Quantum refrigeration method and device based on density matrix index feedback control, terminal and medium

Abstract

The invention provides a quantum refrigeration method and device based on density matrix index feedback control, a terminal and a medium, and the method comprises the steps: carrying out controlled index evolution on a working substance based on controlled DME operation when a control bit is in a quantum superposition state; under the condition that the quantum state takes a positive eigenstate and a negative eigenstate of a Fouli X operator as a substrate, measuring a control bit in an evolution result; when the measurement result is that the quantum state of the control bit is in the positive eigenstate of the Fouli X operator, it is indicated that the working substance absorbs heat from the cold storage, and the working substance is controlled to make contact with the heat storage so as to release the heat absorbed from the cold storage; and when feedback control of the controlled DME is completed, the working substance is controlled to be in contact with the refrigeration house to recover to the temperature the same as that of the refrigeration house, and the control bit is reset to be in a pure state. According to the method, efficient refrigeration is achieved through the processes of density matrix exponential evolution, feedback measurement, thermal contact heat release and resetting, and the energy expenditure of feedback information obtaining and processing is reduced.

Description

Technical Field

[0001] The present invention relates to the field of quantum technology, and in particular to a quantum refrigeration method, device, terminal and medium based on density matrix exponential feedback control. Background Art

[0002] Currently, conventional quantum refrigeration schemes are typically based on a quantum version of Maxwell's demon mechanism, which measures the state of the working material and selects different cooling operations based on the results. Such schemes can operate effectively under low particle count conditions and have been initially verified in small-scale experimental systems.

[0003] However, as the system scale expands, traditional quantum refrigeration solutions will have the following problems:

[0004] First, most existing quantum heat engine or quantum refrigerator models, such as the quantum Otto refrigerator, are generally limited by technical bottlenecks such as initial state preparation, individual particle manipulation, control of interparticle interactions, and measurement feedback. This is particularly true in multi-body systems, where each particle must be precisely initialized and independently controllable. The technical difficulty and energy cost of preparation and control increase rapidly, limiting practical scalability.

[0005] Secondly, as the number of particles increases, the dimension of the quantum system expands, resulting in an increase in the amount of measurement data and the scale of feedback operations, which increases the information processing overhead and leads to lower cooling efficiency.

[0006] In summary, traditional quantum cooling solutions rely on direct measurement and selective manipulation of the system's microscopic state, resulting in complex operations, high energy costs, and low cooling efficiency. Therefore, finding a solution to these technical problems is a pressing issue for those skilled in the art. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a quantum refrigeration method, device, terminal and medium based on density matrix exponential feedback control in response to the above-mentioned defects of the prior art, which can reduce the energy consumption of feedback information acquisition and processing and significantly improve the refrigeration efficiency.

[0008] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0009] A quantum refrigeration method based on density matrix exponential feedback control, wherein the method comprises:

[0010] When the control bit in the quantum system is in a quantum superposition state, the working material in the quantum system is subjected to controlled exponential evolution based on the controlled density matrix exponential operation to obtain the corresponding evolution result;

[0011] When the quantum state is based on the positive eigenstate and the negative eigenstate of the Pauli X operator, measuring the control bit in the evolution result to obtain a corresponding measurement result;

[0012] When the measurement result indicates that the quantum state of the control bit is in a positive eigenstate of the Pauli X operator, it indicates that the working substance has absorbed heat from a cold storage in the quantum system, and the working substance is controlled to contact a hot storage in the quantum system to release the heat absorbed from the cold storage;

[0013] When the controlled density matrix exponential feedback control is completed, the working substance is controlled to contact the cold storage to restore to the same temperature as the cold storage, and the control bit is reset to a pure state.

[0014] In one implementation, when the control bit in the quantum system is in a quantum superposition state, before performing the controlled exponential evolution of the working material in the quantum system based on the controlled density matrix exponential operation, the method further includes:

[0015] The control bit in the quantum system is initialized to a pure state, and the working substance and cold storage particles in the quantum system are in an initial thermal equilibrium state.

[0016] In one implementation, the evolution result is:

[0017]

[0018] in, represents the control evolution operation, |+><+| represents the matrix form of the quantum state as a positive eigenstate, ρ c represents the density matrix of the cold storage particles, ρ s Represents the density matrix of the working substance, and the density matrix of the cold storage particles commutes with the density matrix of the working substance. represents the tensor product;

[0019] And, the operator of the controlled density matrix exponential operation is:

[0020]

[0021] Where I represents a unit operation with the same dimension as the density matrix of the working substance, |0> represents the quantum state in vector form of the Pauli Z operator ground state, |0><0| represents the quantum state in matrix form of the Pauli Z operator ground state, |1> represents the quantum state in vector form of the Pauli Z operator excited state, and |1><1| represents the quantum state in matrix form of the Pauli Z operator excited state.

