbitrary four-dimensional quantum states has been given, but nine gate operations are still required.

[0076] Similarly, in this embodiment, step 460 is further optimized by constructing an equivalent gate, requiring only the execution of... The equivalent door constructed by a revolving door operation: ; The equivalent gate consists of three equivalent gate sequences: , and ; For ease of representation, let's remember it similarly: ; .

[0077] In step 460, dynamic control is performed to adjust the system parameters, including: In the quantum system After time evolution, the state of the quantum system is represented as: ; Will Substituting the equivalent gate sequence into the above equation, we get: ; Let the equivalent initial state prepared by the equivalent gate be: ; but: .

[0078] Assume the Hamiltonian of the quantum system is ,according to: ,available: ; in: ; ; ; ; In actual initial state preparation operations, phase gate operations are not required: ; Then, the control parameters are used in the dynamic process. , The corresponding adjustment is as follows: This allows us to obtain the final equivalent scheme for preparing the target quantum state that guarantees dynamic equivalence.

[0079] Similarly, in step 470, for the state Perform state tomography to remove the omitted global phase gate and surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

[0080] The universal quantum state optimization preparation method based on quantum equivalent gates provided by this invention is not a simple optimization of traditional methods, but a fundamental paradigm shift. Its technical effects are mainly reflected in the following three aspects: (1) This invention will prepare any The number of quantum gates required for a quantum state is compressed to the theoretical lower limit, achieving a substantial breakthrough in quantum resource utilization from the theoretical limit to engineering practice, paving the way for high-dimensional quantum computing in the current era of quantum computer applications. Specifically, the method of this invention directly reaches the theoretical limit for the number of gates, while traditional methods can only prepare one... Arbitrary quantum states typically require multiple quantum gate operations, usually on the order of 1 / 2 Ω. For example, a three-dimensional state initially requires six gates, but this scheme, through the core ideas of "equivalent gate operations" and "phase gate shifting and merging," drastically reduces the number of core quantum logic gates required for the fabrication process to [number missing]. (For example, only 2 gates are needed for a three-dimensional state and only 3 gates are needed for a four-dimensional state). This is not only a significant reduction in quantity, but also reaches the theoretical minimum limit and is mathematically optimal.

[0081] (2) The method of this invention achieves a dual leap in the performance of quantum state preparation, namely, preparation efficiency and state fidelity. Specifically, by performing the fewest necessary operations, this scheme achieves significant improvements in preparation speed and final output quality, providing key advantages for the practical application of quantum computing, including extreme preparation efficiency and high fidelity. Performing fewer gate operations directly translates to shorter state preparation time. For computational tasks that require frequent initialization of quantum states (such as variable quantum algorithm VQE, quantum machine learning) or quantum error correction cycles, this scheme can significantly shorten the overall running time of the algorithm, improve throughput and computational efficiency, and lay the foundation for solving larger-scale problems. Quantum gates (logic gates) are one of the main sources of error. Reducing the number of gates to the limit means that the probability of errors is systematically reduced from the root. This is not only a theoretical improvement, but also indicates that the target quantum state with significantly higher fidelity can eventually be prepared on real hardware, providing a fundamental guarantee for obtaining reliable computational results.

[0082] (3) The technology of this invention has extremely broad applicability, applicable to both closed and open quantum systems. Its unique "front-end simplification, back-end compensation" mechanism innovatively and seamlessly applies efficient preparation technology to open quantum systems. Traditional efficient state preparation schemes are usually only applicable to ideal closed quantum systems. This scheme perfectly solves this limitation through an innovative synergistic adjustment strategy. Through the "front-end simplification, back-end compensation" mechanism, the technical solution of this invention is also perfectly applicable to open quantum systems with energy dissipation and information decoherence. This greatly expands its application scope, enabling it to be used to simulate real chemical and biological systems (which are necessarily coupled with the environment) and to study cutting-edge fields such as non-Hermitian physics, achieving an order-of-magnitude expansion in application scope and usage scenarios.

