A non-orthogonal quantum state discrimination method based on quantum machine learning
By constructing variable quantum circuits and auxiliary qubits, the problem of distinguishing non-orthogonal quantum states in the NISQ era has been solved, achieving efficient and reliable distinction under multiple categories and noise conditions, thus improving the real-time performance and security of quantum communication.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ANHUI UNIV
- Filing Date
- 2026-05-09
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies struggle to effectively distinguish non-orthogonal quantum states in the NISQ era, especially under multi-class and noisy conditions. Traditional methods are difficult to achieve efficient and robust distinctions and are not suitable for small sample conditions.
By employing a quantum machine learning-based approach, a variable quantum circuit is constructed, utilizing auxiliary qubits and alternating single-qubit rotating gates and double-qubit gates, combined with single-shot measurement and pre-defined decision rules, to distinguish quantum states.
It achieves efficient and reliable differentiation on practical noisy quantum devices, is applicable to multiple types of non-orthogonal quantum states, and has real-time performance and robustness. It breaks through the application limitations of traditional schemes and improves the security and real-time performance of quantum communication.
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Figure CN122198173A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of quantum communication and cryptography, and particularly relates to a method for distinguishing non-orthogonal quantum states. Background Technology
[0002] Quantum state discrimination is a core fundamental task in quantum information science, playing a crucial role in quantum cryptography, quantum communication, and quantum computing. Due to the limitation of the no-cloning theorem, non-orthogonal quantum states cannot be perfectly distinguished; therefore, achieving optimal or near-optimal discrimination of non-orthogonal quantum states is a key focus of theoretical and experimental research.
[0003] Traditional non-orthogonal quantum state discrimination schemes, such as minimum error discrimination and unambiguous discrimination, typically rely on analytical derivation of the specific representation of the quantum state to be distinguished in order to obtain the optimal generalized measurement operator. These methods have significant drawbacks: First, analytical solutions are often difficult to obtain, especially for three or more types of quantum states or mixed states; second, theoretically optimal measurements often require complex joint measurements or nonlocal operations, which are difficult to physically realize on current noisy medium-scale (NISQ) quantum devices; finally, traditional schemes are extremely sensitive to experimental noise, decoherence, and other disturbances, resulting in a significant performance degradation in real-world environments.
[0004] In recent years, quantum machine learning has provided a new paradigm for distinguishing non-orthogonal quantum states. However, the feasibility of existing methods, which rely on intermediate measurements and classical feedback conditional operations based on measurement results, is low. This is because it requires measuring a qubit midway through the circuit and rapidly feeding the measurement result back to the control system to determine the quantum gate sequence for subsequent applications in real time. The entire feedback delay must be much smaller than the coherence time of the qubit; otherwise, the state will decoherent. Most research focuses on distinguishing two classes of non-orthogonal pure states under ideal conditions and assumes sufficient training samples. These approaches fail to effectively address the prevalent noise interference problem in real quantum systems and are not suitable for distinguishing multiple classes of non-orthogonal quantum states or for efficient learning under small sample conditions. Therefore, there is an urgent need for a non-orthogonal quantum state distinction technique that can adapt to the hardware limitations of the NISQ era, is robust to noise, and can handle more complex distinction scenarios. Summary of the Invention
[0005] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a method for distinguishing non-orthogonal quantum states.
[0006] Technical solution: This invention discloses a method for distinguishing non-orthogonal quantum states based on quantum machine learning, specifically as follows: Acquire quantum state sample data under different types; For different types of quantum states, construct corresponding variable quantum circuits; Prepare quantum states onto input qubits; For any type of quantum state, the input qubit is input into the corresponding variable quantum circuit to identify the state type of the quantum state; Quantum state types include two or more types of non-orthogonal quantum states.
[0007] Furthermore, the variable quantum circuit adopts an architecture of input qubits plus auxiliary qubits. The variable quantum circuit includes alternating single-qubit rotating gates and two-qubit gates. The design of the variable quantum circuit follows the hardware awareness principle, inputting the input qubits to the corresponding variable quantum circuits, performing single-shot measurements on the auxiliary qubits, and obtaining the prediction results according to the preset judgment rules.
[0008] Furthermore, the two types of non-orthogonal quantum states include two types of single-qubit non-orthogonal quantum states. These quantum states are prepared onto the input qubit, and auxiliary qubits are constructed. The variable quantum circuit constructed for these quantum states includes: a first to a third two-qubit gate, a first and second cascaded rotating gate structure, a first and a second Rx gate, and a first Rz gate. The auxiliary qubit and the input qubit are respectively input to the two input terminals of the first two-qubit gate. The output of the first two-qubit gate is connected to the input terminal of the first cascaded rotating gate structure. The output terminal of the first cascaded rotating gate structure and the input qubit are respectively connected to the two input terminals of the second two-qubit gate. The input qubit is also input to the input terminal of the second Rx gate. The output terminal of the second two-qubit gate is connected to the input terminal of the first Rx gate. The output terminal of the first Rx gate is connected to the input terminal of the first Rz gate. The output terminals of the first Rz gate and the second Rx gate are respectively connected to the two input terminals of the third two-qubit gate. The output terminal of the third two-qubit gate is connected to the second cascaded rotating gate structure.