[0022] In one implementation, the interaction between particles in the working material is an Ising interaction;

[0023] Among them, the Hamiltonian including the Ising interaction is:

[0024]

[0025] in, is the Pauli X operator representing the i-th particle, g is the energy level difference, is the Pauli Z operator for the ith example, is the Pauli Z operator of the jth particle, J is the coupling strength, represents the particle's own energy, represents the energy of interaction coupling, and n represents the total number of particles.

[0026] In one implementation, performing controlled exponential evolution on a working substance in a quantum system based on a controlled density matrix exponential operation includes:

[0027] When the quantum state of the control bit is in an excited state, a partial exchange gate operation is triggered to perform a controlled exponential evolution on the working substance in the quantum system;

[0028] The partial exchange gate operation is an information exchange performed at a preset time step, and after the partial exchange gate exchange operation is triggered multiple times, quantum entanglement is formed between the working substance and the cold storage particles, and the quantum state of the working substance and the control bit evolves to the target quantum state over time;

[0029] Furthermore, the target quantum state is:

[0030]

[0031] Among them, |1><0| and |0><1| represent the matrix form of the coherent part of the control bit quantum state.

[0032] In one implementation, after measuring the control bit in the evolution result to obtain a corresponding measurement result, the method further includes:

[0033] When the measurement result shows that the quantum state of the control bit is in the negative eigenstate of the Pauli X operator, the state of the quantum system is initialized, and the step of performing controlled exponential evolution on the working material in the quantum system based on the controlled density matrix exponential operation is re-executed to obtain a corresponding evolution result.

[0034] In one implementation, resetting the control bit to a pure state includes:

[0035] The control bit is reset to a pure state through an information erasure operation.

[0036] The present invention also discloses a quantum refrigeration device based on density matrix exponential feedback control, wherein the device comprises:

[0037] An exponential evolution module is used to perform controlled exponential evolution on the working material in the quantum system based on a controlled density matrix exponential operation when the control bit in the quantum system is in a quantum superposition state, and obtain corresponding evolution results;

[0038] A measurement module, configured to measure the control bit in the evolution result to obtain a corresponding measurement result when the quantum state is based on the positive eigenstate and the negative eigenstate of the Pauli X operator;

[0039] a heat reservoir contact module, configured to, when the measurement result indicates that the quantum state of the control bit is in a positive eigenstate of the Pauli X operator, indicate that the working substance has absorbed heat from the cold reservoir in the quantum system, and control the working substance to contact the heat reservoir in the quantum system to release the heat absorbed from the cold reservoir;

[0040] The cold storage contact module is used to control the working substance to contact the cold storage to restore to the same temperature as the cold storage when the controlled density matrix exponential feedback control is completed, and reset the control bit to a pure state.

[0041] The present invention also discloses a terminal, which includes: a memory, a processor, and a quantum refrigeration program based on density matrix exponential feedback control stored in the memory and executable on the processor. When the quantum refrigeration program based on density matrix exponential feedback control is executed by the processor, the steps of the quantum refrigeration method based on density matrix exponential feedback control as described above are implemented.

[0042] The present invention also discloses a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program can be executed to implement the steps of the quantum refrigeration method based on density matrix exponential feedback control as described above.

[0043] The present invention provides a quantum refrigeration method, device, terminal, and medium based on density matrix exponential feedback control. The quantum refrigeration method based on density matrix exponential feedback control includes: when a control bit in a quantum system is in a quantum superposition state, performing controlled exponential evolution on a working substance in the quantum system based on a controlled density matrix exponential operation to obtain a corresponding evolution result; measuring the control bit in the evolution result to obtain a corresponding measurement result when the quantum state is based on positive eigenstates and negative eigenstates of a Pauli X operator; when the measurement result indicates that the quantum state of the control bit is in a positive eigenstate of the Pauli X operator, it indicates that the working substance has absorbed heat from a cold storage in the quantum system, and controlling the working substance to contact a hot storage in the quantum system to release the heat absorbed from the cold storage; when the controlled density matrix exponential feedback control is completed, controlling the working substance to contact the cold storage to restore to the same temperature as the cold storage, and resetting the control bit to a pure state. It can be seen from this that the present invention utilizes control bits and realizes efficient cooling on a working material composed of high-temperature particles through controlled density matrix indexation operations. No complex measurements are required, and feedback is controlled only by projecting measurements of the control bits. Moreover, the cooling efficiency can continuously improve as the number of particles in the working material increases. That is, efficient cooling is achieved through the process of density matrix indexation evolution, feedback measurement, thermal contact heat release, and reset. Specifically, through controlled density matrix indexation evolution, heat flow regulation can be directly implemented on the working material of the quantum system without the need for complete measurement of the quantum system state, thereby reducing the technical threshold and energy consumption of feedback control. In addition, projection measurement based on the positive and negative eigenstates of the Pauli X operator in the quantum state is used as the sole basis for feedback control, without the need to obtain all information about the working material. This simplifies the control loop, reduces the energy overhead of feedback information acquisition and processing, and has excellent scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of a preferred embodiment of the quantum refrigeration method based on density matrix exponential feedback control in the present invention;

