Regulation and control method for coherent period regeneration in quantum simulation phase damping noise channel

Abstract

The invention discloses a regulation and control method for coherent period regeneration in a quantum simulation phase damping noise channel. Firstly, a reference basis vector is selected, and a phase damping noise channel is simulated by using a noise injection technology based on a nuclear magnetic resonance system. Then, calculating a density matrix of a single-bit maximum coherence state after passing through a noise channel under different reference basis vectors, and measuring quantum coherence by adopting an l1 norm; research finds that under a Z reference basis vector, quantum coherence is directly related to a de-coherence function, and periodic complete regeneration of quantum coherence can be realized by regulating and controlling noise fundamental frequency to enable the noise fundamental frequency to meet conditions; under an X / Y reference basis vector, the quantum coherence is jointly decided by a system bit frequency omega k and a de-coherence function, and omega 0 and omega k are cooperatively regulated and controlled to meet complete regeneration of a period capable of realizing coherence. The invention provides an effective method for period regeneration regulation and control of quantum coherence under different reference basis vectors.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of quantum noise regulation and quantum information processing, and particularly relates to a regulation method for realizing quantum coherence periodic complete rebirth in a quantum simulation phase damping noise channel. BACKGROUND

[0002] Quantum coherence is the core resource of quantum computing, quantum communication and quantum sensing, and its maintenance and regulation are key scientific problems in this field. However, quantum systems inevitably interact with the environment, leading to quantum decoherence. Among them, phase damping noise is one of the main mechanisms of quantum bit decoherence, which keeps the population of quantum states unchanged but randomizes the phase information.

[0003] Traditional theoretical research shows that, under Markov approximation, phase damping noise will cause quantum coherence to decay exponentially with time. However, actual quantum systems (such as nuclear magnetic resonance, superconducting quantum bits and ion traps) often exhibit non-Markovian characteristics, and their dynamic behavior may exhibit non-classical phenomena such as quantum coherence recovery and quantum entanglement rebirth. Therefore, how to understand and regulate quantum coherence in a more general noise environment has become an important challenge in quantum information science.

[0004] In addition, the coherence of quantum states has reference basis vector dependence. In the ideal phase damping noise channel model, the coherence of quantum states under the energy eigenbasis (Z basis vector) and X / Y basis vector shows a decay trend. However, on controllable quantum simulation platforms such as nuclear magnetic resonance, it is still lacking of systematic research to construct a generalized phase damping noise channel and reveal its basis vector-dependent coherence dynamics. Although existing work has explored quantum dynamics in non-Markovian environments, active regulation strategies for noise parameters and long-term quantum coherence maintenance schemes still need to be further explored. SUMMARY

[0005] The present application aims to solve the problems of the above prior art. A regulation method for coherence periodic rebirth in a quantum simulation phase damping noise channel is proposed. The technical solution of the present application is as follows:

[0006] A regulation method for coherence periodic rebirth in a quantum simulation phase damping noise channel, comprising the following steps:

[0007] (1) Select a reference basis vector and simulate a phase damping noise channel based on a nuclear magnetic resonance system;

[0008] (2) Input the maximum coherence state, and calculate the density matrix of the maximum coherence state after passing through the quantum simulation phase damping noise channel under different reference basis vectors;

[0009] (3) Based on the density matrix, the quantum coherence of the system is calculated by using the l1 norm method, and the quantum coherence of the system under the Z reference basis is The quantum coherence of the system under the X / Y reference basis is The quantum coherence of the system under the Z / X / Y reference basis is calculated by using the l1 norm, and the subscript K z / x / y represents the selection of different reference basis, and the subscript l represents the l1 norm method, wherein ρ(t) represents the density matrix of the system at time t, Γ(t) represents the decoherence function of the system, ω k represents the bit frequency of the system;

[0010] (4) According to the function expression satisfied by the quantum coherence, the quantum coherence of the system under different reference basis is regulated; under the Z reference basis, within the time range t∈[0,t max ] (t max represents the upper limit of time), the noise base frequency value is regulated to satisfy The period of quantum coherence can be completely regenerated within this time range, and the corresponding regeneration period is The number of regeneration periods is n; under the X / Y reference basis, the noise base frequency ω0 and the bit frequency ω k of the system are jointly regulated to satisfy The period of quantum coherence can be completely regenerated, and the corresponding regeneration period is The number of regeneration periods is n.