[0009] Furthermore, the two types of non-orthogonal quantum states include two-qubit separable non-orthogonal quantum states; these quantum states are prepared onto the first and second input qubits to construct the first and second auxiliary qubits; the variable quantum circuits constructed for these quantum states include: fourth to seventh two-qubit gates, a third and fourth rotating gate cascade structure, and first and second composite quantum gates; the first auxiliary qubit and the first input qubit are respectively input to the two input terminals of the fourth two-qubit gate, the output of the fourth two-qubit gate and the second input qubit are respectively input to the two input terminals of the fifth two-qubit gate, and the output terminal of the fifth two-qubit gate is connected to the input terminal of the third rotating gate cascade structure; the second auxiliary qubit and the first input qubit are respectively input to the two input terminals of the sixth two-qubit gate, the output of the sixth two-qubit gate and the second input qubit are respectively input to the two input terminals of the seventh two-qubit gate, and the output terminal of the seventh two-qubit gate is connected to the input terminal of the fourth rotating gate cascade structure; the output of the third rotating gate cascade structure, the output of the fourth rotating gate cascade structure, and the first and second input qubits are respectively input to the first composite quantum gate, and the first composite quantum gate is connected to the second composite quantum gate.
[0010] Furthermore, the first and second composite quantum gates have the same structure, both including the eighth to thirteenth two-qubit gates and the fifth and sixth rotating gate cascade structures. The outputs of the third and fourth rotating gate cascade structures, along with the first and second input qubits, are used as the four inputs of the first composite quantum gate. Specifically, the output of the third rotating gate cascade structure and the first input qubit are respectively input to the two input terminals of the eighth two-qubit gate; the output of the eighth two-qubit gate and the output of the fourth rotating gate cascade structure are respectively input to the two input terminals of the ninth two-qubit gate; the output of the ninth two-qubit gate and the second input qubit are respectively input to the two input terminals of the tenth two-qubit gate; and the output of the tenth two-qubit gate is connected to... The input terminals of the fifth rotating gate cascade structure are connected to the two input terminals of the eleventh two-bit gate, respectively. The output of the eleventh two-bit gate and the first input qubit are respectively input to the two input terminals of the twelfth two-bit gate. The output of the twelfth two-bit gate and the second input qubit are respectively input to the two input terminals of the thirteenth two-bit gate. The output terminal of the thirteenth two-bit gate is connected to the sixth rotating gate cascade structure. The output of the fifth rotating gate cascade structure of the first composite quantum gate, the output of the sixth rotating gate cascade structure of the first composite quantum gate, and the first and second input qubits are used as the four inputs of the second composite quantum gate, and the connection method is the same as that of the first composite quantum gate.
[0011] Furthermore, the two types of non-orthogonal quantum states include complex quantum states containing impurities. This type of quantum state includes a first quantum state and a second quantum state, where the first quantum state contains a state with a variable parameter, and the second quantum state contains two states with different phases. Third and fourth auxiliary qubits are constructed, and this type of quantum state is prepared onto the third and fourth input qubits. The variable quantum circuit constructed for this type of quantum state includes: an amplitude encoding circuit, fourteenth to twenty-third two-qubit gates, and a cascaded structure of seventh to tenth rotation gates. The third and fourth auxiliary qubits and the third and fourth input qubits are respectively input to the amplitude encoding circuit, and the amplitude-encoded third and fourth auxiliary qubits are denoted as... , The third and fourth input qubits after amplitude encoding are denoted as , ; Will and The inputs are respectively fed to the two input terminals of the fourteenth double-bit gate, and the output of the fourteenth double-bit gate is summed with the output of the fourteenth double-bit gate. The inputs are respectively fed to the two input terminals of the fifteenth double-bit gate, and the outputs are... and The inputs are respectively fed to the two input terminals of the sixteenth double-bit gate, and the output of the sixteenth double-bit gate is summed with the output of the double-bit gate. The inputs are respectively connected to the two input terminals of the seventeenth double-bit gate; the output terminal of the fifteenth double-bit gate is connected to the input terminal of the seventh rotary gate cascade structure, and the output terminal of the seventeenth double-bit gate is connected to the input terminal of the eighth rotary gate cascade structure. The output of the seventh rotary gate cascade structure and... The outputs of the eighteenth double-bit gate and the cascaded eighth rotary gate are respectively input to the two inputs of the nineteenth double-bit gate. The inputs are respectively connected to the two input terminals of the twentieth double-bit gate. The output terminal of the twentieth double-bit gate is connected to the input terminal of the ninth rotary gate cascade structure. The output terminals of the ninth rotary gate cascade structure and the eighth rotary gate cascade structure are respectively connected to the two input terminals of the twentieth double-bit gate. The output terminal of the twentieth double-bit gate and... Connect the two input terminals of the 22nd double-bit gate, and the output terminal of the 22nd double-bit gate respectively. The two inputs of the twenty-third double-bit gate are connected to each other, and the output of the twenty-third double-bit gate is connected to the input of the tenth cascaded rotating gate structure to store the output results of the ninth and tenth cascaded rotating gate structures.
