Patent Description:
Embodiments of this application relate to the field quantum noise process analysis technology.

A quantum noise process is a quantum information pollution process caused by the interaction between a quantum system or quantum device with a bath or by the imperfect control.

In the related art, information about a dynamical map of a quantum noise process is extracted through quantum process tomography (QPT). The QPT is a mathematical description of inputting a group of standard quantum states to a noise channel and reconstructing a quantum noise process through a series of measurement processes.

The limited information about the quantum noise process obtained through pure QPT is insufficient to accurately and comprehensively analyze the quantum noise process.

<NPL>, discloses a Non-Markovian dynamical maps. The initial stages of the evolution of an open quantum system encode the key information of its underlying dynamical correlations, which in turn can predict the trajectory at later stages. A general approach based on non-Markovian dynamical maps is proposed to extract this information from the initial trajectories and compress it into non-Markovian transfer tensors. Assuming time-translational invariance, the tensors can be used to accurately and efficiently propagate the state of the system to arbitrarily long time scales. The non-Markovian transfer tensor method (TTM) demonstrates the coherent-to-incoherent transition as a function of the strength of quantum dissipation and predicts the noncanonical equilibrium distribution due to the system-bath entanglement. TTM is equivalent to solving the Nakajima-Zwanzig equation and, therefore, can be used to reconstruct the dynamical operators (the system Hamiltonian and memory kernel) from quantum trajectories obtained in simulations or experiments. The concept underlying the approach can be generalized to physical observables with the goal of learning and manipulating the trajectories of an open quantum system.

Embodiments of this application provide a quantum noise process analysis method and apparatus, a device, and a storage medium, to resolve the foregoing technical problem in the related art. The present invention is set out in the set of appended claims.

The technical solutions provided in the embodiments of this application may include at least the following beneficial effects:.

In the technical solutions provided in this application, QPT is performed on a quantum noise process, to obtain dynamical maps of the quantum noise process, and a TTM of the quantum noise process is further extracted from the dynamical maps of the quantum noise process. The TTM is used for representing a dynamical evolution of the quantum noise process, that is, reflecting the law of evolution of the dynamical maps of the quantum noise process over time. Compared with pure QPT, this application can obtain richer and more comprehensive information about the quantum noise process. Therefore, when the quantum noise process is analyzed based on the TTM of the quantum noise process, a more accurate and comprehensive analysis of the quantum noise process can be achieved based on the richer and more comprehensive information.

To describe the technical solutions of the embodiments of this application more clearly, the following briefly describes the accompanying drawings required for describing the embodiments. Apparently, the accompanying drawings in the following description show only some embodiments of this application, and a person of ordinary skill in the art may still derive other accompanying drawings according to these accompanying drawings without creative efforts.

To make the objectives, technical solutions, and advantages of this application clearer, the following further describes implementations of this application in detail with reference to the accompanying drawings.

Before the embodiments of this application are described, some terms involved in this application are explained first.

In quantum information processing, all information of the quantum system is represented by an evolution ρ(t) of a quantum state over time t. ρ(t) is a d × d complex matrix. Any quantum process, either a quantum information processing process or a quantum noise process, may be represented by using a dynamical map in a case that the system and the bath are in a separable state initially: <MAT>.

In this way, the following may be obtained: <MAT>
where <MAT>, and is an element of a complex transformation matrix χ whose index is m, n, <MAT> represents a Hermitian conjugate of En, En is an element in {Ei}, and ρ represents an input state.

In the related art, a quantum noise process analysis method based on QPT is provided. d<NUM> × d<NUM> linearly independent input states ρj are used, and each input state ρj is transferred to a quantum noise process to obtain an output state ε(ρj). Because of completeness of the input states, the output state may be represented as a linear combination of the input states: <MAT> where <MAT>.

Because {ρi} is linearly independent, the following may be obtained: <MAT>.

By transposing Bm,n,j,k, the following may be obtained: <MAT>
χm,n includes all information about dynamical maps of the quantum noise process. Therefore, once χm,n is obtained through QPT, all the information about the dynamical maps of the quantum noise process is obtained.

However, the limited information about the quantum noise process obtained through pure QPT is insufficient to accurately and comprehensively analyze the quantum noise process. For example, whether the quantum noise process is a Markov process or a non-Markov process is not determined, a frequency spectrum of the quantum noise process is not obtained, and a correlated noise between different quantum devices in the quantum system is not analyzed.