[0045] Figure 2 This is a specific schematic diagram of the controlled DME operation disclosed in the present invention;

[0046] Figure 3 This is a specific refrigeration cycle schematic diagram disclosed in the present invention;

[0047] Figure 4 This is a specific quantum circuit diagram for realizing a refrigeration cycle disclosed in the present invention;

[0048] Figure 5 It is a schematic diagram of refrigeration performance of different working material scales disclosed in the present invention;

[0049] Figure 6 This is a schematic diagram of refrigeration performance of a specific coupling strength between different working substances disclosed in the present invention;

[0050] Figure 7 This is a flow chart of a specific quantum refrigeration method based on density matrix exponential feedback control disclosed in the present invention;

[0051] Figure 8 This is a functional principle block diagram of a preferred embodiment of a quantum refrigeration device based on density matrix exponential feedback control in the present invention;

[0052] Figure 9 It is a functional principle block diagram of a preferred embodiment of the terminal in the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clear and distinct, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0054] See Figure 1 , Figure 1 This is a flow chart of the quantum refrigeration method based on density matrix indexed feedback control in the present invention. Figure 1 As shown, the quantum refrigeration method based on density matrix exponential feedback control according to the embodiment of the present invention includes:

[0055] Step S11: When the control bit in the quantum system is in a quantum superposition state, a controlled exponential evolution is performed on the working material in the quantum system based on a controlled density matrix exponential operation to obtain a corresponding evolution result.

[0056] In this embodiment, the quantum system consists of a control bit (i.e., a quantum monster), a working substance, a hot storage, and a cold storage. When the control bit in the quantum system is in a quantum superposition state, the exponential evolution of the working substance is achieved through a series of controlled density matrix exponential operations. It should be noted that traditional quantum refrigeration solutions require direct measurement and selective operation of the microscopic state of the quantum system to achieve refrigeration, which has the problems of complex operation and high energy consumption. Using density matrix exponential technology, by constructing controlled exponential evolution, it is possible to directly implement heat flow regulation on the working substance without the need to fully measure the microscopic state of the quantum system, which can reduce the technical threshold and energy consumption of feedback control. Since DME (Density Matrix Exponentiation) evolution itself has quantum information processing capabilities, it provides a new possibility of combining refrigeration functions with information extraction, storage, or transmission functions. Therefore, it is also possible to consider taking into account certain information processing tasks while performing refrigeration tasks to form a new type of quantum thermal information device.

[0057] The operator for the controlled density matrix exponential operation is:

[0058]

[0059] where I represents a unit operation with the same dimension as the density matrix of the working substance, i.e. |0> indicates that the quantum state is in the vector form of the Pauli Z operator ground state, |0><0| indicates that the quantum state is in the matrix form of the Pauli Z operator ground state, |1> indicates that the quantum state is in the vector form of the Pauli Z operator excited state, |1><1| indicates that the quantum state is in the matrix form of the Pauli Z operator excited state, ρ c Represents the density matrix of the cold storage particles.

[0060] And the evolution result is:

[0061]

[0062] in, represents the control evolution operation, |+><+| represents the matrix form of the quantum state as a positive eigenstate, ρ c represents the density matrix of the cold storage particles, ρ s The density matrix of the working substance can be a 2n-dimensional matrix, and the density matrix of the cold storage particles and the density matrix of the working substance are mutually commuted, that is, [ρ c , ρ s ], Represents a tensor product.

[0063] It should be pointed out that when |0> and |1> are selected as the basis, for the state |+>, that is: And the state|->, that is:

[0064] Therefore, |+><+|, that is: |-><-|, that is:

[0065] In this embodiment, when the control bit in the quantum system is in a quantum superposition state, before the controlled exponential evolution of the working substance in the quantum system is performed based on the controlled density matrix exponential operation, the following steps may be specifically included: initializing the control bit in the quantum system to a pure state, and the working substance and the cold storage particles in the quantum system are in an initial thermal equilibrium state. It is understandable that the control bit is initialized to a pure state, and the particles in the working substance and the cold storage particles (temperature is T c ) are in their respective thermal equilibrium states, requiring no further purification. Furthermore, the number of control bits can be one. Compared to traditional refrigeration mechanisms that require large-scale particle purification, in this embodiment, all particles in the working material and the cold storage particles, except for the one control bit, can be in a high-temperature thermal state. This simplifies the quantum system initialization steps, reduces costs, and improves the feasibility of large-scale quantum system expansion.