[0012] Furthermore, two or more types of non-orthogonal quantum states include three types of non-orthogonal quantum states. These quantum states are prepared onto the fifth and sixth input qubits to construct the fifth and sixth auxiliary qubits. The variable quantum circuits constructed for this type of quantum state include: the 24th to 30th two-qubit gates and the 11th to 16th rotating gate cascade structures. The fifth auxiliary qubit and the fifth input qubit are respectively input to the two input terminals of the 24th two-qubit gate. The output terminal of the 24th two-qubit gate and the sixth input qubit are respectively connected to the two input terminals of the 25th two-qubit gate. The sixth auxiliary qubit and the fifth input qubit are respectively input to the two input terminals of the 26th two-qubit gate. The output terminal of the 26th two-qubit gate and the sixth input qubit are respectively connected to the two input terminals of the 27th two-qubit gate. The output terminal of the 25th two-qubit gate is connected to the input terminal of the 11th rotating gate cascade structure. The output of the 27th two-bit gate is connected to the input of the 12th rotating gate cascade structure. The fifth input qubit is input to the input of the 13th rotating gate cascade structure, and the sixth input qubit is input to the input of the 14th rotating gate cascade structure. The outputs of the 11th and 12th rotating gate cascade structures are connected to the two inputs of the 28th two-bit gate, respectively. The outputs of the 28th and 13th rotating gate cascade structures are connected to the two inputs of the 29th two-bit gate, respectively. The outputs of the 29th and 14th rotating gate cascade structures are connected to the two inputs of the 30th two-bit gate, respectively. The output of the 11th rotating gate cascade structure is connected to the input of the 15th rotating gate cascade structure, and the output of the 30th two-bit gate is connected to the input of the 16th rotating gate cascade structure. The outputs of the 15th, 16th, 13th, and 14th rotating gate cascade structures are stored.
[0013] Furthermore, the cascaded rotating door structure includes a third Rx door, a second Rz door, and a fourth Rx door connected in sequence.
[0014] Furthermore, if the quantum state is either a two-qubit separable non-orthogonal quantum state or a complex quantum state containing impurities, and the variable quantum circuit of this type of quantum state supports unambiguous distinction, the following loss function L is designed when training the parameters of the variable quantum circuit corresponding to this type of quantum state: ; in, and They are weights, For error rate, This represents the probability that the outcome is uncertain.
[0015] Furthermore, a unified training framework is adopted for different variable quantum circuits, specifically: gradient updates of parameters are performed using differentials based on parameter translation.
[0016] Beneficial effects:
[0017] The variable quantum circuit designed in this invention has a simple and shallow structure, actively reducing noise accumulation by minimizing the number of quantum gates. It can be easily integrated into existing quantum receiver hardware. Furthermore, the quantum circuit tolerates uncertain output results, implementing an unambiguous discrimination strategy. Even when faced with noise or highly overlapping quantum states, it guarantees the determinism of the determined result, significantly improving the operational reliability on practical noisy quantum devices. This invention achieves true end-to-end real-time discrimination; input is the result, processing is the decision. The entire decision-making process requires no classical post-processing, no storage of state information, and no multiple attempts, achieving ultra-low latency from reception to decision, which is crucial for the real-time performance of quantum communication.
[0018] The general framework proposed in this invention is not only applicable to distinguishing between two types of non-orthogonal quantum states, but can also be extended to distinguishing between three or more types of non-orthogonal quantum states, breaking through the application limitations of traditional schemes. Furthermore, the scheme can distinguish sets of non-orthogonal quantum states containing impurity states, making it closer to real-world application scenarios. Within the framework of single-shot measurement, this invention, through clever design of the number of auxiliary qubits and the measurement basis, also outputs "uncertain" results. This allows the system to choose to "abstain" when channel noise is high or state overlap is too high, ensuring the absolute reliability of the determined results. This feature has special value in improving the security of the QKD protocol.
[0019] This invention employs an auxiliary qubit probe mechanism. Its core idea lies in enhancing discrimination capability by introducing auxiliary qubits and controlling the output state of the auxiliary qubits using information from the input qubits. The introduction of auxiliary qubits achieves a Nemac space expansion, transforming unitary evolution in the data space into non-unitary evolution. This process is achieved through generalized measurement operators. Specifically, in each iteration, the auxiliary qubits are first prepared to a known reference state, forming a joint initial state with the target substate of the main system. Then, a parameterized unitary transformation is applied, establishing a specific correlation between the main system and the auxiliary probe. By adjusting the circuit parameters, the output state distribution of the auxiliary qubits can be controlled, maximizing their discriminability for different types of input states.