[0011] Further, when selecting Z as the reference basis, the same maximum coherence state is prepared in the nuclear magnetic resonance system as the input quantum state ensemble; the control Hamiltonian of the nuclear magnetic resonance system is regulated and the noise injection technology is adopted, and the Hamiltonian acting on the ensemble is wherein is the control Hamiltonian, H0(t)=β(t)σ z is the injected transverse relaxation noise Hamiltonian, ω k is the quantum bit frequency of the system, is the random error generated by the phase modulation on the carrier, describes the distribution of the noise in the time domain, and the parameter α represents the noise amplitude, ω0 is the base frequency of the noise power spectrum, ω J is the noise cutoff frequency, ψ j is a series of random phases, is a modulation function, and the value of p determines the type of noise, such as p=0, then F(j)=j -1 represents white noise; under the action of the Hamiltonian, the ensemble density matrix at time t is averaged to obtain the system evolution state When X / Y is selected as the reference basis vector, N maximum coherent states are also prepared in the nuclear magnetic resonance system As an input quantum state ensemble, the ensemble is acted on by a Hamiltonian U z→x / y The conversion matrix from the Z basis vector to the X / Y is represented as U, which satisfies The matrix U is represented as U z→x / y Take the transpose complex conjugate, and further obtain the density matrix of the system at time t as

[0012] Further, based on the density matrix of the system at time t, the quantum coherence of the system is calculated using the l1 norm, that is, the sum of the absolute values of the off-diagonal elements of the density matrix, and it can be obtained that the quantum coherence of the system at time t under the Z reference basis vector satisfies The quantum coherence of the system under the X / Y reference basis vector satisfies

[0013] Further, according to the system decoherence function Combined with the formula that the quantum coherence of the system satisfies under different reference basis vectors, the regulation method of the quantum coherence of the system under different reference basis vectors can be obtained: under the Z reference basis vector, the noise base frequency value is regulated to satisfy The quantum coherence can be completely regenerated in the time t∈[0,t max ] period, and the regenerated period is Under the X / Y reference basis vector, the noise base frequency and the system bit frequency are jointly regulated to satisfy The quantum coherence can be completely regenerated, and the regenerated period is

[0014] A storage medium internally stores a computer program, and when the computer program is read by a processor, the quantum simulation phase damping noise channel coherence period regeneration regulation method of any one of the above is executed.

[0015] The advantages and beneficial effects of the present application are as follows:

[0016] 1. Basis vector universal regulation advantage:

[0017] The present application first establishes a unified regulation framework for quantum coherence period regeneration covering Z, X, and Y reference basis vectors, and realizes active regulation of quantum coherence under different basis vectors by accurately quantifying the coupling relationship between noise parameters and basis vector selection. Under the Z basis vector, the quantum coherence can be completely regenerated by regulating the noise base frequency ω0; under the X / Y basis vector, the quantum coherence can be completely regenerated by jointly regulating the noise base frequency ω0and the system bit frequency ω kThe periodic full rebirth of coherence can also be realized, and flexible technical support is provided for multi-base vector quantum information processing.

[0018] 2. Platform compatibility and experimental feasibility:

[0019] Based on the noise injection technology of the nuclear magnetic resonance system, a general phase damping noise channel model is constructed, which has significant platform adaptability and can be extended to superconducting quantum bits, ion traps and other quantum manipulation systems. Combined with the GRAPE algorithm and quantum state tomography technology, high-precision quantum state evolution and measurement are realized, ensuring the experimental operability and repeatability of the method. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a specific embodiment schematic diagram of the present application for realizing periodic rebirth of coherence in a quantum simulation noise channel based on a nuclear magnetic resonance system.

[0021] Figure 2 The figure of periodic rebirth of coherence under the Z reference basis vector, (a)-(c) represent that in the time t∈[0, 50] (ms), t∈[0, 100] (ms), t∈[0, 300] (ms), the noise base frequency is respectively: The curve of the change of coherence with time.

[0022] Figure 3 The figure of periodic rebirth of coherence under the X / Y reference basis vector, (a)-(c) represent that in the time t∈[0, 50] (ms), t∈[0, 100] (ms), t∈[0, 300] (ms), the noise base frequency ω0 and the system bit frequency are respectively: The curve of the change of coherence with time.

[0023] Figure 4 is a flow chart of the method for regulating and controlling the periodic rebirth of coherence in the quantum simulation phase damping noise channel provided by the preferred embodiment of the present application. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present application will be described in detail below with reference to the drawings in the embodiments of the present application. The described embodiments are only a part of the embodiments of the present application.