To resolve the foregoing technical problems, an embodiment of this application provides a quantum noise process analysis method. <FIG> is an overall flowchart of a technical solution of this application. In the technical solution provided in this application, QPT is performed on a quantum noise process, to obtain dynamical maps of the quantum noise process, a TTM of the quantum noise process is further extracted from the dynamical maps of the quantum noise process, and then the quantum noise process is analyzed according to the TTM. The TTM is used for representing a dynamical evolution of the quantum noise process, that is, reflecting the law of evolution of the dynamical maps of the quantum noise process over time. Therefore, richer and more comprehensive information about the quantum noise process can be obtained by analyzing the quantum noise process based on the TTM of the quantum noise process than by pure QPT, thereby achieving a more accurate and comprehensive analysis of the quantum noise process.

The technical solution provided in this application is applicable to analysis of a quantum noise process of any quantum system such as a quantum computer, secure quantum communication, the quantum Internet or another quantum system. The interference to the quantum system by quantum noise severely affects the performance of the quantum system, which is the primary barrier hindering the practical application of the quantum system. Therefore, analyzing the quantum noise process and understanding the properties of the noise are crucial for the development of the quantum system. In the technical solution provided in this application, the analyzing the quantum noise process based on the TTM of the quantum noise process may include, for example, the following analysis content as shown in <FIG>: Markov process determination, that is, whether the quantum noise process is a Markov process or a non-Markov process can be determined, and a special noise suppression solution may be designed for a non-Markov noise, where the solution is, for example, suppressing the occurrence of noise through dynamical decoupling; state evolution prediction, that is, a state evolution of the quantum noise process can be predicted; extraction of correlation function and frequency spectrum, that is, a correlation function and a frequency spectrum of the quantum noise process can be obtained, facilitating the integration of a filter of a corresponding frequency band in the process of quantum device manufacturing; and correlated noise analysis, that is, a correlated noise between different quantum devices in the quantum system can be analyzed, to learn the source of the correlated noise and accordingly design a corresponding solution to suppress the correlated noise. Therefore, the technical solution provided in this application can obtain richer and more comprehensive information about the quantum noise process, thereby providing more information to support the improvement in the performance of the quantum system.

<FIG> is a flowchart of a quantum noise process analysis method according to an embodiment of this application. The method is applicable to a computer device, and the computer device may be any electronic device having data processing and storage capabilities, such as a personal computer (PC), a server, or a computing host. The method may include the following steps (step <NUM> to step <NUM>):
Step <NUM>. Perform quantum process tomography (QPT) on a quantum noise process of a target quantum system, to obtain dynamical maps of the quantum noise process.

The performing quantum process tomography (QPT) on a quantum noise process to obtain dynamical maps of the quantum noise process has been described above, so the details are not described herein again.

QPT is performed on the quantum noise process at discrete time points. Given that QPT is performed at K different time points, dynamical maps of the quantum noise process at the K time points are obtained, K being an integer greater than or equal to <NUM>. Optionally, among the K time points, intervals between neighboring time points are equal. Certainly, intervals between neighboring time points may also be not equal, which is not limited in this embodiment.

Step <NUM>. Extract TTMs of the quantum noise process from the dynamical maps.

The TTM of the quantum noise process is used for representing a dynamical evolution of the quantum noise process, that is, reflecting the law of evolution of the dynamical maps of the quantum noise process over time.

If dynamical maps of the quantum noise process at the K time points are obtained in step <NUM>, a possible implementation of step <NUM> may be calculating the TTMs of the quantum noise process at the K time points according to the dynamical maps of the quantum noise process at the K time points. The TTMs at the K time points are extracted recursively. For example, a TTM Tn of the quantum noise process at an nth time point is calculated according to the following formula: <MAT>
where T<NUM> = ε<NUM>, εn represents a dynamical map of the quantum noise process at the nth time point, εm represents a dynamical map of the quantum noise process at an mth time point, and Tn-m represents a TTM of the quantum noise process at an (n-m)th time point, both n and m being positive integers.

Step <NUM>. Analyze the quantum noise process according to the TTMs.

After the TTMs of the quantum noise process at the K time points are extracted, the quantum noise process may be analyzed accordingly.

After Tn is determined, the quantum noise process may be considered as a Markov process if the value of |Tn| is negligibly small for n><NUM> according to the definition. Otherwise, the quantum noise process may be considered as a non-Markov process. That is, it is determined that the quantum noise process is a Markov process in a case that each of moduli of TTMs of the quantum noise process at first time points is less than a preset threshold, the first time points being time points other than the foremost time point of the K time points; and it is determined that the quantum noise process is a non-Markov process in a case that a modulus of a TTM of the quantum noise process at a second time point is greater than the preset threshold, the second time point being at least one time point other than the foremost time point of the K time points.

By means of the above method, based on the TTMs of the quantum noise process, whether the quantum noise process is a Markov process or a non-Markov process can be determined, and a special noise suppression solution may be designed for a non-Markov noise, where the solution is, for example, suppressing the occurrence of noise through dynamical decoupling.