[0020] This invention performs a single-shot measurement on an auxiliary qubit to complete a classification task. Due to the inherent characteristics of quantum measurement, a complete quantum measurement would ideally involve performing the same measurement multiple times on multiple copies of the same quantum state to obtain a probability distribution. However, the no-cloning theorem restricts perfect copying of unknown states. Therefore, to avoid the copying difficulties in quantum measurement, this invention directly utilizes the results of a single-shot measurement. Specifically, in each iteration, one hundred quantum states are extracted from the dataset, and a single-shot measurement is performed on the auxiliary probe of each state to obtain the discrimination result. Then, based on the label, the probability of successful discrimination and the probability of uncertain results in these one hundred single-shot measurements are calculated and substituted into the effective loss function to update the parameters. Each unknown master system state is used only once and is not repeatedly measured or copied, naturally avoiding the restriction of the no-cloning theorem. Through multiple rounds of iterative optimization, the system can automatically learn the optimal parameters, resulting in classification results based on single-shot measurements of auxiliary qubits that possess high discriminative power and low ambiguity, making it particularly suitable for scenarios where the sample copy number in quantum state discrimination is strictly one. Attached Figure Description
[0021] Figure 1 For two types of single-qubit non-orthogonal quantum states, there are variable quantum circuits;
[0022] Figure 2 The variable quantum circuits corresponding to two-bit separable non-orthogonal quantum states are shown; where (a) is the overall circuit diagram and (b) is the composite quantum gate circuit diagram.
[0023] Figure 3 For complex quantum states containing impurities, the variable quantum circuit is used.
[0024] Figure 4 These are the variable quantum circuits corresponding to three types of non-orthogonal quantum states;
[0025] Figure 5 Training diagrams of variable quantum circuits corresponding to two types of single-qubit non-orthogonal quantum states;
[0026] Figure 6 The training diagrams for the variable quantum circuits corresponding to two-bit separable non-orthogonal quantum states are shown; where (a) is a graph of the number of iterations versus the loss, and (b) is a graph of the number of iterations versus the accuracy.
[0027] Figure 7 The training diagrams for the variable quantum circuits corresponding to complex quantum states containing impurities are shown; where (a) is a graph of the number of iterations versus the loss, and (b) is a graph of the number of iterations versus the accuracy.
[0028] Figure 8 The training diagrams for the variable quantum circuits corresponding to the three types of non-orthogonal quantum states are shown; (a) is a curve of the number of iterations versus the loss, and (b) is a curve of the number of iterations versus the accuracy. Detailed Implementation
[0029] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0030] This invention employs a modular design, with data flowing from top to bottom through three core layers. First, at the data preparation layer, the system generates or collects a set of quantum state samples containing the target category (which may contain impurity states) according to task requirements. Second, at the variable quantum processing layer, the system constructs a shallow parameterized quantum circuit consisting of an input qubit and an auxiliary qubit, serving as a trainable non-orthogonal quantum state distinguisher. Third, single-shot measurements are performed on the output of the auxiliary qubit in the variable quantum circuit. Finally, at the classical optimization and control layer, the system uses a classical optimizer (such as Adam) combined with a specially designed hybrid loss function to train the circuit parameters, and performs rapid determination of the quantum state category through single-shot measurements of the auxiliary qubit.
[0031] Single-bit non-orthogonal state pairs (two types of single-bit non-orthogonal quantum states):
[0032] To verify the basic capabilities of the framework, this invention constructs a pair of simple single-qubit non-orthogonal quantum states: ; ;
[0033] Among them, fixed Its inner product is 0.5. According to the minimum error discrimination theory formula... The calculated value is 93.3%, of which , This represents the prior probability information of the quantum states to be distinguished. By preparing different numbers of samples of these states, the sample efficiency can be studied. and These represent the positive and negative states, respectively. Since they are qubits, this indicates a two-state quantum system. A two-state quantum system has two basis states. and An arbitrary quantum state of a qubit can be represented by the linear superposition of these two basis states. Such a qubit can be realized using specific physical systems, such as the two polarization states of a photon and the two energy levels of an electron in an atomic system. The superposition coefficients before the two basis states are called probability amplitudes, and their squared modulus represents the probability that the quantum system is in a certain basis state. The sum of these two probabilities is one, meaning that the two probability amplitudes satisfy the normalization condition. Changing the superposition coefficients changes the state of the quantum system, so parameters can be used. The superposition coefficient is used to define a single-qubit quantum state. This embodiment takes a specific... To verify the validity of the model, we will construct a simple pair of single-qubit non-orthogonal quantum states as described above. For simplicity, subsequent quantum states will be defined in this manner.
[0034] Two-bit separable nonorthogonal pairs
[0035] To demonstrate the ability to distinguish between non-orthogonal quantum states that are more complex, this embodiment constructs a pair of non-orthogonal two-qubit separable states. and :
[0036] ;
[0037] ;
[0038] and The inner product is The theoretical discrimination limit is 97.4%. This example is used to verify the effectiveness of the framework on two-bit systems.
[0039] A collection of complex quantum states containing impurities
[0040] To simulate a real-world noisy environment, a more complex task is constructed to distinguish between nonorthogonal quantum states. This task aims to differentiate between two classes of nonorthogonal quantum states, but one class (class A) contains a variable parameter. state Another type (Type B) contains two states with different phases. and .