[0025] The technical solution of the present application to solve the above technical problems is:

[0026] The principle of this invention is that the coherence of a quantum state is explicitly related to the chosen reference basis vector. In an ideal phase-damped noise channel model, due to the Markov approximation, the coherence of quantum states under the three different reference basis vectors Z / X / Y all decrease monotonically with time. However, efficient quantum simulation of phase-damped noise channels can be achieved in systems such as nuclear magnetic resonance (NMR) and superconducting systems, without being constrained by the Markov approximation. This invention simulates a phase-damped noise channel based on an NMR system, and further uses the l1 norm to measure the quantum coherence of the system based on the system density matrix after the noise channel.

[0027] Specifically, when the Z reference basis is selected, the input is the maximum coherent state. Quantum states in Hamiltonian Under the influence of the system, at time t, the system will evolve into... Then, according to the l1 norm method (adding the off-diagonal terms of the density matrix), the system coherence can be calculated as follows: Because the system's decoherence function satisfies At the noise cutoff frequency ω J Given a fixed value, Γ(t) is a periodic function related to ω0, and ω0 determines its oscillation period. Therefore, under the Z reference basis, the noise fundamental frequency ω0 can be adjusted to satisfy... It can realize t∈[0,t max Within a given time period, the period of complete regeneration of quantum coherence is [missing information]. As attached Figure 2 As shown, within the time intervals t∈[0,50](ms), t∈[0,100](ms), and t∈[0,300](ms), let the noise fundamental frequencies be respectively: All achieved coherent 4-cycle complete regeneration (where noise intensity α = 0.5 and noise cutoff frequency ω). J =50 (MHz), where the coherent regeneration time corresponding to t∈[0,50](ms) is approximately t=[12.5,25,37.6,50](ms) (the slight difference in value is mainly affected by the number of significant bits retained during calculation), the coherent regeneration time corresponding to t∈[0,100](ms) is approximately t=[25,50,75,100](ms), and the coherent regeneration time corresponding to t∈[0,300](ms) is approximately t=[75,150,225,300](ms).

[0028] When X / Y is chosen as the reference basis vector, the same maximally coherent states are prepared in the nuclear magnetic resonance system. As an input quantum state ensemble, the Hamiltonian acts on the ensemble. U z→x / y This represents the transformation matrix from the Z basis vectors to X / Y. The density matrix of the system at time t is further obtained as follows: The system's quantum coherence is given by the following formula: The system's quantum coherence under the X / Y reference basis is given by the following formula: Based on the coherent expression, it can be obtained that, under the X / Y reference basis, by jointly controlling the noise fundamental frequency and the system bit frequency to satisfy respectively... It can achieve complete periodic regeneration of quantum coherence, with a regeneration period of... As attached Figure 3 As shown, within the time intervals t∈[0,50](ms), t∈[0,100](ms), and t∈[0,300](ms), let the noise fundamental frequency ω0 and the system bit frequency be respectively: All achieved coherent 4-cycle complete regeneration (where noise intensity α = 0.5 and noise cutoff frequency ω). j =50 (MHz), where the coherent regeneration time corresponding to t∈[0,50](ms) is approximately t=[12.5,25,37.6,50](ms) (the slight difference in value is mainly affected by the number of significant bits retained during calculation), the coherent regeneration time corresponding to t∈[0,100](ms) is approximately t=[25,50,75,100](ms), and the coherent regeneration time corresponding to t∈[0,300](ms) is approximately t=[75,150,225,300](ms).

[0029] This invention provides a method for controlling the coherent periodic complete regeneration in a quantum-simulated phase-damped noise channel. The steps include:

[0030] (1) The coherence of the quantum state is closely related to the selected reference basis. Under the premise of selecting the reference basis, the phase damped noise channel is simulated based on the nuclear magnetic resonance system.

[0031] (2) Input the maximum coherent state and calculate the density matrix of the maximum coherent state under different reference basis vectors after passing through the quantum simulation phase-damped noise channel.

[0032] (3) Based on the density matrix, the quantum coherence of the system is calculated using the l1 norm, and the quantum coherence of the system under the Z reference basis is obtained as follows: The quantum coherence of the system under the X / Y reference basis is

[0033] (4) Based on the functional expression satisfied by quantum coherence, the quantum coherence of the system under different reference basis vectors is controlled. Under the Z reference basis vector, the noise fundamental frequency value is controlled to satisfy... It can realize t∈[0,t maxWithin a given time, the periodicity of quantum coherence is completely regenerated. Under the X / Y reference basis, the noise fundamental frequency and the system bit frequency are jointly controlled to satisfy the following conditions: It can achieve complete periodic regeneration of quantum coherence.