[0066] Moreover, in this embodiment, the working substance in the quantum system is subjected to controlled exponential evolution based on the controlled density matrix exponential operation, which may specifically include: when the quantum state of the control bit is in an excited state, a partial exchange gate operation is triggered to perform a controlled exponential evolution on the working substance in the quantum system; wherein the partial exchange gate operation is an information exchange performed at a preset time step, and after the partial exchange gate exchange operation is triggered multiple times, quantum entanglement is formed between the working substance and the cold storage particles, and the quantum state of the working substance and the control bit evolves to the target quantum state over time. It can be understood that the core of using density matrix exponential technology to achieve feedback control is to associate the working substance and the control bit through the controlled density matrix exponential operation, so as to obtain the overall working substance information by measuring the control bit, thereby achieving the effect of reverse regulation of heat flow without the need to fully measure the microscopic state of the quantum system. Wherein, the target quantum state is:

[0067]

[0068] Among them, |1><0| and |0><1| represent the matrix form of the coherent part of the control bit quantum state, and I represents the unit operation with the same dimension as the density matrix of the working substance, that is, ρ s The density matrix of the working substance can be a 2n-dimensional matrix, so It is a 2n+1 dimensional matrix.

[0069] It is understood that the controlled DME operation is achieved by a stepwise approximation of successive partial-SWAP operations. Figure 2 As shown, each partial exchange gate operation is equivalent to a tiny information exchange over a preset (small) time step Δt. The partial exchange gate operation is triggered only when the control bit is in the |1> state (excited state), thus forming a controlled exponential evolution. After sufficient multiple exchanges, quantum entanglement is formed between the working material and the cold storage particles, and their state evolves over time, deviating from the initial thermal equilibrium state, ultimately evolving to the target quantum state described above.

[0070] It should be noted that there are two forms of quantum state representation, namely vector form and density matrix form. The advantage of vector form is convenience, because the matrix form is more complicated. For the simplest state |0>, its vector form is The vector form of its conjugate vector <0| is [1 0]. Another form is the density matrix form or matrix form. |0><0| is a matrix form, which represents the result of multiplying the normal vector |0> and its conjugate vector <0|, that is:

[0071] Step S12: When the quantum state is based on the positive eigenstate and the negative eigenstate of the Pauli X operator, the control bit in the evolution result is measured to obtain a corresponding measurement result.

[0072] In this embodiment, after the controlled DME evolution is complete, the control bits are measured on the |+> and |-> basis. Specifically, when the quantum state is based on the positive and negative eigenstates of the Pauli X operator, the control bits in the evolution result are measured to obtain the corresponding measurement results. Using the projection measurements on the |+> and |-> basis as the sole basis for feedback decision-making eliminates the need to obtain full information about the working substance, simplifying the control loop and reducing the energy overhead of feedback information acquisition and processing, thereby achieving a highly efficient and low-cost quantum heat engine system.

[0073] Step S13: When the measurement result indicates that the quantum state of the control bit is in the positive eigenstate of the Pauli X operator, it indicates that the working substance has absorbed heat from the cold storage in the quantum system, and the working substance is controlled to contact the hot storage in the quantum system to release the heat absorbed from the cold storage.

[0074] In this embodiment, the control bit is measured on the |+> and |-> substrates. When the measurement result is |+>, it indicates that the working substance has absorbed heat from the cold storage in the quantum system. In other words, the quantum state of the working substance has been projected to a state with energy higher than the initial thermal equilibrium energy. The next step can be carried out, which is to control the working substance to contact the hot storage in the quantum system to release the heat absorbed from the cold storage. The projection measurement enables feedback control based on the direction of energy change of the working substance without the need to recover complete state information, thereby significantly simplifying the complexity of the cooling process. In addition, the interaction between particles in the working substance can further enhance the working substance's ability to absorb heat from the cold storage, significantly improving cooling efficiency.

[0075] It can be understood that the heat release by thermal contact only occurs when the measurement result is |+>, at which time the energy of the working substance is higher than the initial thermal equilibrium energy. Under this condition, the working substance will release heat in the presence of the high temperature heat reservoir (temperature T h ) to release energy and eventually become a higher temperature state ρ h .

