Multi-parameter quantum estimation method and system based on indefinite evolution

Abstract

The application provides a multi-parameter quantum estimation method and system based on indefinite evolution, which comprises the following steps: initializing a probe quantum register and an auxiliary quantum register in a coherent superposition state by a quantum sensing device, and dividing a total sensing time into multiple time slices; in each time slice, decomposing the auxiliary quantum state according to historical path component coherence recorded by the auxiliary quantum register, performing at least one of control gate selection and signal term symbol configuration according to a signal generating element relationship, and making the probe quantum register coherently experience two parameter encoding evolution branches; then, selecting a corresponding conditional compensation operation according to different historical path components and iterating to the total sensing time, and measuring the two registers to obtain at least two parameters to be estimated. The application can reduce parameter information aliasing and restore the distinguishability of parallel or linearly dependent parameters.

Description

Technical Field

[0001] This invention belongs to the field of quantum information processing and quantum computing control technology. Specifically, it relates to a multi-parameter quantum estimation method and system based on indeterminate evolution. In particular, it relates to a multi-parameter quantum estimation method, device and quantum sensing device based on indeterminate evolution for the joint estimation of multiple physical parameters, including high-precision estimation of magnetic field, electric field, frequency, phase, coupling strength, inertial quantity, multi-axis field components and multiple quantum control parameters. Background Technology

[0002] Quantum precision measurement utilizes quantum resources such as quantum coherence, quantum superposition, and quantum entanglement to improve the estimation accuracy of unknown physical parameters. In single-parameter estimation, by using appropriate probe initial states, parameter encoding Hamiltonians, and measurement methods, it is possible to achieve accuracy better than the standard quantum limit, and even reach the Heisenberg limit, under ideal conditions. Therefore, quantum sensing has become one of the important application directions of quantum technology.

[0003] However, in practical applications, many physical quantities to be measured are not single parameters, but multiple parameters existing simultaneously. For example, multi-axis magnetic field measurement requires simultaneous estimation of magnetic field components in different directions; quantum device calibration requires simultaneous estimation of multiple control parameters; and in atomic or superconducting quantum systems, it is often necessary to simultaneously estimate multiple parameters such as frequency, phase, coupling strength, and noise intensity. Compared with single-parameter estimation, multi-parameter quantum estimation faces more complex challenges.

[0004] First, multiple parameters to be estimated are typically encoded by different quantum signal generators. When these signal generators are non-commuting, anti-commuting, parallel, or linearly correlated, information about different parameters will mix within the same probe system. For example, for a single-qubit Hamiltonian, the two parameters are encoded by generators in the X and Z directions, respectively. Since they are non-commuting, it is difficult for the probe system to evolve simultaneously along the optimal encoding directions of both parameters. In the case of parallel generators, the two parameters only appear as a sum, and conventional free evolution cannot even independently distinguish between the two parameters.

[0005] Secondly, multi-parameter estimation is also limited by measurement incompatibility. The optimal measurement of one parameter is usually not the optimal measurement of another parameter. Therefore, even if the quantum Fisher information matrix has high precision in theory, the classical Fisher information matrix that can be obtained in practice through the same measurement scheme may not be able to achieve the optimal precision for multiple parameters simultaneously.

[0006] Existing quantum error correction, dynamic decoupling, or deterministic evolution methods are typically better suited for protecting a single target signal component. In multi-parameter estimation, these methods may treat another signal component as an error and suppress it, leading to the loss of some parameter information. Indeterminate evolution offers a novel solution. Unlike deterministic evolution, where the probe system follows only a fixed evolutionary path, indeterminate evolution allows the probe system to coherently undergo multiple different evolutionary branches under the control of an auxiliary quantum system.

[0007] The paper "Evading noise in multiparameter quantum metrology withindefinite causal order" (arXiv:2309.07220) discloses a method for controlling the evolution order of multiple quantum channels using indefinite causal order (ICO), realizing multi-parameter quantum metrology through an auxiliary quantum control system, and obtaining quantum channel parameter information through a measurement control system. However, this scheme mainly uses indefinite causal order to improve the performance of noisy quantum metrology, and does not establish a multi-time-slice parameter routing mechanism for parallel or linearly correlated signal generators to perform condition compensation according to historical paths. It cannot solve the problems of parameter information aliasing during multi-parameter encoding and parameter indistinguishability caused by parallel or linearly correlated generators.

[0008] The paper "Qubit-assisted quantum metrology under a time-reversal strategy" (arXiv:2404.12649) discloses a quantum metrology method based on auxiliary qubits and a time-reversal strategy. By having auxiliary qubits participate in the forward and reverse evolution of the probe system, and by using joint measurements to improve the accuracy of single-parameter phase estimation, this scheme is mainly aimed at single phase parameter estimation and cannot solve the problems of encoding incompatibility and measurement incompatibility in multi-parameter estimation.

[0009] The paper "Noise-Resilient Heisenberg-limited Quantum Sensing via Indefinite-Causal-Order Error Correction" (arXiv:2601.01404) discloses a quantum error correction protocol based on indefinite causal order. By assisting in controlling the indefinite causal relationship between qubits and the noise evolution process, it realizes noise error labeling and real-time error correction, thereby improving the parameter estimation accuracy in noisy quantum sensing. However, this scheme mainly targets noise suppression and error correction in the quantum sensing process and cannot realize the independent encoding and joint estimation of multiple parameters to be estimated.

[0010] Therefore, a new multi-parameter quantum estimation method is needed to enable the information of different parameters to be estimated to be separated, coherently accumulated and compatiblely read out in the same experimental protocol, and to be coherently accumulated and read out separately across multiple time slices. Summary of the Invention

[0011] To address the shortcomings of existing technologies, the purpose of this invention is to provide a multi-parameter quantum estimation method and system based on indeterminate evolution.

[0012] A multi-parameter quantum estimation method based on indeterminate evolution provided by the present invention includes: Step S1: Initialize the probe quantum register and initialize the auxiliary quantum register to a coherent superposition state. Construct a quantum sensing Hamiltonian containing the parameters to be estimated and the corresponding signal generators based on the physical quantity to be estimated. Divide the total sensing time into multiple time slices. Step S2: For each time slice, coherently decompose the auxiliary quantum state of the auxiliary quantum register according to different historical path components; Step S3: Based on the relationship between the signal generators corresponding to the parameters to be estimated, select the control gate, symbol configuration and / or signal inversion mode so that the probe quantum register coherently undergoes two parameter encoding evolution branches under the control of the auxiliary quantum register, forming a coherent path; Step S4: Select condition compensation based on different historical path components, and perform condition compensation on coherent paths to separate and encode the information of different parameters to be estimated into probe quantum registers and auxiliary quantum registers; Using the joint quantum state after condition compensation as the input for the next time slice, repeat steps S2 to S4 until the total sensing time is reached. Measure the probe quantum register and the auxiliary quantum register respectively, and obtain the estimated result of the parameter to be estimated based on the measurement results.