Additionally, compared with the dynamical map, a universal equation for describing the evolution of the quantum system in an open bath is a non-temporal localized quantum master equation, and can better reveal the mathematical structure of the quantum noise process. This equation is a differential-integral equation: <MAT>
where ρ(t) represents a quantum state of the quantum system at time t and is represented by using a d × d complex matrix; Ls is a Liouville operator and represents a coherent part in the evolution process of the quantum system; s is an integral parameter; and κ(t) is a memory kernel, and includes all information about system decoherence triggered by the bath. If Ls and κ(t) of the quantum noise process are obtained, the noise mechanism may be completely understood. The basic idea of the technical solution of this application is to calculate a TTM through an experiment and QPT, thereby extracting information about Ls and κ(t).

In addition, a joint evolution of the quantum system and the bath is determined by a joint Hamiltonian. The joint Hamiltonian may be represented as: <MAT>
where Hs is a Hamiltonian of the quantum system; Hsb is an interactive Hamiltonian of coupling between the quantum system and the bath; <MAT> is an αth type of Pauli operator acting on an ith qubit of the system, both i and α being positive integer indexes; <MAT> is an αth type of bath operator coupled to the ith qubit; α = x, y, z represents three temporal-spatial directions; and gi is a coupling strength between the system and the bath.

The evolution of a state function of the quantum system follows: <MAT>
where ρ(t) represents a quantum state of the quantum system at time t, ρ(<NUM>) represents an initial quantum state of the quantum system, ρB is a quantum state of the bath, TrB represents calculation of a partial trace of the degree of freedom of the bath, exp+, exp_ are clockwise and counterclockwise time-ordered exponential operators respectively, ε(t) represents a dynamical evolution of the quantum system at the time t, i is a unit pure imaginary number, and s is an integral parameter.

If time is discretized by tk+<NUM> - tk = δt (k is a positive integer), a group of dynamical maps {εk ≡ ε(tk)} evolving over time may be defined. Experimentally, the dynamical maps may be obtained by performing QPT at different time points.

With reference to the foregoing definition about the formula of the TTM, by using Tn to express εn and substituting the expression into the formula of the foregoing state function, the following may be obtained: <MAT>
where ρ(tn) represents a quantum state at an nth time point tn, ρ(tn-m) represents a quantum state at an (n-m)th time point tn-m, and Tm represents a TTM at an mth time point. This formula clearly indicates that in the presence of a noise, the state evolution of the quantum system depends on the historical evolution the quantum system. Generally, the dependence of the dynamical evolution on history does not exceed a certain time span. This means that the influence of the noise on the state may be precisely estimated by truncating a convolution of the foregoing formula and keeping K (where K is a positive integer) time points, that is, all items for which t > tK are discarded. In this way, through QPT on a dynamical map in a short period of time, a TTM in this period of time may be obtained. Then, an evolution of an open system in a long time may be predicted by using the TTM in this short period of time. The quantum state ρ(tn) at the nth time point tn may be calculated through the foregoing formula. In addition, the predicted quantum state may be directly compared with an experiment to verify the effectiveness of dynamics of the open system described through the TTM. That is to say, this provides a preliminary basis for determining the effectiveness of the technical solution of this application.

To sum up, in the technical solutions provided in this application, QPT is performed on a quantum noise process, to obtain dynamical maps of the quantum noise process, and a TTM of the quantum noise process is further extracted from the dynamical maps of the quantum noise process. The TTM is used for representing a dynamical evolution of the quantum noise process, that is, reflecting the law of evolution of the dynamical maps of the quantum noise process over time. Compared with pure QPT, this application can obtain richer and more comprehensive information about the quantum noise process. Therefore, when the quantum noise process is analyzed based on the TTM of the quantum noise process, a more accurate and comprehensive analysis of the quantum noise process can be achieved based on the richer and more comprehensive information.

Additionally, in the technical solution provided in this application, the determining of whether the quantum noise process is a Markov process or a non-Markov process according to the TTM of the quantum noise process is further implemented; and the prediction, according to a TTM of the quantum noise process within a period of time, of a state evolution of the quantum noise process within a subsequent time is further implemented.

In an exemplary embodiment, after the TTM of the quantum noise process is extracted, a correlation function and a frequency spectrum of the quantum noise process may be further obtained accordingly. The process may include the following steps.

For a steady noise (for example, Gaussian steady noise), the properties of the noise are determined by a correlation function of the noise process. The correlation function of the noise process may be calculated according to a second-order memory kernel of the noise process.

In this embodiment of this application, for a quantum noise process, a second-order memory kernel of the quantum noise process is extracted according to the TTMs of the quantum noise process in a case that the quantum noise process is a steady noise.