[0076] Step S14: When the controlled density matrix exponential feedback control is completed, the working substance is controlled to contact the cold storage to restore to the same temperature as the cold storage, and the control bit is reset to a pure state.

[0077] In this embodiment, after completing the above-mentioned DME feedback control, the working substance contacts the cold storage to return to the cold storage temperature, that is, to the same temperature as the cold storage, and the control bit is reset to the pure state. Specifically, the control bit is reset to the pure state through an information erasure operation.

[0078] It should be noted that the above steps form a complete refrigeration process, see Figure 3 As shown, the controlled density matrix exponential evolution, feedback measurement, thermal contact heat release and reset, the refrigeration process cycle can be carried out continuously, periodically absorbing heat from the cold storage and releasing it to the hot storage, completing a stable and efficient refrigeration process, that is, feedback control is achieved through density matrix exponentialization, and decision-making is completed through a pure state control bit and simple projection measurement, forming a low-energy, minimum resource feedback control quantum refrigeration mechanism. Based on the single DME feedback mechanism in this embodiment, multiple rounds of iterative feedback control processes can be achieved, that is, through the superposition of multiple measurements and controlled evolution, the gradual strengthening of the heat flow regulation of the working substance can be achieved, forming a progressive quantum cooling strategy. The quantum refrigeration mechanism based on DME can be used as a model system for studying basic processes of quantum thermodynamics, such as information entropy flow, energy flow, quantum correlation and the relationship between the second law of thermodynamics.

[0079] Also, see Figure 4As shown, the implementation of the refrigeration process in a quantum processor can be represented by a quantum circuit diagram. Since there are no other restrictions on the working material system except that the working material state and the cold storage state are required to be commuted during the refrigeration process, the technical solution of the present application is scalable, and there is no difference in the overall process. More importantly, the resources consumed in the measurement process are the same for any system, that is, the technical solution of the present application has good scalability and platform adaptability. Since the controlled DME evolution does not depend on the particle type and the specific implementation mechanism, but only depends on the partial-SWAP gate and basic control logic, the solution can be directly applied to nuclear magnetic resonance (NMR), superconducting quantum bits, solid-state color center systems, cold atom systems, and even optical quantum platforms. By increasing the number of particles in the working material or enhancing the interaction between particles, the refrigeration efficiency can be continuously improved, and it can play an important role in the fields of quantum computing, quantum chip thermal management, etc.

[0080] For example, see Figure 5 As shown in the figure, the refrigeration performance is measured to increase with the number of particles. Since the refrigeration performance under controlled DME operation is related to the actual operation time, the results shown on the vertical axis are the results after optimizing the time parameter. The solid line is the experimental verification result, and the dotted line is the theoretical simulation result. In particular, after adding Ising-type interactions between particles, the working material's ability to absorb heat from the cold storage can be further enhanced, significantly improving the refrigeration efficiency. The refrigeration performance is further improved due to the synergistic effect, and the COP can exceed 100%. Figure 6 As shown, the correctness and superiority of the technical solution of this application can be verified, wherein the vertical axis also shows the result after optimizing the time parameter, and Figure 6 The upper middle part is the result when the total number of particles is n=2. Figure 6 The lower middle part shows the result when the total number of particles is n=3.

[0081] The interaction between particles in the working material is the Ising interaction, and the Hamiltonian including the Ising interaction is:

[0082]

[0083] in, is the Pauli X operator representing the i-th particle, g is the energy level difference, is the Pauli Z operator for the ith example, is the Pauli Z operator of the jth particle, J is the coupling strength, represents the particle's own energy, is the Ising interaction term, which represents the energy of interaction coupling, and n represents the total number of particles.

[0084] It can be seen that in the embodiments of the present invention, efficient cooling is achieved on a working material composed of high-temperature particles by utilizing control bits and controlled density matrix indexation operations. No complex measurements are required, and feedback is controlled only by projecting measurements of the control bits. Moreover, the cooling efficiency can continuously improve as the number of particles in the working material increases. That is, efficient cooling is achieved through the process of density matrix indexation evolution, feedback measurement, thermal contact heat release, and reset. Specifically, through controlled density matrix indexation evolution, heat flow regulation can be directly implemented on the working material of the quantum system without the need for complete measurement of the quantum system state, thereby reducing the technical threshold and energy consumption of feedback control. In addition, the projection measurement of the positive and negative eigenstate basis of the Pauli X operator in the quantum state is used as the sole basis for feedback control, without the need to obtain all information about the working material. This simplifies the control loop, reduces the energy overhead of feedback information acquisition and processing, and has excellent scalability.