[0013] Preferably, the quantum sensing Hamiltonian for:

[0014] The length of the time slice for

[0015]

[0016] The parametric coding evolution branch includes a first parametric coding evolution branch and a second parametric coding evolution branch.

[0017] The evolution operator for the first parameter encoding evolution branch is:

[0018] The evolution operator for the second parameter encoding evolution branch is:

[0019] in, , Indicates different parameters to be estimated. , They represent , The corresponding signal generator; Indicates the total sensing time. Indicates the number of time slices; Indicates by parameters and The parameter encoding evolution operator is jointly determined. This represents the control gate acting on the probe quantum register. The natural constant is represented by i, which represents the imaginary unit. This indicates the configuration parameters for the signal item symbol, with values ​​ranging from 1 to 2. or ; express The conjugate transpose of .

[0020] Preferably, in step S3, when and When orthogonal or anti-orthogonal, let and choose with Easy and Opposing Easy Control Gate Through the control door The conjugate transformation of the quantum sensing Hamiltonian makes The signs are the same in the two parametric coding evolution branches and The sign is the opposite.

[0021] when and When parallel or linearly dependent, let In the second parameter encoding evolution branch, effective sign inversion is performed on the signal term corresponding to at least one parameter to be estimated.

[0022] Preferably, in step S4, based on the auxiliary quantum register... Historical path component selection first condition compensation According to the auxiliary quantum register Historical path component selection second condition compensation :

[0023]

[0024] in, This represents the unit operation on the probe quantum register; This represents a compensation gate that matches the signal generator corresponding to the parameter to be estimated that is routed to the auxiliary quantum register; , These represent the projection operators for two different historical path components of the auxiliary qubit; and middle, and The correspondences on the two historical path components are opposite.

[0025] Preferably, in step S3, when and When they are neither orthogonal nor parallel, Decomposed into relative Parallel and orthogonal components.

[0026] Configure the first auxiliary qubit and set the corresponding The orthogonal components are encoded into the first auxiliary qubit.

[0027] Configure the second auxiliary qubit and set the corresponding Parallel components are encoded into the second auxiliary qubit by effectively reversing the sign of the signal term.

[0028] The present invention provides a multi-parameter quantum estimation system based on indeterminate evolution, comprising a probe quantum register, an auxiliary quantum register, a quantum control component, a quantum measurement component, and a classical processing component.

[0029] The quantum control component is connected to the probe quantum register and the auxiliary quantum register respectively. The probe quantum register is initialized and the auxiliary quantum register is initialized to a coherent superposition state. A quantum sensing Hamiltonian containing the parameters to be estimated and the corresponding signal generators is constructed according to the physical quantity to be estimated. The total sensing time is divided into multiple time slices. For each time slice, the auxiliary quantum state of the auxiliary quantum register is coherently decomposed according to different historical path components; Based on the relationship between the signal generators corresponding to the parameters to be estimated, the control gate, symbol configuration and / or signal inversion method are selected so that the probe quantum register coherently undergoes two parameter encoding evolution branches under the control of the auxiliary quantum register, forming a coherent path; Conditional compensation is selected based on different historical path components, and conditional compensation is performed on coherent paths. The joint quantum state after conditional compensation is used as the input for the next time slice. The quantum measurement component is connected to the probe quantum register and the auxiliary quantum register respectively. After the total sensing time is reached, the probe quantum register and the auxiliary quantum register are measured respectively to obtain the measurement results. The classical processing component is connected to the quantum measurement component to obtain the estimated result of the parameter to be estimated based on the measurement result.

[0030] Preferably, the quantum control component includes a quantum state initialization module, a time slice control module, a parameter encoding module, an indeterminate evolution control module, and a condition compensation module.

[0031] The parameter encoding module constructs the quantum sensing Hamiltonian:

[0032] The time slice control module determines the length of each time slice:

[0033] The indeterminate evolution control module forms the first parameter encoding evolution branch:

[0034] And this forms the second parameter encoding evolution branch:

[0035] The condition compensation module is configured to feed back the joint quantum state after condition compensation to the indeterminate evolution control module; in, , Indicates different parameters to be estimated. , They represent , The corresponding signal generator; Indicates the total sensing time. Indicates the number of time slices; Indicates by parameters and The parameter encoding evolution operator is jointly determined. This represents the control gate acting on the probe quantum register. The natural constant is represented by i, which represents the imaginary unit. This indicates the configuration parameters for the signal item symbol, with values ​​ranging from 1 to 2. or ; express The conjugate transpose of .

[0036] Preferably, the quantum control component further includes a control pulse module and a signal inversion module.

[0037] when and When orthogonal or anti-orthogonal, the control pulse module commands... And choose with Easy and Opposing Easy Control Gate ,make The signs are the same in the two parametric coding evolution branches and The sign is the opposite.

[0038] when and When parallel or linearly correlated, the signal inversion module makes And in the second parameter coding evolution branch, effective sign inversion is performed on the signal item corresponding to at least one parameter to be estimated.

[0039] Preferably, the condition compensation module is based on the auxiliary quantum register. Historical path component selection first condition compensation According to the auxiliary quantum register Historical path component selection second condition compensation :

[0040]

[0041] in, This represents the unit operation on the probe quantum register; This represents a compensation gate that matches the signal generator corresponding to the parameter to be estimated that is routed to the auxiliary quantum register; , These represent the projection operators for two different historical path components of the auxiliary qubit; and middle, and The correspondences on the two historical path components are opposite.

[0042] Preferably, the auxiliary quantum register includes a first auxiliary qubit and a second auxiliary qubit.

[0043] when and When they are neither orthogonal nor parallel, the parameter encoding module will Decomposed into relative Parallel and orthogonal components.

[0044] The indeterminate evolution control module will control the first auxiliary qubit corresponding to... Encode the orthogonal components; assign the second auxiliary qubit to... Parallel components are encoded by reversing the effective sign of the signal term.

[0045] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention uses an auxiliary quantum register to coherently control the probe quantum register through two parameter encoding evolution branches, and encodes the information of different parameters to be estimated into the probe quantum register and the auxiliary quantum register respectively, thereby reducing the aliasing of parameter information in the same probe readout channel and improving the joint identifiability of multiple hardware control parameters or physical quantities to be measured.