[0083] Furthermore, in another embodiment, the present invention also provides a universal quantum state optimization preparation device based on quantum equivalent gates, comprising: The first module is used to input the material to be prepared. We determine the target quantum state and perform quantum state analysis to ensure that the target quantum state satisfies the normalization condition. The second module is used to reverse-engineer the target quantum state to obtain the preparation gate sequence of the target quantum state; the preparation gate sequence contains multiple two-dimensional unitary operations for preparing the quantum state; The third module is used to divide the n-dimensional Hilbert space into multiple two-dimensional subspaces using two-dimensional unitary operations, with each two-dimensional unitary operation acting on one two-dimensional subspace. The fourth module is used to optimize the preparation of gate sequences, including: decomposing each two-dimensional unitary operation into a combination of rotation gates and phase gates, and reducing the actual number of gate operations to be performed by shifting and merging phase gates; The fifth module is used to construct equivalent gates using equivalent gate sequences, including: retaining only the core rotation gate operation as the equivalent gate sequence, omitting all global phase gates and mergeable rotation gates. Axial phase gates rewrite the unitary operation that prepares the gate sequence into an equivalent gate operation. The sixth module is used for dynamic control, including: initializing the preparation system to the ground state based on the dynamic evolution process, and applying the equivalent gate operation to the preparation system to obtain the equivalent initial state; adjusting the control parameters according to the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate to obtain the quantum state after dynamic evolution; The seventh module is used to perform quantum state tomography on the dynamically evolved quantum state using a modified state tomography operation; the modified state tomography operation removes the omitted global phase gate and the surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

[0084] On the other hand, the present invention provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the general quantum state optimization preparation method based on quantum equivalent gates provided in any of the above embodiments. This computer device can be a server. The computer device includes a processor, a memory, a network interface, and a database connected via a system bus. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device stores sample data. The network interface of the computer device is used for communication with external terminals via a network connection.

[0085] On the other hand, the present invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the general quantum state optimization preparation method based on quantum equivalent gates provided in any of the above embodiments.

[0086] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0087] Matters not covered in this invention are common knowledge.

[0088] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0089] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

[0090] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A general quantum state optimization preparation method based on quantum equivalent gates, characterized in that, include: Step 110, input the material to be prepared. We determine the target quantum state and perform quantum state analysis to ensure that the target quantum state satisfies the normalization condition. Step 120: The target quantum state is deduced in reverse to obtain the preparation gate sequence of the target quantum state; the preparation gate sequence contains multiple two-dimensional unitary operations for preparing the quantum state; Step 130, use two-dimensional unitary operation to... The Wiehirbert space is divided into multiple two-dimensional subspaces, and each two-dimensional unitary operation acts on one of the two-dimensional subspaces. Step 140 involves optimizing the preparation gate sequence, including: decomposing each two-dimensional unitary operation into a combination of rotation gates and phase gates, and reducing the actual number of gate operations to be performed by shifting and merging phase gates. Step 150: Construct equivalent gates using an equivalent gate sequence, including: retaining only the core rotation gate operation as the equivalent gate sequence, omitting all global phase gates and mergeable rotation gates. Axial phase gates rewrite the unitary operation that prepares the gate sequence into an equivalent gate operation. Step 160, performing dynamic control, includes: initializing the preparation system to the ground state based on the dynamic evolution process, and applying the equivalent gate operation to the preparation system to obtain the equivalent initial state; adjusting the control parameters according to the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate to obtain the quantum state after dynamic evolution; Step 170: Perform quantum state tomography on the dynamically evolved quantum state using a modified state tomography operation; the modified state tomography operation removes the omitted global phase gate and the surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

2. The method for optimizing the preparation of universal quantum states based on quantum equivalent gates according to claim 1, characterized in that, set up express The target quantum state of dimension, All values ​​are taken in the complex field, representing the probability amplitude of the target quantum state; therefore, in step 120, the preparation gate sequence of the target quantum state is represented as follows: , , of which each It is a two-dimensional unitary operation. This represents matrix transpose; the preparation of the gate sequence is achieved by processing the target quantum state. Perform reverse derivation, starting from the ground state Obtained during the preparation and evolution process: 。 3. The method for optimizing the preparation of a universal quantum state based on a quantum equivalent gate according to claim 2, characterized in that, In step 130, Wichbert space Divided into multiple two-dimensional subspaces: ； The two-dimensional unitary operation Acting on the corresponding two-dimensional subspace Up, and keep and The energy levels other than those remain unchanged.

4. The method for optimizing the preparation of universal quantum states based on quantum equivalent gates according to claim 3, characterized in that, Step 140 includes: Each two-dimensional unitary operation in the preparation gate sequence It can be broken down into a combination of revolving door and phase door operations: ； in, , , and These are real-valued parameters used to construct the decomposition backdoor operation. It is the global phase factor; This is the first step of the door operation. It is the initial phase provided by the first gate operation; This is the second step of the door operation. It is the angle parameter used to control the probability amplitude shift in the second step of the gate operation; This is the third step of the door operation. It is the relative phase of the third-step gate operation; and Indicates phase gate, Indicates a revolving door; , and They are given by the following formulas respectively: ； ； ； The phase gate of the first step gate operation Moving the operation forward and merging it with the second and third gate operations reduces the number of required gate operations, resulting in the optimized two-dimensional unitary operation representation: ； Among them, the merged revolving door operation , defined by the following formula: ； In the above formula, , .