[0085] See also Figure 7 As shown, the embodiment of the present invention discloses a specific quantum refrigeration method based on density matrix exponential feedback control. Compared with the previous embodiment, this embodiment further illustrates and optimizes the technical solution.

[0086] Step S21: When the control bit in the quantum system is in a quantum superposition state, a controlled exponential evolution is performed on the working material in the quantum system based on a controlled density matrix exponential operation to obtain a corresponding evolution result.

[0087] Step S22: When the quantum state is based on the positive eigenstate and the negative eigenstate of the Pauli X operator, the control bit in the evolution result is measured to obtain a corresponding measurement result.

[0088] Step S23: When the measurement result indicates that the quantum state of the control bit is in the negative eigenstate of the Pauli X operator, the state of the quantum system is initialized, and the controlled exponential evolution of the working matter in the quantum system based on the controlled density matrix exponential operation is performed again to obtain a corresponding evolution result.

[0089] In this embodiment, when the control bit is measured on the |+> and |-> basis and the measurement result is |->, that is, when the measurement result shows that the quantum state of the control bit is in the negative eigenstate of the Pauli X operator, it is necessary to reinitialize the quantum system state and re-perform the control operation.

[0090] For the specific contents of the above steps S21 to S22, reference may be made to the corresponding contents disclosed in the above embodiments, which will not be repeated here.

[0091] It can be seen that in the embodiments of the present invention, efficient cooling is achieved on a working material composed of high-temperature particles by utilizing control bits and controlled density matrix indexation operations. No complex measurements are required, and feedback is controlled only by projecting measurements of the control bits. Moreover, the cooling efficiency can continuously improve as the number of particles in the working material increases. That is, efficient cooling is achieved through the process of density matrix indexation evolution, feedback measurement, thermal contact heat release, and reset. Specifically, through controlled density matrix indexation evolution, heat flow regulation can be directly implemented on the working material of the quantum system without the need for complete measurement of the quantum system state, thereby reducing the technical threshold and energy consumption of feedback control. In addition, the projection measurement of the positive and negative eigenstate basis of the Pauli X operator in the quantum state is used as the sole basis for feedback control, without the need to obtain all information about the working material. This simplifies the control loop, reduces the energy overhead of feedback information acquisition and processing, and has excellent scalability.

[0092] It should be noted that the control bit is measured on the |+> and |-< basis, and the quantum system states corresponding to the above two measurement results are:

[0093]

[0094] Among them, P + Indicates the probability when the measurement result is |+>, P - It represents the probability when the measurement result is |->, and Tr represents the trace operation of the operator.

[0095] Furthermore, the performance index of the cooling solution of the present application may be the coefficient of performance (COP), which is the ratio of the heat released by the working substance to the heat reservoir to the power consumption required to reset the control bit, that is:

[0096]

[0097] Among them, P + is the probability of measuring the result to be |+>, that is, the probability of measuring the projection to the |+> state, Q is the heat transferred by the cooling process of measuring |+>, T R The temperature of the reset environment.

[0098] The technical solution of this application can be verified on a nuclear magnetic resonance platform, using a seven-bit nuclear magnetic resonance quantum processor. 13 The trans-butenoic acid molecule labeled with C is the sample. 13 The C nuclear spin is initialized to a pseudo-pure state as the quantum monster, i.e., the control bit, while the other spins constitute the working material and the cold storage particles. Through a preset pulse sequence and optimized partial gate exchange operation, DME feedback control is achieved at the scale of one to three free particles, namely:

[0099]

[0100] Here, g is the energy level difference.

[0101] In one embodiment, if Figure 8 As shown, based on the above-mentioned quantum refrigeration method based on density matrix exponential feedback control, the present invention also provides a quantum refrigeration device based on density matrix exponential feedback control, including:

[0102] The exponential evolution module 11 is used to perform controlled exponential evolution on the working material in the quantum system based on the controlled density matrix exponential operation when the control bit in the quantum system is in a quantum superposition state, and obtain corresponding evolution results.

[0103] The measurement module 12 is configured to measure the control bit in the evolution result to obtain a corresponding measurement result when the quantum state is based on the positive eigenstate and the negative eigenstate of the Pauli X operator.

[0104] The heat reservoir contact module 13 is configured to, when the measurement result indicates that the quantum state of the control bit is in the positive eigenstate of the Pauli X operator, indicate that the working substance has absorbed heat from the cold reservoir in the quantum system, and control the working substance to contact the heat reservoir in the quantum system to release the heat absorbed from the cold reservoir.

[0105] The cold storage contact module 14 is used to control the working substance to contact the cold storage to restore to the same temperature as the cold storage when the controlled density matrix exponential feedback control is completed, and reset the control bit to a pure state.