[0046] 2. This invention configures control gates or signal term symbols according to the relationship between signal generators. In the case of orthogonal or anticommutative generators, the conjugate transformation of the control gates is used to achieve parameter separation. In the case of parallel or linearly correlated generators, the difference response between branches is used to restore parameter identifiability, thus realizing unified processing of different generator relationships.

[0047] 3. This invention performs corresponding conditional compensation based on the historical path components recorded by the auxiliary quantum register, and feeds back the compensated joint quantum state to the next time slice, so that the phase of the routed parameter continues to accumulate coherently across multiple time slices, avoiding phase mismatch between historical paths caused by fixed compensation, and improving the stability of multi-time-slice parameter encoding.

[0048] 4. This invention utilizes superconducting quantum chips to achieve parameter encoding and readout. In the case of orthogonal generators, there is no need to actively reverse the external physical field to be measured. By adopting corresponding degree-of-freedom encoding and control elements, it can also be extended to optical, multi-qubit, neutral atom or ion trap platforms, thus improving applicability. Attached Figure Description

[0049] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the process of a multi-parameter quantum estimation method based on indeterminate evolution; Figure 2 This is a schematic diagram of the indeterminate evolution time slice in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the implementation process of the superconducting quantum platform in an embodiment of the present invention. Detailed Implementation

[0050] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0051] This invention provides a multi-parameter quantum estimation method based on indeterminate evolution, such as... Figure 1 and Figure 2As shown, the process includes steps such as quantum sensor system initialization, multi-parameter signal response modeling, indeterminate evolution time slice construction, beam splitting module execution, encoding module execution, decoding module execution, multi-time slice iteration, quantum measurement, acquisition of measurement probability distribution, classical parameter estimation, and output of parameters to be estimated. This solves the problems of parameter information aliasing, generator incompatibility, measurement incompatibility, and indistinguishability of parallel signals in existing multi-parameter quantum estimation methods.

[0052] Specifically, by using an auxiliary quantum register to coherently control the probe quantum register through different parameter encoding evolution branches, the probe system no longer accumulates parameter information along a single, predetermined evolution path, but instead simultaneously experiences multiple different evolution paths in a quantum coherent manner. By applying control gates, signal symbol configurations, or signal inversion operations in different evolution branches, and performing conditional compensation after the evolution branches are merged, the information of different parameters to be estimated is encoded into the probe quantum register and the auxiliary quantum register, respectively. By performing compatible measurements on different registers, a joint estimation result of multiple parameters is obtained.

[0053] Quantum sensor system initialization: The physical system selected for multi-parameter quantum estimation mainly includes superconducting qubits and an optical platform. The superconducting qubit platform is suitable for realizing discrete-variable quantum sensing models. Its advantages include strong qubit controllability, mature single-qubit and two-qubit gates, and the ability to construct effective Hamiltonians through microwave pulses and frequency modulation. The optical platform is suitable for realizing probes and auxiliary systems through degrees of freedom such as path, polarization, time mode, or orbital angular momentum. Its advantages include relatively direct coherent beam splitting, interference, phase modulation, and mode measurement, making it suitable for verifying path coherent superposition and parameter information routing mechanisms in indeterminate evolution.

[0054] The overall sensing process is divided into multiple short time slices, and the same indeterminate evolution operation is performed within each time slice. Each indeterminate evolution time slice consists of a beam splitting module, an encoding module, and a decoding module. The beam splitting and decoding modules have a unified structure that does not change with the relationship between signal generators; the differences corresponding to different signal relationships are mainly reflected in the encoding module, which selects different control gates, symbol configurations, or signal inversion methods based on the signal generator corresponding to the parameter to be estimated.

[0055] Figure 2 middle, , These represent the quantum states of the auxiliary quantum register and the probe quantum register, respectively. Represents the tensor product. , This represents two distinct coherent history path components of an auxiliary qubit under the corresponding basis. and This represents two different computational ground states of the auxiliary qubit. Indicates by parameters and The parameter encoding evolution operator is jointly determined. This represents the control gate acting on the probe quantum register. Indicates the symbol configuration parameters for signal items. , Indicates corresponding to respectively , Conditional compensation for historical path components. This indicates the unit operation on the probe quantum register. This represents the signal generator or corresponding compensation gate corresponding to the routing parameters, which is uniformly represented in the conditional compensation formula. This indicates the compensation gate that matches the signal generator.

[0056] Initialize the probe quantum register and auxiliary quantum register. The probe quantum register carries the quantum encoding of the parameter to be estimated, and the auxiliary quantum register is used for coherent control of different evolution branches. For a single-qubit probe, the probe qubit can be initialized to a coherent superposition state sensitive to the parameter to be estimated, for example, Or other input states suitable for a specific signal generator. Auxiliary qubits are typically initialized to... , where subscript This refers to auxiliary qubits. For multi-qubit probes, the probe register can be initialized to a direct product coherent state, a GHZ state (Greenberg-Horn-Zailinger state), an entangled state, or other quantum states sensitive to collective signals; the auxiliary register can be initialized to multiple... The direct product state or other coherent superposition state.

[0057] In a superconducting qubit platform, probe qubits and auxiliary qubits can be implemented using transmon qubits, flux qubits, or other superconducting qubits. The initialization process can be performed via microwave. The single-qubit rotation gate and reset operation are completed. In the optical platform, the probe qubit can be encoded by polarization, path, time-bin, or orbital angular momentum modes, while the auxiliary qubit can be encoded by another degree of freedom or another photon's degree of freedom. The initialization process can be completed by a beam splitter, polarization beam splitter, waveplate, phase plate, spatial light modulator, or mode converter.

[0058] Multi-parameter signal response modeling: After the quantum sensor is initialized, a multi-parameter quantum sensing Hamiltonian needs to be constructed based on the physical quantity to be estimated.

[0059] For a two-parameter single-qubit model, the sensing Hamiltonian can be written as:

[0060] in, and For the parameter to be estimated, and This is the signal generator acting on the probe qubit. In a typical implementation, if we take:

[0061] The sensing Hamiltonian is then:

[0062] in, and This represents the Pauli operator. The model corresponds to two non-commuting orthogonal signal generators. In conventional free evolution, the information from the two parameters is coupled within the same probe qubit, leading to encoding incompatibility issues in multi-parameter estimation. If we take:

[0063] The sensing Hamiltonian is then:

[0064] This model corresponds to parallel or linearly correlated signal generators. In conventional free evolution, the probe quantum state depends only on the combination of parameters. Therefore, it cannot be directly and independently estimated. and .