[0034] As attached Figure 1 As shown, a single-qubit quantum state ensemble is prepared in a nuclear magnetic resonance system using a pseudopure state preparation method. When Z / X / Y are chosen as the reference basis vectors, the same maximally coherent states are initially prepared respectively. Furthermore, by manipulating the Hamiltonian of the nuclear magnetic resonance system and employing noise injection techniques to apply noise to the ensemble, the Hamiltonian of the ensemble under the Z reference basis is affected. Hamiltonian of ensemble action under X / Y reference basis vectors U z→x / y This represents the transformation matrix from the Z basis vectors to X / Y. in It is a random error generated by carrier phase modulation, used to describe the noise distribution in the time domain. For the X / Y reference basis, it can also be represented by the maximally coherent state under the Z basis, followed by the application of the Hamiltonian. The density matrix measured at time t is transformed to the X / Y reference basis vectors using a basis vector transformation. Both system evolution processes hold true. In the experiment, the relationship between the noise power spectral density S(ω) and the modulation function F(j) (S(ω)∝|F(ω)|) is utilized. 2 A modulation function F(j) is designed, and a Gaussian random noise signal is generated using a signal generator. By adjusting parameters such as sampling frequency and bandwidth, the noise component characteristics in β(t) are matched. The signal is then loaded into the radio frequency channel of the NMR spectrometer via an RF cable. Using carrier phase modulation technology, the noise information is mapped to the Hamiltonian H0(t) = β(t)σ. z In the experiment, the noise intensity α can be directly set by controlling the output power knob of the signal generator or the software power adjustment module; its value is positively correlated with the output power. After the single-bit system is subjected to Hamiltonian action, averaging the ensemble can effectively simulate the phase-damped noise channel. In the experiment, the GRAPE algorithm can be used to implement the system's evolution operator, and quantum state tomography can be used to measure the final state information after passing through the noise channel.

[0035] Based on the final state of the system, the quantum coherence of the quantum states under different reference basis vectors is obtained using the l1 norm metric method, where the quantum coherence of the system under the Z reference basis vector is: The quantum coherence of the system under the X / Y reference basis is Therefore, according to the coherence expression, different control strategies exist for achieving periodic regeneration of quantum coherence within a certain time frame under different reference basis vectors. Under the Z reference basis vector, this is achieved by controlling the noise fundamental frequency ω0 to satisfy... The quantum coherence in t∈[0, t max ] can be completely regenerated, and the corresponding coherence complete regeneration period is As shown in the accompanying Figure 2 , in t∈[0, 50] (ms), t∈[0, 100] (ms), and t∈[0, 300] (ms), the noise base frequency is respectively: All achieve 4 times of complete regeneration of coherence (wherein the noise intensity α=0.5, and the noise cutoff frequency ω J =50 (MHz)), wherein when t∈[0, 50] (ms), the corresponding coherence regeneration time is approximately t=[12.5, 25, 37.6, 50] (ms) (the slight difference in the numerical value is mainly affected by the effective number of bits reserved during calculation), when t∈[0, 100] (ms), the corresponding coherence regeneration time is approximately t=[25, 50, 75, 100] (ms), and when t∈[0, 300] (ms), the corresponding coherence regeneration time is approximately t=[75, 150, 225, 300] (ms); under the X / Y reference base vector, the noise base frequency value and the system bit frequency are jointly regulated to satisfy The quantum coherence can be completely regenerated, and the regenerated period is As shown in the accompanying Figure 3 , in t∈[0, 50] (ms), t∈[0, 100] (ms), and t∈[0, 300] (ms), the noise base frequency ω0 and the system bit frequency are respectively: All achieve 4 times of complete regeneration of coherence (wherein the noise intensity α=0.5, and the noise cutoff frequency ω J =50 (MHz)), wherein when t∈[0, 50] (ms), the corresponding coherence regeneration time is approximately t=[12.5, 25, 37.6, 50] (ms) (the slight difference in the numerical value is mainly affected by the effective number of bits reserved during calculation), when t∈[0, 100] (ms), the corresponding coherence regeneration time is approximately t=[25, 50, 75, 100] (ms), and when t∈[0, 300] (ms), the corresponding coherence regeneration time is approximately t=[75, 150, 225, 300] (ms).

[0036] The system, device, module or unit illustrated in the above embodiments can be specifically implemented by a computer chip or entity, or by a product with certain functions.

[0037] Computer-readable media includes permanent and non-permanent, movable and non-movable media that can implement information storage by any method or technology. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible to a computing device. According to the definition herein, computer-readable media does not include transitory media such as modulated data signals and carriers.