[0106] In some specific embodiments, the quantum refrigeration device based on density matrix exponential feedback control may further include:

[0107] The first initialization module is used to initialize the control bit in the quantum system to a pure state, and the working substance and cold storage particles in the quantum system are in an initial thermal equilibrium state.

[0108] In some specific embodiments, the exponential evolution module 11 may specifically include:

[0109] a partial exchange gate operation triggering unit, configured to trigger a partial exchange gate operation when the quantum state of the control bit is in an excited state, so as to perform a controlled exponential evolution on the working substance in the quantum system;

[0110] The partial exchange gate operation is an information exchange performed at a preset time step, and after the partial exchange gate exchange operation is triggered multiple times, quantum entanglement is formed between the working substance and the cold storage particles, and the quantum state of the working substance and the control bit evolves to the target quantum state over time;

[0111] Furthermore, the target quantum state is:

[0112]

[0113] Among them, |1><0| and |0><1| represent the matrix form of the coherent part of the control bit quantum state.

[0114] In some specific embodiments, the quantum refrigeration device based on density matrix exponential feedback control may further include:

[0115] A second initialization module is configured to, when the measurement result indicates that the quantum state of the control bit is in the negative eigenstate of the Pauli X operator, initialize the state of the quantum system and re-execute the step of performing controlled exponential evolution on the working matter in the quantum system based on the controlled density matrix exponential operation to obtain a corresponding evolution result.

[0116] In some specific embodiments, the cold storage contact module 14 may specifically include:

[0117] The state resetting unit is used to reset the control bit to a pure state through an information erasing operation.

[0118] In addition, it is worth noting that the working process of the quantum refrigeration device based on density matrix exponential feedback control provided in this embodiment is the same as the working process of the quantum refrigeration method based on density matrix exponential feedback control. It will not be described in detail here. For details, please refer to the working process of the quantum refrigeration method based on density matrix exponential feedback control.

[0119] Figure 9 This is a schematic diagram of the structure of a terminal provided in an embodiment of the present application. The terminal may include:

[0120] Memory 501 , processor 502 , and computer programs stored in the memory 501 and executable on the processor 502 .

[0121] When the processor 502 executes the program, the quantum refrigeration method based on density matrix exponential feedback control provided in the above embodiment is implemented.

[0122] Furthermore, the terminal further includes:

[0123] The communication interface 503 is used for communication between the memory 501 and the processor 502 .

[0124] The memory 501 is used to store computer programs that can be run on the processor 502 .

[0125] The memory 501 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0126] If the memory 501, processor 502, and communication interface 503 are implemented independently, the communication interface 503, memory 501, and processor 502 can be interconnected via a bus to enable communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus. Buses can be classified as address buses, data buses, control buses, etc. For ease of illustration, the figure shows only one line, but this does not mean that there is only one bus or only one type of bus.

[0127] Optionally, in a specific implementation, if the memory 501, the processor 502 and the communication interface 503 are integrated on a chip, the memory 501, the processor 502 and the communication interface 503 can communicate with each other through an internal interface.

[0128] The processor 502 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0129] This embodiment further provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the quantum refrigeration method based on density matrix exponential feedback control as described above is implemented.

[0130] Other embodiments of the present invention will readily occur to those skilled in the art after considering the specification and practicing the invention disclosed herein. The present invention is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the claims.

[0131] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0132] The logic and / or steps represented in the flowchart or otherwise described herein may be considered, for example, as a sequenced list of executable instructions for implementing logical functions, and may be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other system that can read and execute instructions from an instruction execution system, apparatus, or device).

[0133] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used to implement: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field-programmable gate array (FPGA), etc.

[0134] It should be understood that the application of the present invention is not limited to the above examples. For those skilled in the art, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A quantum refrigeration method based on density matrix exponential feedback control, characterized in that: The method includes: When the control qubit in the quantum system is in a quantum superposition state, performing a controlled exponential evolution on the working substance in the quantum system based on the controlled density matrix exponentiation operation to obtain a corresponding evolution result; When the quantum state is based on the positive and negative eigenstates of the Pauli X operator, measuring the control qubit in the evolution result to obtain a corresponding measurement result; When the measurement result indicates that the quantum state of the control qubit is in the positive eigenstate of the Pauli X operator, it indicates that the working substance has absorbed heat from the cold reservoir in the quantum system, and controls the working substance to contact the heat reservoir in the quantum system to release the heat absorbed from the cold reservoir; When the controlled density matrix exponentiation feedback control is completed, control the working substance to contact the cold reservoir to return to the same temperature as the cold reservoir, and reset the control qubit to a pure state.