[0065] In more preferred embodiments, a quantum sensing Hamiltonian containing multiple parameters to be estimated is constructed. For the quantum sensing Hamiltonian derived from... A multi-body quantum sensing system consisting of probe qubits can be used to construct a Hamiltonian with local parameter encoding, for example:

[0066] in, The number of probe qubits. and They respectively represent the effects on the first Pauli operators on probe qubits. This form is suitable for many-body quantum sensing, arrayed superconducting qubit sensors, or multi-mode optical sensing systems. In superconducting platforms, The terms can be implemented by microwave drive amplitude, drive phase, or lateral control terms. The term can be achieved by frequency detuning, magnetic flux bias, energy level shift caused by the external field being measured, or longitudinal coupling. In the optical platform, The effect can be achieved by polarization reversal, mode switching, or path switching. The phase effect can be achieved by phase delay, path phase, polarization phase or orbital angular momentum mode phase.

[0067] Indeterminate evolution time slice construction: Let the first... At the start of each time slice, the joint state of the probe quantum register and the auxiliary quantum register is: After the indeterminate evolution of this time slice, the system state is updated to... Repeat this process until... This allows for the accumulation of coherent parameters over the entire sensing time.

[0068] Furthermore, quantum sensing devices will increase the total sensing time. Divided into There are several short time slices, each with a length of:

[0069] in, Indicates the length of a single time slice. Indicates the total sensing time. Indicates the total number of time slices. , They represent the first Probe-aided joint quantum state before and after time slice processing, subscript Indicates auxiliary quantum register, subscript Indicates probe quantum register, superscript Indicates the current time slice number. The value is to .

[0070] Within each time slice, an indeterminate evolution time slice is executed. This time slice comprises the following three fixed modules: The beam splitting module identifies the coherent path history accumulated in the previous time slice, providing input for subsequent path-dependent decoding. The beam splitting module then divides the input auxiliary quantum state according to the auxiliary qubits. and The historical components are coherently decomposed. If the auxiliary state before entering the current time slice is... The probe state is The beam splitter module then decomposes the input state into a series of components. Historical path-related components and Components related to historical paths.

[0071] This beam splitting process does not measure auxiliary qubits, but maintains quantum coherence, allowing the two historical components to enter subsequent coding modules with the same structure.

[0072] In a superconducting platform, the beam-splitting module serves to establish or extend the superposition of coherent paths in auxiliary degrees of freedom. In a superconducting platform, this process can be achieved through Hadamard gates. This can be achieved through microwave pulses, basis transformations before and after controlled gates, or equivalent single-qubit rotations. In an optical platform, this process can be implemented using beam splitters, polarization beam splitters, interferometers, waveplates, or path superposition structures. For example, if the auxiliary qubit is encoded by path degrees of freedom, the beam splitter can transform the input path state into two coherent paths; if the auxiliary qubit is encoded by polarization degrees of freedom, a half-wave plate and a polarization beam splitter can achieve corresponding coherent beam splitting.

[0073] The encoding module is selected based on the signal relationship. For each input history component, the encoding module causes the probe quantum register to undergo two coherent evolution branches under the control of auxiliary qubits. Each branch corresponds to the original parameter encoding evolution:

[0074] The other branch corresponds to the parameter encoding evolution modified by control gates and symbol configuration:

[0075] in, This is the control gate acting on the probe quantum register. The natural constant is represented by i, which represents the imaginary unit. express The conjugate transpose of . This indicates the configuration parameters for the signal item symbol. Indicates whether to perform sign inversion on a specific signal component. When, no signal inversion is introduced; when At that time, sign inversion is performed on the corresponding signal item in that evolutionary branch.

[0076] Because the auxiliary qubits are in a coherent superposition state, the probe quantum register does not classically and randomly choose a certain path, but rather coherently experiences two evolutionary branches simultaneously.

[0077] In a superconducting platform, the encoding module can be implemented using controlled gates, single-qubit rotation pulses, frequency modulation, microwave phase switching, and echo sequences. Control gates can be Signal inversion can be achieved through pulses; it can be accomplished by changing the driving phase, adjusting the effective Hamiltonian sign, or using echo pulses or digital quantum simulation sequences. In the optical platform, the encoding module can be implemented using waveplates, phase plates, spatial light modulators, Dove prisms, polarization controllers, or mode converters in different paths. Control gates... It can be achieved by a half-wave plate or a mode inverter; signal inversion can be achieved by path-dependent phase modulation or optical phase delay with opposite signs.

[0078] The decoding module performs conditional compensation on the encoded coherent path. The structure of this module remains consistent across different signal relationships. For signals from... Input of historical components, execution Compensation; for those from Input of historical components, execution Compensation. The compensation module can be written as:

[0079]

[0080] in, This refers to the unit operation on the probe quantum register. This represents a compensation gate that matches the signal generator corresponding to the parameter to be estimated, which is routed to the auxiliary quantum register. and These represent the two history path projection operators of the auxiliary qubit. and The two items in the text respectively define unit operations With compensation gate The correspondence between the two historical path components.

[0081] Path-dependent compensation differs from fixed-gate operation correction based solely on the current branch. The auxiliary quantum register already carries some phase of the parameter to be estimated after the previous time slice; if the next time slice uses the same fixed compensation as the initial time slice without distinguishing historical paths, phase mismatches may occur in different historical paths, preventing the target parameter phase from continuously accumulating coherently. Within each time slice, the selection is based on the historical path components recorded by the auxiliary quantum register. or This allows for the continuation of existing historical paths.

[0082] Taking single-auxiliary qubits and single-probe qubits as examples, the first The joint input state at the beginning of each time slice is:

[0083] In the formula, Indicates the first The joint input state of the auxiliary qubit and the probe qubit at the start of each time slice. Indicates that the auxiliary qubit is in front. The coherent path state formed after a time slice Indicates that the probe qubit is in front. The quantum state after a time slice.

[0084] forward In each time slice, the routing parameters Already accumulated on auxiliary qubits, making Include and Historical path components. The beam splitting operation will... According to the coherent decomposition of the two historical path components, The historical path component enters the first type of encoding-decoding channel, making The historical path component enters the second type of encoding-decoding channel, and no measurement is performed on the auxiliary qubit.

[0085] for Historical path components, probe qubit experience and Two coherent evolutionary branches, followed by execution ;for The historical path component, employing two coherent evolutionary branches of the same form, is then executed. .