[0041] ;
[0042] ;
[0043] ;
[0044] in, Representing different quantum states, and and They are two fixed quantum states, differing by only one relative phase.
[0045] A set containing three types of non-orthogonal quantum states
[0046] To overcome the binary classification limitation of the current framework, a three-class classification method is proposed. (Current analytical methods for distinguishing non-orthogonal quantum states only apply to cases where the number of non-orthogonal states to be distinguished is two. This embodiment innovatively proposes a three-class non-orthogonal quantum state distinction method based on quantum machine learning. Here, all three types of non-orthogonal quantum states are quantum superposition states of two-qubit systems, and are basis vector states.) Each with the other three basis states As a result of superposition, all three types of quantum states are pairwise non-orthogonal. (Data set of non-orthogonal states:) ; ; ;
[0047] and The superposition coefficient represents the quantum state. In this embodiment, the number of samples in each class is equal, which is used to verify the framework's ability to distinguish between multiple classes of non-orthogonal quantum states.
[0048] In quantum computing, a state cannot be directly input; instead, it must first be prepared into the qubits of the quantum computer. During this preparation process, each quantum gate will generate unexpected states (impurity states) due to noise. Therefore, with the introduction of noise, the circuit will acquire multiple impurity states. Thus, distinguishing non-orthogonal states in the presence of impurity states has significant scientific and practical value.
[0049] General circuit architecture
[0050] The core of this invention is a general variable quantum distinguishing circuit architecture, as shown in the attached figure. Figure 1 , 2 As shown in Figures 3 and 4. Its core idea is to introduce auxiliary qubits as distinguishing probes. The circuit consists of three parts:
[0051] 1. State Preparation / Encoding Section: The quantum state to be distinguished is prepared on the input qubit. This can be achieved using a fixed sequence of quantum gates. accomplish.
[0052] 2. Variational Evolution Part: The input qubit and the auxiliary qubit are connected through a parameterized quantum circuit. . It consists of alternating single-bit rotation gates and double-bit gates (such as CNOT gates), and has a relatively shallow depth. Single-bit rotation gates include Rx gates (rotation gates around the X-axis) and Rz gates (rotation gates around the Z-axis).
[0053] 3. Measurement and Decision Section: Single-shot measurement is performed on the auxiliary qubit. The measurement result is mapped to a category label according to a pre-defined decision rule obtained through training.
[0054] For different task-specific circuit variants, and for two types of single-qubit non-orthogonal quantum states, the constructed variational circuits are as follows: Figure 1 As shown, an auxiliary qubit is introduced; for a two-qubit separable non-orthogonal quantum state, the constructed variational circuit is as follows. Figure 2As shown in (a) and (b), two auxiliary qubits are introduced to become entangled with the input quantum state and extract partial information; for complex quantum states containing impurities, the corresponding variable quantum circuit is as follows: Figure 3 As shown, two auxiliary qubits are introduced; for the three types of non-orthogonal quantum states, the constructed variable quantum circuit is as follows. Figure 4 As shown, it is typically necessary to measure all or more qubits to obtain sufficient output information. Distinguishing between multiple classes of non-orthogonal quantum states is achieved by defining a mapping between the measurement results of multiple auxiliary qubits and class labels.
[0055] In the QNN model, the Rx gate and Ry gate represent rotation operations around the X and Y axes of the Bloch sphere, respectively. Their rotation angle parameters are denoted as... The value range is from 0 to (Radian system), that is This range covers a complete circular rotation and can express any possible quantum state evolution. Since the rotation operation is periodic, angles outside this range can be expressed using modulo operations. Reduced to this interval, therefore take The standard parameter range is sufficient to meet all application requirements, without the need for more complex constraints. Therefore, the rotation angle parameters of Rx and Rz in this embodiment range from 0 to... between.
[0056] To train quantum circuits that support complex strategies such as unambiguous discrimination, this invention innovatively employs a hybrid loss function that simultaneously considers error probability and uncertainty probability. This function can characterize both unambiguous discrimination and minimum error discrimination, and adjusting their weights allows the model output to be either unambiguous or minimum error discrimination. Large coefficient A small coefficient indicates unambiguous distinction. and The coefficient is equivalent to the minimum error in discrimination. For example: ; Or based on the form of cross-entropy: ; in For error rate, For the probability of an uncertain outcome, This loss function can simultaneously guide the model to minimize error and make reasonable use of uncertain options.
[0057] This embodiment uses mini-batch gradient descent for training. Gradient calculation is precisely obtained using parameter shifting rules. The optimizer uses Adam to accommodate potential noise in the gradients. A decay strategy can be set for the learning rate to improve convergence.
[0058] This invention employs single-shot measurement, which refers to sampling a quantum system only once to directly obtain a random eigenvalue (such as "up" or "down"). However, this result cannot reveal all the information of the quantum state, and quantum state differentiation does not require all information. Through the quantum circuit described earlier, this embodiment can differentiate quantum states with just a single-shot measurement. Complete measurement, on the other hand, requires multiple single-shot measurements on a large number of identical quantum states (usually under different measurement bases). Only by collecting the statistical distribution of these results can the complete information of the quantum state (such as the density matrix) be uniquely reconstructed. In short, single-shot measurement is a point sampling of the result of a single experiment, while complete measurement is a statistical process of reconstructing the entire quantum state through a large number of point samples.