5. The method for optimizing the preparation of a universal quantum state based on a quantum equivalent gate according to claim 4, characterized in that, Step 150 includes: It will act on two adjacent two-dimensional subspaces and The optimized two-dimensional unitary operation is used to perform the following phase gate shift and merge operations: ； in, , ; Following the steps described above, the gate sequence will be prepared. The phase gates of all optimized two-dimensional unitary operations are shifted and merged, retaining only the ones that are optimized in the first place. A core rotary gate operation, omitting all global phase gates and mergeable z-axis phase gates. ; Will Rewritten as an equivalent gate sequence Tensor product form: ； in, , For phase gate; It is a tensor product; It is an equivalent gate.

6. The method for optimizing the preparation of a universal quantum state based on a quantum equivalent gate according to claim 5, characterized in that, In step 160: The process of initializing the quantum system to its ground state based on the dynamic evolution process, and applying the equivalent gate operation to the prepared system to obtain an equivalent initial state, includes: Using the Liouville superoperator, we can express that after... The state of the quantum system after the evolution at time: ； in, It is the density matrix describing the state of a quantum system; It is the Liouville superoperator, represented in matrix form as: ； In the above formula, yes Dimensional unit operator, This indicates taking the conjugate complex number; It is the imaginary unit; The Hamiltonian is a function of the control parameters that govern the transitions between quantum energy levels. To describe from energy level arrive Dissipation operators between states; Will Substituting the equivalent gate into the state of the quantum system, we get: ； The initial state prepared by the equivalent gate is defined as the equivalent initial state. : ； The process of adjusting control parameters based on the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate to obtain the dynamically evolved quantum state includes: Representing the state of a quantum system using an equivalent initial state: ; Let the Hamiltonian of the quantum system be... ,in: ； ； ； ； In the above formula, and Hamiltonian and Control parameters that control the transitions between quantum energy levels; By further postponing the phase gate operation in the state of the quantum system to after the dynamical manipulation, we obtain: ； in: ； 。 7. The method for optimizing the preparation of a universal quantum state based on a quantum equivalent gate according to claim 6, characterized in that, In step 170, the state of the quantum system is... Perform modified state tomography: The state of the quantum system prepared at the initial moment is ; The true state of the quantum system at time t is: ; Using state tomography, the following phase gate operations omitted in step 150 are corrected: 。 8. The method for optimizing the preparation of a universal quantum state based on a quantum equivalent gate according to claim 1, characterized in that, The dimension of the target quantum state By adjusting the gate operations used in the state tomography operation, the final measurement result is made consistent with the tomography result of the target quantum state; The door operation before adjustment included: ； The adjusted door operation includes: ， ， 。 9. The method for optimizing the preparation of a universal quantum state based on a quantum equivalent gate according to claim 1, characterized in that, The dimension of the target quantum state By adjusting the gate operations used in the state tomography operation, the final measurement result is made consistent with the tomography result of the target quantum state; The door operation before adjustment included: ， ， ； The adjusted door operation includes: ， ， ， ， ， ， ， 。 10. A universal quantum state optimization preparation device based on quantum equivalent gates, characterized in that, include: The first module is used to input the material to be prepared. We determine the target quantum state and perform quantum state analysis to ensure that the target quantum state satisfies the normalization condition. The second module is used to reverse-engineer the target quantum state to obtain the preparation gate sequence of the target quantum state; the preparation gate sequence contains multiple two-dimensional unitary operations for preparing the quantum state; The third module is used to utilize two-dimensional unitary operations to... The Wiehirbert space is divided into multiple two-dimensional subspaces, and each two-dimensional unitary operation acts on one of the two-dimensional subspaces. The fourth module is used to optimize the preparation of gate sequences, including: decomposing each two-dimensional unitary operation into a combination of rotation gates and phase gates, and reducing the actual number of gate operations to be performed by shifting and merging phase gates; The fifth module is used to construct equivalent gates using equivalent gate sequences, including: retaining only the core rotation gate operation as the equivalent gate sequence, omitting all global phase gates and mergeable rotation gates. Axial phase gates rewrite the unitary operation that prepares the gate sequence into an equivalent gate operation. The sixth module is used for dynamic control, including: initializing the preparation system to the ground state based on the dynamic evolution process, and applying the equivalent gate operation to the preparation system to obtain the equivalent initial state; adjusting the control parameters according to the dynamic evolution process and the phase gate information omitted when constructing the equivalent gate to obtain the quantum state after dynamic evolution; The seventh module is used to perform quantum state tomography on the dynamically evolved quantum state using a modified state tomography operation; the modified state tomography operation removes the omitted global phase gate and the surrounding... The influence of the axis phase gate is embedded in the measurement operation. By adjusting the control parameters of the gate operation used in the tomography, the final measurement result is consistent with the tomography result of the target quantum state.

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