[0086] In the two-condition compensation, the compensation gate is in Branches and The correspondence on the branches is reversed, so that the phase of the parameters that have been mapped to the auxiliary qubit in the previous time slice is not canceled out in the subsequent time slice.

[0087] In a more specific embodiment, orthogonal or anticommutative signal generators are used and let For example, repeat the following situation. After a time slice, under the short time slice limit, the system output state approximately satisfies:

[0088] The corresponding phase is accumulated in the auxiliary quantum register. The corresponding phase is accumulated in the probe quantum register. Among them, Indicates the total sensing time At the end of the probe-assisted joint quantum state, and These represent the initial states of the auxiliary quantum register and the probe quantum register, respectively. It is the Pauli-Z operator that operates on the auxiliary qubit. This represents the first signal generator acting on the probe quantum register.

[0089] For orthogonal or anticommutative signal generators, the encoding module selects... That is, do not perform signal inversion; at the same time, select the control gate. So that it is related to the first signal generator. Easier, and with the second signal generator Opposition is easy, that is, satisfaction:

[0090] In the formula, express and The exchange of children, express and The opposition to the change of the child; the equation being zero respectively represents and Easy and and Oppose it easily.

[0091] From the above relationship, we can conclude that:

[0092]

[0093] Furthermore:

[0094] Wherein, the left-hand side represents the control gate. The conjugate transformation of the original parameter encoding evolution is expressed on the right, which represents the equivalent evolution after the conjugate transformation. The terms have the same sign in both branches. The signs of the terms are opposite in the two branches. This represents the duration of a single evolution segment in which the probe quantum register encodes parameters under the influence of the quantum sensing Hamiltonian during each indeterminate evolution cycle.

[0095] therefore, The combined effect of the two paths is retained in the probe quantum register. It exerts a relative effect on the two paths and maps them to an auxiliary quantum register.

[0096] Using orthogonal signal model For example, you can choose to control the door. .because and Easy, and with Opposing it is easy, and you get:

[0097] At this point, there is no need for signal inversion, that is, there is no need to invert the external physical field to be measured, there is no need to invert the sign of the real physical signal corresponding to a certain parameter to be estimated, and there is no need to actively implement the reverse evolution of the Hamiltonian term of the signal in the hardware. The relative sign change of the terms comes from the control gate. Conjugate transformation:

[0098] For parallel or linearly correlated signal generators, For example, the conventional free evolution operator is:

[0099] This evolution depends only on parameters and .

[0100] For any satisfying Parameters and The quantum states and measurement probability distributions are the same after the same evolution time, so the measurement data cannot be uniquely determined. and , , , , Different parameters correspond to singular multi-parameter Fisher information matrices.

[0101] make In the second parameter encoding evolution branch, for The corresponding signal item undergoes a sign inversion, resulting in the two branches being:

[0102]

[0103] In the formula, This indicates the first parameter encoding evolution without sign inversion of the signal items. Indicates will The second parameter encoding evolution corresponds to the effective inversion of the signal term. Two branches... The response is the opposite, to The responses are the same, therefore, it will depend only on the parameters and The response is converted into two parameter responses that can be distinguished by their interaction and their relative interaction.

[0104] The sign inversion of signal terms can be achieved through control pulses or equivalent Hamiltonian engineering. After beam splitting and path-dependent condition compensation, the original signal terms, mixed in parameters and... The information in the matrix is ​​routed to different registers, thereby transforming the originally singular Fisher information matrix into a non-singular matrix and restoring the independent identifiability of the two parameters.

[0105] For non-orthogonal and non-parallel signal generators, the same beam splitting and decoding modules are still used. The parameter encoding operation is adjusted only according to the generator decomposition results. In the encoding module, the control gate and signal inversion method are selected according to the generator decomposition results.

[0106] Specifically, in the encoding module, control gates and signal inversion methods are selected based on the generator decomposition results. The signal generator corresponding to one of the parameters to be estimated is decomposed into components parallel to and orthogonal to the other signal generator. Then, orthogonal signal encoding modules and parallel signal encoding modules are used to route the parameter information. For example, for:

[0107] in, This represents the decomposition angle of the second signal generator relative to the first signal generator. . The parameter consists of two parts: one is related to... Parallel components and a with Orthogonal components Two auxiliary qubits are used: the encoding module corresponding to the first auxiliary qubit is selected. Used to extract orthogonal components Selection of the encoding module corresponding to the second auxiliary qubit Used to extract parallel components by reversing a controlled signal. .

[0108] thus, Parameter information is stored in the probe qubit. Different components of the parameter are encoded into auxiliary qubits.

[0109] Repeat the above-described indeterminate evolution time slice consisting of the beam splitting module, encoding module, and decoding module until the total sensing time is reached. .go through After a time slice, information from multiple parameters to be estimated is coherently accumulated in the probe quantum register and the auxiliary quantum register, respectively. When large enough, this discrete-time slice protocol approximates the continuous-time uncertain evolution multi-parameter sensing process.

[0110] Multi-time-slice iteration: After completing the splitting, encoding, and decoding of a time slice, update the current time slice number. And determine whether the total number of time slices has been reached. If not achieved If the current output state is used as the input for the next time slice, the beam splitting, encoding, and decoding operations will continue. If the time slice has been reached... If the parameter encoding stage ends, the measurement stage begins.

[0111] For multi-qubit probes, the aforementioned indeterminate evolution time slice can be executed locally on each probe qubit. Consider... A many-body quantum sensing system consisting of probe qubits has the Hamiltonian as follows:

[0112] Configure a corresponding auxiliary qubit for each probe qubit. For the first... Each probe-auxiliary pair performs local beam splitting, encoding, and decoding operations. The beam splitting and decoding modules are the same as in the single-qubit case, while the encoding module follows the local signal generator... and The appropriate control gate is selected based on the relationship. For and In the orthogonal case, one can choose to... Easy, and Oppose easy local control gates, making local control... The signal components are mapped to the first In each auxiliary qubit, and locally Signal components are preserved in the first... In each probe qubit.

[0113] After the parallel indeterminate evolution of all probe-auxiliary pairs, the effective evolution of the system can be written as:

[0114]

[0115] in, The collective Pauli-Z operator representing the auxiliary quantum register. The collective Pauli-X operator representing the probe quantum register, Indicates the action on the first Pauli-Z operator with auxiliary qubits Indicates the action on the first Pauli-X operator for probe qubits and These represent the initial collective quantum states of the auxiliary quantum register and the probe quantum register, respectively.

[0116] If the probe register and auxiliary register are prepared into appropriate entangled states, such as GHZ states, then and The parameter information can be accumulated collectively in two separate registers, thereby improving the accuracy of multi-parameter estimation.