[0059] This invention directly targets a fundamental and widespread application scenario in quantum information processing: the instantaneous differentiation of a received single-copy unknown quantum state. A typical application scenario for this mechanism is in quantum communication (such as quantum key distribution, QKD), quantum networks, or distributed quantum computing, where the sender transmits a quantum state to the receiver via a quantum channel. According to the no-cloning theorem, the receiver can only obtain a physical copy of this quantum state. It is impossible to replicate or repeatedly measure it without destroying the state. In this case, the receiver's task is to differentiate this single-copy quantum state as accurately as possible based on limited prior information, in order to decode information or trigger subsequent operations.
[0060] The preset determination rule in this embodiment is:
[0061] For single-qubit binary classification: the auxiliary qubit measurement result is → Category A, for → Category B.
[0062] For binary classifications with unambiguous distinctions (two-qubit separable non-orthogonal quantum states or complex quantum states containing impurities): the measurement result is... → Category A, for or → Category B, for → Uncertain.
[0063] For the three-category classification: the measurement result belongs to the set. → , → ,
[0064] , , → .
[0065] This invention employs the parameter-shift method for gradient calculation. This analytical differentiation method, specifically designed for variational quantum algorithms, effectively avoids the numerical truncation error introduced by the finite difference method. Its core principle demonstrates that the gradient of a parameterized quantum gate can be calculated by shifting the parameter... Translate in the positive and negative directions respectively And it is obtained by calculating the difference between their expected values, that is, by following the formula:
[0066] ;
[0067] Where f is the objective function, This is for differential calculations.
[0068] An embodiment of the present invention:
[0069] At the model architecture level, in order to find the optimal balance between limited quantum resource consumption and model expressive power, this invention captures quantum correlations in the data by alternately laying single-qubit rotation gates and two-qubit gates, and sets the circuit depth to 2 layers (DEPTH=2). This circuit design not only effectively reduces the interference of quantum noise on the calculation results, but also ensures that the model has sufficient parameter space to fit the characteristic boundaries of complex non-orthogonal quantum states.
[0070] The entire discrimination process of this invention operates on and consumes only the received quantum state copy, fully complying with the fundamental principles of quantum mechanics and practical resource constraints. The trained circuit itself encodes optimal (or near-optimal) discrimination knowledge.
[0071] (a) This invention successfully designed a quantum state discrimination scheme based on variable quantum circuits. Numerical simulation results show that the scheme exhibits high accuracy in distinguishing entangled states from separable states, and verifies the robustness of the designed quantum state discrimination model under various noise environments, demonstrating its ability to effectively handle complex situations with multiple impurity states in reality. A quantum computing experiment using the Origin Quantum Cloud Platform and the Origin Wuyuan superconducting quantum computer was successfully conducted, and the experimental results highly agree with the numerical simulation results, demonstrating strong practical value. For specific quantum state discrimination quantum circuit models, a quantitative relationship between the number of training samples and model performance is given, providing a decision-making basis for quantum circuit learning under limited resources.
[0072] (b) This embodiment considers the case where there are more than two types of quantum states to be distinguished, which is a problem that traditional quantum state distinction methods cannot effectively solve.
[0073] (c) This implementation designs a quantum circuit that can effectively distinguish a set of three non-orthogonal quantum states, providing a novel solution to the problem of distinguishing multiple non-orthogonal quantum states.
[0074] (d) To address the physical constraints imposed by the no-cloning theorem, this embodiment proposes a quantum state classification method based on single-shot measurement of auxiliary bits. This method abandons the traditional approach of repeatedly measuring or copying the same unknown master state. Instead, it performs a single-shot measurement only once on the auxiliary probe of each unknown state. The measurement operation is limited to the auxiliary bit, and each master state is discarded after use, thus naturally circumventing the limitations of the no-cloning theorem.
[0075] Distinguishing between two types of single-qubit non-orthogonal quantum states: such as Figure 5 As shown, when the number of training samples reaches approximately 2500, the discrimination accuracy exceeds 85%; when the number of samples increases to 20000, the accuracy is approximately 93%, approaching the theoretical limit. This verifies the basic effectiveness of the framework and clarifies sample efficiency.
[0076] Distinguishing between two-qubit separable non-orthogonal quantum states: such as Figure 6 As shown in (a) and (b), only about 14,200 samples were used to achieve an accuracy of 96.27% on the 142nd training iteration, which is close to the theoretical limit of 97.4%.
[0077] Distinguishing complex quantum states containing impurities: such as Figure 7 As shown in (a) and (b), after noise-free training, the accuracy remains above 95% in a noisy testing environment (reaching 97.44% in noise-free conditions), demonstrating the strong robustness of this scheme. This scheme was further successfully deployed on the Wuyuan real superconducting quantum computer, achieving an accuracy exceeding 95%.