2. The quantum refrigeration method based on density matrix exponential feedback control according to claim 1, characterized in that: Before performing the controlled exponential evolution on the working substance in the quantum system based on the controlled density matrix exponentiation operation when the control qubit in the quantum system is in a quantum superposition state, it further includes: Initializing the control qubit in the quantum system to a pure state, and the working substance and cold reservoir particles in the quantum system are in an initial thermal equilibrium state.

3. The quantum refrigeration method based on density matrix exponential feedback control according to claim 1, characterized in that: The evolution result is: in, represents the control evolution operation, |+><+| represents the matrix form of the quantum state as a positive eigenstate, ρ c represents the density matrix of the cold storage particles, ρ s Represents the density matrix of the working substance, and the density matrix of the cold storage particles commutes with the density matrix of the working substance. represents the tensor product; And, the operator of the controlled density matrix exponentiation operation is: Where, I represents the identity operation with the same dimension as the density matrix of the working substance, |0> represents the vector form of the quantum state as the ground state of the Pauli Z operator, |0><0| represents the matrix form of the quantum state as the ground state of the Pauli Z operator, |1> represents the vector form of the quantum state as the excited state of the Pauli Z operator, and |1><x| represents the matrix form of the quantum state as the excited state of the Pauli Z operator.

4. The quantum refrigeration method based on density matrix exponential feedback control according to claim 1, characterized in that: The interaction between particles in the working substance is the Ising interaction; Where, the Hamiltonian containing the Ising interaction is: in, is the Pauli X operator representing the i-th particle, g is the energy level difference, is the Pauli Z operator for the ith example, is the Pauli Z operator of the jth particle, is the coupling strength, represents the particle's own energy, represents the energy of interaction coupling, and n represents the total number of particles.

5. The quantum refrigeration method based on density matrix exponential feedback control according to claim 4, characterized in that: Performing the controlled exponential evolution on the working substance in the quantum system based on the controlled density matrix exponentiation operation includes: When the quantum state of the control qubit is in the excited state, triggering a partial swap gate operation to perform a controlled exponential evolution on the working substance in the quantum system; Where, the partial swap gate operation is an information exchange performed at a preset time step, and after triggering the partial swap gate exchange operation multiple times, quantum entanglement is formed between the working substance and the cold reservoir particles, and the quantum states of the working substance and the control qubit evolve into the target quantum state over time; And, the target quantum state is: Where, |1><0| and |0><1| represent the matrix forms of the coherent part of the control qubit quantum state.

6. The quantum refrigeration method based on density matrix exponential feedback control according to claim 1, characterized in that: After measuring the control qubit in the evolution result to obtain a corresponding measurement result, it further includes: When the measurement result is that the quantum state of the control qubit is in the negative eigenstate of the Pauli X operator, initializing the state of the quantum system and re-executing the step of performing the controlled exponential evolution on the working substance in the quantum system based on the controlled density matrix exponentiation operation to obtain a corresponding evolution result.

7. The quantum refrigeration method based on density matrix exponential feedback control according to any one of claims 1 to 6, characterized in that: Resetting the control qubit to a pure state includes: The control bit is reset to a pure state through an information erasure operation.

8. A quantum refrigeration device based on density matrix exponential feedback control, characterized in that: The device comprises: An exponential evolution module is used to perform controlled exponential evolution on the working material in the quantum system based on a controlled density matrix exponential operation when the control bit in the quantum system is in a quantum superposition state, and obtain corresponding evolution results; A measurement module, configured to measure the control bit in the evolution result to obtain a corresponding measurement result when the quantum state is based on the positive eigenstate and the negative eigenstate of the Pauli X operator; a heat reservoir contact module, configured to, when the measurement result indicates that the quantum state of the control bit is in a positive eigenstate of the Pauli X operator, indicate that the working substance has absorbed heat from the cold reservoir in the quantum system, and control the working substance to contact the heat reservoir in the quantum system to release the heat absorbed from the cold reservoir; The cold storage contact module is used to control the working substance to contact the cold storage to restore to the same temperature as the cold storage when the controlled density matrix exponential feedback control is completed, and reset the control bit to a pure state.

9. A terminal, characterized in that: include: A memory, a processor, and a quantum refrigeration program based on density matrix exponential feedback control stored in the memory and executable on the processor, wherein the quantum refrigeration program based on density matrix exponential feedback control, when executed by the processor, implements the steps of the quantum refrigeration method based on density matrix exponential feedback control according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which can be executed to implement the steps of the quantum refrigeration method based on density matrix exponential feedback control according to any one of claims 1 to 7.

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