[0117] After the total sensing time is reached, the quantum measurement components measure the probe quantum register and the auxiliary quantum register respectively. In the superconducting platform, measurements can be performed using a readout resonant cavity. The readout signal is then processed by a cryogenic amplifier, a room-temperature amplifier, and data acquisition electronics to convert it into a binary measurement result or a continuous readout signal. In the optical platform, a polarization analyzer, path detector, single-photon detector, balanced detector, interferometer, or camera readout system can be used to measure the probe degrees of freedom and the auxiliary degrees of freedom.

[0118] By repeating the experiment multiple times, the statistical frequencies of different measurement results can be obtained, and the measurement probability distribution can be estimated accordingly. ,in Indicates the measurement result. Represents the vector of parameters to be estimated, for example .

[0119] After the total sensing time is completed, measurements are performed on the probe quantum register and the auxiliary quantum register. Measurement methods can include local Pauli measurement, joint measurement, projection measurement, or readout measurement suitable for a specific platform. The probability distribution is obtained from the measurement results. ,in The measurement results are then presented. The classic Fisher information matrix is ​​subsequently calculated:

[0120] in . Represents the classic Fisher information matrix. Line 1 Column elements, Indicates the measurement result. This represents a parameter vector consisting of multiple parameters to be estimated. and Represents the first in the parameter vector The and the first One parameter, Represents a given parameter vector Time to obtain measurement results The conditional probability is summed and iterated through all measurement results.

[0121] Classic processing components can also employ maximum likelihood estimation, Bayesian estimation, least squares estimation, neural network estimators, or adaptive estimation methods to invert unknown parameters based on multiple measurement results.

[0122] Taking maximum likelihood estimation as an example, let the data set obtained from multiple repeated measurements be... The parameter estimates are:

[0123] in, This represents the maximum likelihood estimate of the parameter vector to be estimated. Represents a given set of measurement data Time parameter vector The likelihood function, This represents the parameter vector corresponding to the maximum value of the likelihood function.

[0124] The final output is the estimation results for multiple parameters to be estimated, for example... and Under the same superconducting quantum chip, the same number of probe qubits, and the same total sensing time, the probe qubit readout channel and the auxiliary qubit readout channel can each provide two distinguishable parameter responses; for orthogonal signal generators, the effective Fisher information of the two parameters can vary with sensing time. Scale growth; for parallel signal generators, the two parameters can be estimated separately from the non-singular Fisher information matrix.

[0125] In more preferred embodiments, additional auxiliary qubits are set in addition to the auxiliary qubits used for parameter information separation to extract noise syndromes. If the probe is subjected to X-type or Z-type noise and the noise operator is parallel to a signal generator, the noise event is marked on the additional auxiliary qubits by controlling the sign of the signal term or by using a controlled gate structure; the additional auxiliary qubits are measured, and the corresponding noise is determined based on the measurement result, and corresponding corrections are performed on the probe qubits. When both X-type and Z-type noise are present, multiple additional auxiliary qubits can be set to extract syndromes from different noise channels respectively.

[0126] In this system, one auxiliary qubit is used to receive a signal component from the parameter to be estimated, while the other auxiliary qubits are used for noise diagnosis and correction. This not only enables the separation of multi-parameter information but also allows for integration with noise syndrome extraction mechanisms, improving the robustness of multi-parameter estimation in practical open quantum systems.

[0127] In more preferred embodiments, the optical platform uses polarization degrees of freedom to encode probe qubits and path degrees of freedom to encode auxiliary qubits:

[0128]

[0129] Among them, subscript and These represent the probe's degrees of freedom and the auxiliary degrees of freedom, respectively. and These represent the horizontal polarization state and the vertical polarization state, respectively. and These represent the path states corresponding to the two optical paths, respectively.

[0130] The auxiliary path degrees of freedom are prepared into a coherent superposition state using a beam splitter or polarization beam splitter, so that the polarization probe in the first path undergoes... This causes the polarization probe in the second path to undergo... Control door It can be implemented using a half-wave plate, a quarter-wave plate, a liquid crystal phase modulator, a spatial light modulator, or a mode converter. For orthogonal generators, the equivalent in the second path... Gatekeeper The signal acquires a relative sign change; for parallel generators, branch differences are formed through opposite sign phase delays, opposite direction rotation angles, or adjustable phase modulations in different paths. Path combiners, interferometers, and path-dependent optical gates perform conditional compensation, while polarization analyzers, path detectors, or interferometric measurement devices provide readout. When using a classical coherent light source, the complex amplitudes of different optical field modes can be used as a mechanism to separate information from the quantum state amplitude components to verify parameters; when quantum-enhanced sensing is required, single-photon sources, entangled photon sources, or compressed light sources can be used.

[0131] According to the present invention, a multi-parameter quantum estimation system based on indeterminate evolution is provided, such as... Figure 3 As shown, it includes a probe quantum register, an auxiliary quantum register, a quantum control component, a quantum measurement component, and a classical processing component. The quantum control component is connected to the probe quantum register and the auxiliary quantum register, and includes a quantum state initialization module, a time slice control module, a parameter encoding module, an indeterminate evolution control module, a control pulse module, a signal inversion module, and a condition compensation module; the quantum measurement component is connected to both quantum registers; and the classical processing component is connected to the quantum measurement component.

[0132] The probe quantum register carries the quantum encoding of the parameter to be estimated. The auxiliary quantum register is used to form a coherent history path and control the probe quantum register to undergo different parameter encoding evolution branches. For two parameters to be estimated, the auxiliary quantum register may include one auxiliary qubit; for the fractional encoding of non-orthogonal and non-parallel generators, the auxiliary quantum register may include a first auxiliary qubit and a second auxiliary qubit; for multi-qubit probes, auxiliary qubits can be configured for each probe qubit.

[0133] The quantum state initialization module acts on the probe quantum register and the auxiliary quantum register respectively to prepare the initial quantum states of the two quantum registers.

[0134] In a superconducting quantum bit platform, the quantum state initialization module includes an arbitrary waveform generator, a microwave source, and a pulse control module. This is achieved through reset operations and microwave... Initial states are prepared using pulses and single-qubit rotating gates. In the optical platform, the quantum state initialization module includes a beam splitter, a polarization beam splitter, a waveplate, a phase plate, a spatial light modulator, or a mode converter.

[0135] The time-slice control module is connected to the parameter encoding module, the indeterminate evolution control module, and the condition compensation module, based on the total sensing time. and number of time slices The control timing for each time slice is generated so that beam splitting, encoding, and conditional compensation are executed sequentially within each time slice, and the next time slice is triggered after the current time slice ends.