[0078] Distinguishing between three types of non-orthogonal quantum states: such as Figure 8 As shown in (a) and (b), the accuracy reaches 85% when the number of training samples reaches 8000, and the accuracy increases to 93.4% when the number of samples reaches 20000, successfully achieving the distinction of multi-class non-orthogonal quantum states.
[0079] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.
Claims
1. A method for distinguishing non-orthogonal quantum states based on quantum machine learning, characterized in that, Specifically: Acquire quantum state sample data under different types; For different types of quantum states, construct corresponding variable quantum circuits; Prepare quantum states onto input qubits; For any type of quantum state, the input qubit is input into the corresponding variable quantum circuit to identify the state type of the quantum state; Quantum state types include two or more types of non-orthogonal quantum states.
2. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 1, characterized in that, The variable quantum circuit adopts an architecture of input qubits plus auxiliary qubits. The variable quantum circuit includes alternating single-qubit rotating gates and two-qubit gates. The design of the variable quantum circuit follows the hardware awareness principle. The input qubits are input to the corresponding variable quantum circuits, and single-shot measurements are performed on the auxiliary qubits. According to the preset judgment rules, the prediction results are obtained.
3. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 1, characterized in that, The two types of non-orthogonal quantum states include two types of single-qubit non-orthogonal quantum states. These quantum states are fabricated onto the input qubit, and auxiliary qubits are constructed. The variable quantum circuits constructed for these quantum states include: first to third two-qubit gates, a first and second cascaded rotation gate structure, first and second Rx gates, and a first Rz gate. The auxiliary qubit and the input qubit are respectively input to the two input terminals of the first two-qubit gate. The output of the first two-qubit gate is connected to the input terminal of the first cascaded rotation gate structure. The output terminal of the first cascaded rotation gate structure and the input qubit are respectively connected to the two input terminals of the second two-qubit gate. The input qubit is also input to the input terminal of the second Rx gate. The output terminal of the second two-qubit gate is connected to the input terminal of the first Rx gate. The output terminal of the first Rx gate is connected to the input terminal of the first Rz gate. The output terminals of the first Rz gate and the second Rx gate are respectively connected to the two input terminals of the third two-qubit gate. The output terminal of the third two-qubit gate is connected to the second cascaded rotation gate structure.
4. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 1, characterized in that, Two types of non-orthogonal quantum states include two-qubit separable non-orthogonal quantum states. These quantum states are fabricated onto the first and second input qubits to construct the first and second auxiliary qubits. The variable quantum circuits constructed for these quantum states include: fourth to seventh two-qubit gates, a third and fourth cascaded rotating gate structure, and first and second composite quantum gates. The first auxiliary qubit and the first input qubit are respectively input to the two input terminals of the fourth two-qubit gate. The output of the fourth two-qubit gate and the second input qubit are respectively input to the two input terminals of the fifth two-qubit gate. The output terminal of the fifth two-qubit gate is connected to the input terminal of the third cascaded rotating gate structure. The second auxiliary qubit and the first input qubit are respectively input to the two input terminals of the sixth two-qubit gate. The output of the sixth two-qubit gate and the second input qubit are respectively input to the two input terminals of the seventh two-qubit gate. The output terminal of the seventh two-qubit gate is connected to the input terminal of the fourth cascaded rotating gate structure. The output of the third cascaded rotating gate structure, the output of the fourth cascaded rotating gate structure, and the first and second input qubits are respectively input to the first composite quantum gate. The first composite quantum gate is connected to the second composite quantum gate.
5. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 4, characterized in that, The first and second composite quantum gates have the same structure, both including the eighth to thirteenth two-qubit gates and the fifth and sixth rotating gate cascade structures. The outputs of the third and fourth rotating gate cascade structures, along with the first and second input qubits, are used as the four inputs to the first composite quantum gate. Specifically, the output of the third rotating gate cascade structure and the first input qubit are respectively input to the two input terminals of the eighth two-qubit gate; the output of the eighth two-qubit gate and the output of the fourth rotating gate cascade structure are respectively input to the two input terminals of the ninth two-qubit gate; the output of the ninth two-qubit gate and the second input qubit are respectively input to the two input terminals of the tenth two-qubit gate; and the output of the tenth two-qubit gate is connected to the fifth rotating gate. The input terminals of the rotating gate cascade structure are connected to the output terminals of the fifth and fourth rotating gate cascade structures, respectively. The output terminals of the eleventh two-bit gate and the first input qubit are connected to the two input terminals of the twelfth two-bit gate, respectively. The output terminals of the twelfth two-bit gate and the second input qubit are connected to the two input terminals of the thirteenth two-bit gate, respectively. The output terminal of the thirteenth two-bit gate is connected to the sixth rotating gate cascade structure. The output terminals of the fifth and sixth rotating gate cascade structures of the first composite quantum gate, as well as the first and second input qubits, are used as the four input terminals of the second composite quantum gate, and the connection method is the same as that of the first composite quantum gate.
6. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 1, characterized in that, Two types of non-orthogonal quantum states include complex quantum states containing impurities. This type of quantum state includes a first quantum state and a second quantum state, where the first quantum state contains a state with a variable parameter, and the second quantum state contains two states with different phases. Third and fourth auxiliary qubits are constructed, and this type of quantum state is prepared onto the third and fourth input qubits. The variable quantum circuit constructed for this type of quantum state includes: an amplitude encoding circuit, fourteenth to twenty-third two-qubit gates, and a cascaded structure of seventh to tenth rotation gates. The third and fourth auxiliary qubits and the third and fourth input qubits are respectively input to the amplitude encoding circuit, and the amplitude-encoded third and fourth auxiliary qubits are denoted as... , The third and fourth input qubits after amplitude encoding are denoted as , ; Will and The inputs are respectively fed to the two input terminals of the fourteenth double-bit gate, and the output of the fourteenth double-bit gate is summed with the output of the fourteenth double-bit gate. The inputs are respectively fed to the two input terminals of the fifteenth double-bit gate, and the outputs are... and The inputs are respectively fed to the two input terminals of the sixteenth double-bit gate, and the output of the sixteenth double-bit gate is summed with the output of the double-bit gate. The inputs are respectively connected to the two input terminals of the seventeenth double-bit gate; the output terminal of the fifteenth double-bit gate is connected to the input terminal of the seventh rotary gate cascade structure, and the output terminal of the seventeenth double-bit gate is connected to the input terminal of the eighth rotary gate cascade structure. The output of the seventh rotary gate cascade structure and... The outputs of the eighteenth double-bit gate and the cascaded output of the eighth rotary gate are respectively input to the two inputs of the nineteenth double-bit gate. The output of the nineteenth double-bit gate and... The inputs are respectively connected to the two input terminals of the twentieth double-bit gate. The output terminal of the twentieth double-bit gate is connected to the input terminal of the ninth rotary gate cascade structure. The output terminals of the ninth rotary gate cascade structure and the eighth rotary gate cascade structure are respectively connected to the two input terminals of the twenty-first double-bit gate. The output terminal of the twenty-first double-bit gate and... Connect the two input terminals of the 22nd double-bit gate, and the output terminal of the 22nd double-bit gate respectively. The two inputs of the twenty-third double-bit gate are connected to each other, and the output of the twenty-third double-bit gate is connected to the input of the tenth cascaded rotating gate structure to store the output results of the ninth and tenth cascaded rotating gate structures.
7. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 1, characterized in that, Two or more types of non-orthogonal quantum states include three types of non-orthogonal quantum states. These quantum states are prepared onto the fifth and sixth input qubits to construct the fifth and sixth auxiliary qubits. Variable quantum circuits constructed for this type of quantum state include: the 24th to 30th two-qubit gates and the 11th to 16th rotation gate cascade structures. The fifth auxiliary qubit and the fifth input qubit are respectively input to the two input terminals of the 24th two-qubit gate. The output terminal of the 24th two-qubit gate and the sixth input qubit are respectively connected to the two input terminals of the 25th two-qubit gate. The sixth auxiliary qubit and the fifth input qubit are respectively input to the two input terminals of the 26th two-qubit gate. The output terminal of the 26th two-qubit gate and the sixth input qubit are respectively connected to the two input terminals of the 27th two-qubit gate. The output terminal of the 25th two-qubit gate is connected to the input terminal of the 11th rotation gate cascade structure. The output of the seventeenth two-bit gate is connected to the input of the twelfth rotating gate cascade structure. The fifth input qubit is input to the input of the thirteenth rotating gate cascade structure, and the sixth input qubit is input to the input of the fourteenth rotating gate cascade structure. The outputs of the eleventh and twelfth rotating gate cascade structures are connected to the two inputs of the twenty-eighth two-bit gate, respectively. The outputs of the twenty-eighth two-bit gate and the thirteenth rotating gate cascade structure are connected to the two inputs of the twenty-ninth two-bit gate, respectively. The outputs of the twenty-ninth two-bit gate and the fourteenth rotating gate cascade structure are connected to the two inputs of the thirtieth two-bit gate, respectively. The output of the eleventh rotating gate cascade structure is connected to the input of the fifteenth rotating gate cascade structure, and the output of the thirtieth two-bit gate is connected to the input of the sixteenth rotating gate cascade structure. The outputs of the fifteenth, sixteenth, thirteenth, and fourteenth rotating gate cascade structures are stored.
8. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to any one of claims 3-7, characterized in that, The cascaded rotating door structure includes a third Rx door, a second Rz door, and a fourth Rx door connected in sequence.
9. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 1, characterized in that, If the quantum state is either a two-qubit separable non-orthogonal quantum state or a complex quantum state containing impurities, and the variable quantum circuit of this type of quantum state supports unambiguous distinction, the following loss function L is designed when training the parameters of the variable quantum circuit corresponding to this type of quantum state: ； in, and They are weights, For error rate, This represents the probability that the outcome is uncertain.
10. The method for distinguishing non-orthogonal quantum states based on quantum machine learning according to claim 1, characterized in that, A unified training framework is adopted for different variable quantum circuits, specifically: gradient updates of parameters are performed using differentials based on parameter translation.