[0038] It should also be noted that the terms "comprising", "comprising" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus including a series of elements includes not only those elements, but also other elements not explicitly listed or inherent to such a process, method, article or apparatus. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, article or apparatus including the element.

[0039] The above embodiments should be understood as only for illustrating the present application and not for limiting the protection scope of the present application. After reading the content of the present application, the skilled in the art can make various changes or modifications to the present application, and these equivalent changes and modifications also fall within the scope defined by the claims of the present application.

Claims

1. A method for regulating coherent periodic revivals in a quantum simulation of a phase-damped noisy channel, the method comprising: The method comprises the following steps: (1) selecting a reference basis vector and simulating a phase damping noise channel based on a nuclear magnetic resonance system; (2) inputting a maximum coherent state and calculating a density matrix of the maximum coherent state after passing through the quantum simulation phase damping noise channel under different reference basis vectors; (3) Based on the density matrix, the quantum coherence of the system is calculated by using the l1 norm method, and the quantum coherence of the system under the Z reference basis is The quantum coherence of the system under the X / Y reference basis is The quantum coherence of the system under the Z / X / Y reference basis is calculated by using the l1 norm, and the subscript K z / x / y The different reference basis is selected, and the subscript l represents the l1 norm method, wherein ρ(t) represents the density matrix of the system at time t, Γ(t) represents the decoherence function of the system, ω k The bit frequency of the system is represented. (4) Based on the functional expression satisfied by quantum coherence, regulate the quantum coherence of the system under different reference basis vectors; under the Z reference basis vector, t∈[0,t max Within the time range (t) max (Indicates the upper limit of time), adjust the fundamental frequency of the noise to meet the requirements. It can achieve complete periodic regeneration of quantum coherence within this time range, with the corresponding regeneration period being... The number of regeneration cycles is n; under the X / Y reference basis, the noise fundamental frequency ω0 and the system bit frequency ω are jointly controlled. k Make them satisfy respectively It can achieve complete periodic regeneration of quantum coherence, with a corresponding regeneration period of... The number of rebirth cycles is n.

2. The method of claim 1, wherein the method is applied to a quantum simulation of coherent periodic revivals in a phase-damped noisy channel. When Z is chosen as the reference basis vector, the same N maximally coherent states are prepared in a nuclear magnetic resonance system As the input quantum state ensemble; the control Hamiltonian of the nuclear magnetic resonance system is regulated and the Hamiltonian acting on the ensemble is injected with noise Wherein is the control Hamiltonian, H0(t) = β(t)σ z is the injected transverse relaxation noise Hamiltonian, ω k is the system quantum bit frequency, is the random error generated by phase modulation on the carrier, describes the distribution of noise in the time domain, and the parameter α represents the noise amplitude, ω0 is the base frequency of the noise power spectrum, and ω J is the noise cutoff frequency, ψ j is a series of random phases, is a modulation function, and the value of p determines the type of noise, for example, if p = 0, then F(j) = j -1 represents white noise; the ensemble density matrix at time t is obtained by averaging the system evolution state under the action of the Hamiltonian When X / Y is chosen as the reference basis vector, N maximally coherent states are also prepared in a nuclear magnetic resonance system As the input quantum state ensemble, the Hamiltonian acting on the ensemble is U z→x / y represents the conversion matrix from the Z basis vector to the X / Y basis vector, which satisfies represents the transpose complex conjugate of the matrix U z→x / y , and further the density matrix of the system at time t is 3. The method of claim 2, wherein the method is performed by a quantum simulator. Based on the density matrix of the system at time t, the quantum coherence of the system is calculated by using the l1 norm, that is, the sum of the absolute values of the off-diagonal elements of the density matrix, and it is found that the quantum coherence of the system at time t under the Z reference basis satisfies The quantum coherence of the system under the X / Y reference basis satisfies 4. The method of claim 1, wherein the method is a method of quantum simulation of the regulation of coherent periodic revivals in a phase-damped noisy channel. According to the system de-coherence function Combined with the formula satisfied by the system quantum coherence under different reference basis vectors, the control method of the system quantum coherence under different reference basis vectors can be obtained: under the Z reference basis vector, the noise base frequency value is controlled to satisfy The quantum coherence can be completely regenerated in the time t∈[0,t max ] and the regenerated period is Under the X / Y reference basis vector, the noise base frequency value and the system bit frequency are jointly controlled to satisfy The quantum coherence can be completely regenerated and the regenerated period is 5. A storage medium, which stores a computer program in the inside, characterized by The computer program is read by the processor, and the method for regulating coherent periodic regeneration in the quantum simulation phase damping noise channel in any one of claims 1-4 is executed.

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