[0136] When the current time slice number reaches At that time, the time slice control module stops parameter encoding and triggers the quantum measurement module.

[0137] The parameter encoding module receives the physical parameters to be measured or the external field input, and constructs a quantum sensing Hamiltonian based on the physical quantity to be estimated. In the superconducting platform, the parameters to be estimated can be microwave driving frequency, microwave driving phase, driving amplitude, frequency detuning, effective magnetic flux bias, or coupling strength. Driving amplitude or driving phase can form a transverse effective signal, while frequency detuning or magnetic flux bias can form a longitudinal effective signal.

[0138] The parameter encoding module applies corresponding control actions to the probe qubits through microwave control lines and frequency modulation lines.

[0139] The indeterminate evolution control module is connected to the auxiliary quantum register, the probe quantum register, the control pulse module, and the signal inversion module, respectively. Within each time slice, the quantum state of the auxiliary quantum register is first coherently decomposed according to its historical path components. Then, based on the relationships between multiple signal generators, the control pulse module or the signal inversion module is invoked to ensure the probe quantum register undergoes coherent evolution. and Two branches of parametric encoding evolution.

[0140] The control pulse module applies control gates in the case of orthogonal or anti-easily generators. .

[0141] exist In the superconducting implementation, the control pulse module uses microwaves Pulse implementation ,use and Easy and The anti-easy relationship forms two branches with different parameter responses, thus preventing the active reversal of the external physical field to be measured. Controlled operation of two qubits can be achieved by cross-resonance gates, controlled phase gates, iSWAP gates (switching gates), tunable couplers, or equivalent gate sequences.

[0142] The signal inversion module performs effective sign inversion on the signal term corresponding to at least one parameter to be estimated in the case of parallel or linearly correlated generators.

[0143] In a superconducting platform, the signal inversion module can be generated by changing the microwave drive phase, switching the frequency detuning sign, or using echo pulses or digital quantum simulation. and Two branches. In the optical platform, the signal inversion module can form two branches by using opposite sign phase delays, opposite direction rotation angles, or path-dependent phase modulations in different paths.

[0144] The condition compensation module is connected to both the auxiliary quantum register and the probe quantum register, identifies the historical path components recorded in the auxiliary quantum register, and then... Historical path component selection ,according to Historical path component selection ; and The compensation gate in the code is matched with the signal generator corresponding to the routed parameters. .

[0145] The conditional compensation module feeds back the processed joint quantum state to the indeterminate evolution control module as input for the next time slice. In a superconducting platform, the conditional compensation module may include a controlled Pauli gate, a controlled phase gate, a microwave conditional pulse, or an equivalent gate sequence; in an optical platform, the conditional compensation module may include a path-dependent waveplate, a phase plate, a polarization controller, an interferometer beam combiner, or a spatial light modulator.

[0146] The quantum measurement component is connected to the probe quantum register and the auxiliary quantum register, respectively.

[0147] In a superconducting platform, quantum measurement components include a probe readout resonant cavity, an auxiliary readout resonant cavity, and corresponding cryogenic amplifiers, room-temperature amplifiers, and data acquisition electronics; in an optical platform, quantum measurement components include a polarization analyzer, a path detector, a single-photon detector, a balanced detector, an interferometer, or a camera readout component.

[0148] The quantum measurement component converts the quantum state into a binary measurement result or a continuous readout signal, and transmits it to the classical processing component.

[0149] The classical processing component is connected to the quantum measurement component to obtain the measurement probability distribution based on the repeated measurement results, and to calculate the classical Fisher information matrix or perform maximum likelihood estimation, Bayesian estimation, least squares estimation, neural network estimation or adaptive estimation to output the estimation results of multiple parameters to be estimated.

[0150] In more preferred embodiments, a superconducting qubit platform is employed. One transmon qubit serves as a probe qubit, and another transmon qubit serves as an auxiliary qubit. An arbitrary waveform generator and a microwave source provide control waveforms to a pulse control module, which applies initialization pulses, single-qubit gates, and controlled gates to the probe qubit and auxiliary qubit, respectively. The physical parameter to be measured or the external field is applied to the probe qubit via a parameter encoding module, and a coupler or controlled gate module establishes a controlled interaction between the two qubits.

[0151] After completing multiple indeterminate evolution time slices, the probe readout resonant cavity and the auxiliary readout resonant cavity output readout signals respectively. The amplification and data acquisition module sends the readout signals to the classical processing component, which then outputs multiple parameters to be estimated.

[0152] In more preferred embodiments, the system is expanded to multiple probe-auxiliary qubit pairs. Each probe-auxiliary qubit pair performs beam splitting, parameter encoding, and condition compensation locally, and multiple units are controlled in parallel via an on-chip bus resonant cavity, a tunable coupler, or a fixed coupling network. The probe quantum register and the auxiliary quantum register can also be prepared as entangled states, allowing information on different parameters to be collectively accumulated in the two registers respectively.

[0153] In more preferred embodiments, a neutral atom or ion trap platform is employed. In the neutral atom platform, the probe qubit and auxiliary qubit are encoded by two hyperfine levels, Zeeman levels, or Rydberg levels of the atom. The parameters to be estimated can be external magnetic field, electric field, laser phase, frequency detuning, Rabi frequency, or interatomic interaction strength. The single-qubit gate is realized by microwave pulses or Raman laser pulses, and the controlled gate is realized by the Rydberg blocking mechanism.

[0154] In the ion trap platform, probe qubits and auxiliary qubits are encoded by the internal energy levels of ions, single-qubit rotation is achieved by laser or microwave pulses, and multi-qubit controlled gates are achieved through the collective vibration modes of ions.

[0155] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A multi-parameter quantum estimation method based on indeterminate evolution, characterized in that, include: Step S1: Initialize the probe quantum register and initialize the auxiliary quantum register to a coherent superposition state. Construct a quantum sensing Hamiltonian containing the parameters to be estimated and the corresponding signal generators based on the physical quantity to be estimated. Divide the total sensing time into multiple time slices. Step S2: For each time slice, coherently decompose the auxiliary quantum state of the auxiliary quantum register according to different historical path components; Step S3: Based on the relationship between the signal generators corresponding to the parameters to be estimated, select the control gate, symbol configuration and / or signal inversion mode so that the probe quantum register coherently undergoes two parameter encoding evolution branches under the control of the auxiliary quantum register, forming a coherent path; Step S4: Select condition compensation based on different historical path components, and perform condition compensation on coherent paths to separate and encode the information of different parameters to be estimated into probe quantum registers and auxiliary quantum registers; Using the joint quantum state after condition compensation as the input for the next time slice, repeat steps S2 to S4 until the total sensing time is reached. Measure the probe quantum register and the auxiliary quantum register respectively, and obtain the estimated result of the parameter to be estimated based on the measurement results.

2. The multi-parameter quantum estimation method based on indeterminate evolution according to claim 1, characterized in that, The quantum sensing Hamiltonian for: The length of the time slice for The parametric coding evolution branch includes a first parametric coding evolution branch and a second parametric coding evolution branch; The evolution operator for the first parameter encoding evolution branch is: The evolution operator for the second parameter encoding evolution branch is: in, , Indicates different parameters to be estimated. , They represent , The corresponding signal generator; Indicates the total sensing time. Indicates the number of time slices; Indicates by parameters and The parameter encoding evolution operator is jointly determined. This represents the control gate acting on the probe quantum register. The natural constant is represented by i, which represents the imaginary unit. This indicates the configuration parameters for the signal item symbol, with values ​​ranging from 1 to 2. or ; express The conjugate transpose of .

3. The multi-parameter quantum estimation method based on indeterminate evolution according to claim 2, characterized in that, In step S3, when and When orthogonal or anti-orthogonal, let and choose with Easy and Opposing Easy Control Gate Through the control door The conjugate transformation of the quantum sensing Hamiltonian makes The signs are the same in the two parametric coding evolution branches and The signs are opposite; when and When parallel or linearly dependent, let In the second parameter encoding evolution branch, effective sign inversion is performed on the signal term corresponding to at least one parameter to be estimated.

4. The multi-parameter quantum estimation method based on indeterminate evolution according to claim 2, characterized in that, In step S4, based on the auxiliary quantum register... Historical path component selection first condition compensation According to the auxiliary quantum register Historical path component selection second condition compensation : in, This represents the unit operation on the probe quantum register; This represents a compensation gate that matches the signal generator corresponding to the parameter to be estimated that is routed to the auxiliary quantum register; , These represent the projection operators for two different historical path components of the auxiliary qubit; and middle, and The correspondences on the two historical path components are opposite.

5. The multi-parameter quantum estimation method based on indeterminate evolution according to claim 2, characterized in that, In step S3, when and When they are neither orthogonal nor parallel, Decomposed into relative Parallel and orthogonal components; Configure the first auxiliary qubit and set the corresponding The orthogonal components are encoded into the first auxiliary qubit; Configure the second auxiliary qubit and set the corresponding Parallel components are encoded into the second auxiliary qubit by effectively reversing the sign of the signal term.

6. A multi-parameter quantum estimation system based on indeterminate evolution, comprising a probe quantum register, an auxiliary quantum register, a quantum control component, a quantum measurement component, and a classical processing component, characterized in that, The quantum control component is connected to the probe quantum register and the auxiliary quantum register respectively. The probe quantum register is initialized and the auxiliary quantum register is initialized to a coherent superposition state. A quantum sensing Hamiltonian containing the parameters to be estimated and the corresponding signal generators is constructed according to the physical quantity to be estimated. The total sensing time is divided into multiple time slices. For each time slice, the auxiliary quantum state of the auxiliary quantum register is coherently decomposed according to different historical path components; Based on the relationship between the signal generators corresponding to the parameters to be estimated, the control gate, symbol configuration and / or signal inversion method are selected so that the probe quantum register coherently undergoes two parameter encoding evolution branches under the control of the auxiliary quantum register, forming a coherent path; Conditional compensation is selected based on different historical path components, and conditional compensation is performed on coherent paths. The joint quantum state after conditional compensation is used as the input for the next time slice. The quantum measurement component is connected to the probe quantum register and the auxiliary quantum register respectively. After the total sensing time is reached, the probe quantum register and the auxiliary quantum register are measured respectively to obtain the measurement results. The classical processing component is connected to the quantum measurement component to obtain the estimated result of the parameter to be estimated based on the measurement result.

7. The multi-parameter quantum estimation system based on indeterminate evolution according to claim 6, characterized in that, The quantum control component includes a quantum state initialization module, a time slice control module, a parameter encoding module, an indeterminate evolution control module, and a condition compensation module; The parameter encoding module constructs the quantum sensing Hamiltonian: The time slice control module determines the length of each time slice: The indeterminate evolution control module forms the first parameter encoding evolution branch: And this forms the second parameter encoding evolution branch: The condition compensation module is configured to feed back the joint quantum state after condition compensation to the indeterminate evolution control module; in, , Indicates different parameters to be estimated. , They represent , The corresponding signal generator; Indicates the total sensing time. Indicates the number of time slices; Indicates by parameters and The parameter encoding evolution operator is jointly determined. This represents the control gate acting on the probe quantum register. The natural constant is represented by i, which represents the imaginary unit. This indicates the configuration parameters for the signal item symbol, with values ​​ranging from 1 to 2. or ; express The conjugate transpose of .

8. The multi-parameter quantum estimation system based on indeterminate evolution according to claim 7, characterized in that, The quantum control component also includes a control pulse module and a signal inversion module; when and When orthogonal or anti-orthogonal, the control pulse module commands... And choose with Easy and Opposing Easy Control Gate ,make The signs are the same in the two parametric coding evolution branches and The signs are opposite; when and When parallel or linearly correlated, the signal inversion module makes And in the second parameter coding evolution branch, effective sign inversion is performed on the signal item corresponding to at least one parameter to be estimated.

9. The multi-parameter quantum estimation system based on indeterminate evolution according to claim 7, characterized in that, The condition compensation module is based on the auxiliary quantum register. Historical path component selection first condition compensation According to the auxiliary quantum register Historical path component selection second condition compensation : in, This represents the unit operation on the probe quantum register; This represents a compensation gate that matches the signal generator corresponding to the parameter to be estimated that is routed to the auxiliary quantum register; , These represent the projection operators for two different historical path components of the auxiliary qubit; and middle, and The correspondences on the two historical path components are opposite.

10. The multi-parameter quantum estimation system based on indeterminate evolution according to claim 7, characterized in that, The auxiliary quantum register includes a first auxiliary quantum bit and a second auxiliary quantum bit; when and When they are neither orthogonal nor parallel, the parameter encoding module will Decomposed into relative Parallel and orthogonal components; The indeterminate evolution control module will control the first auxiliary qubit corresponding to... Encoding orthogonal components; The second auxiliary qubit corresponds to Parallel components are encoded by reversing the effective sign of the signal term.

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