Considering that the time has been discretized and approximated to the second order of a time step δt, an approximation of the TTM may be obtained: <MAT>
where δt is the time step, δn,<NUM> is a Kronecker function having a value of <NUM> when n=<NUM> and a value of <NUM> in other cases, n being a positive integer; and κ(tn) is a value of the memory kernel at time tn.

Moreover, according to the open system theory, a precise expression of a dynamical memory kernel κ is: <MAT>
where P = TrB{ρSB} ⊗ ρB is a map operator, and QρSB = ρSB - PρSB; L is a joint Liouville operator acting on the system and the bath, ρSB is a joint state of the system and the bath, and Q = I - P is a difference between P and an identity operator I.

Because a noise is preliminarily controlled through engineering in an ordinary quantum system, the coupling strength between the quantum system and the bath is relatively weak. When a target quantum system and the bath are in a weak coupling relationship, a second-order perturbation approximation may be established, and therefore the following may be obtained: <MAT>
where κ<NUM>(t) is a value of a second-order memory kernel at the time t, and <MAT> is a complex conjugate of Cαα'(t). The foregoing expression is under the Schrödinger representation, and at the same time, it is assumed that a Hamiltonian of a joint system is time-invariant. The second-order correlation function Cαα'(t) is defined as: <MAT>.

It is a bath correlation function. Based on the second-order perturbation, a dynamical map may be extracted from an experiment, and a TTM is obtained through QPT, thereby obtaining a memory kernel κexp through approximation. That is, κexp is an approximate second-order memory kernel obtained through an experiment.

When the target quantum system and the bath are in a strong coupling relationship, the second-order perturbation is no longer a desirable approximation, and a better approximate can be obtained only when there are more high-order items, but a second-order memory kernel can still be extracted by extracting a TTM from experimental data. Specific steps are as follows: selecting N different parameters, performing an experiment on the quantum noise process, and extracting memory kernels respectively corresponding to the N different parameters from the experiment; and performing calculation according to the memory kernels respectively corresponding to the N different parameters, to obtain the second-order memory kernel of the quantum noise process.

First, an N-order truncated approximate memory kernel is defined: <MAT>.

In addition, the following equation is satisfied: <MAT>
where A is an N-order normalized parameter matrix, and a memory kernel on the right side of the equation may be directly extracted from an experiment through QPT and data processing. Because A is a full-rank matrix, a second-order memory kernel is naturally obtained by solving the linear equation to obtain <NUM>-order to N-order memory kernels without physical units.

Calculate a correlation function of the quantum noise process according to the second-order memory kernel of the quantum noise process.

Optionally, the correlation function Cαα' of the quantum noise process is numerically extracted according to the following formula: <MAT>
where κ<NUM> represents the second-order memory kernel of the quantum noise process, tn represents the nth time point, Cαα'(tn) is a second-order correlation function at the nth time point tn, κexp represents an approximate second-order memory kernel obtained through an experiment, δtn,t<NUM> is a Kronecker function (having a value of <NUM> when n=<NUM> and a value of <NUM> in other cases), λn is an adjustable parameter, and Caa'(tn-<NUM>) is a second-order correlation function at an (n-<NUM>)th time point tn-<NUM>. λn is used for ensuring that after the target function is minimized, the correlation function can still be continuous. λn may be determined by first selecting an initial value and observing the value of the target function followed by iterative adjustments, so the selection of the value of λn is robust.

Optionally, for a non-Gaussian steady noise, only a correlation function higher than <NUM>-order can fully represent statistical properties of the noise. Obtaining of a second-order correlation function of a noise by solving this linear equation A[κ̃<NUM>,<NUM> ···κ̃<NUM>N,<NUM>]T = [κ̃(<NUM>)···κ̃(N)]T has been described above. If a non-Gaussian steady noise is processed, it may be assumed that a memory kernel of the noise is written as: <MAT>.

Based on this more generalized memory kernel, the following may be obtained according to the solution described above: <MAT>.

By solving this linear equation, second-order and higher-order correlation functions may be obtained.

Perform a Fourier transform on the correlation function of the quantum noise process, to obtain a frequency spectrum of the quantum noise process.

Once the correlation function of the quantum noise process is obtained, a Fourier transform may be performed on the correlation function, to obtain a frequency spectrum Jαα'(ω) of the quantum noise process: <MAT>.

This method of obtaining the frequency spectrum of the quantum noise process is not limited by whether the noise is a quantum noise (the system has a feedback to the noise source) or a classical noise, and is not limited by a particular noise type.

To sum up, in the technical solution provided in this application, after the TTM of the quantum noise process is extracted, the correlation function and the frequency spectrum of the quantum noise process may be further obtained accordingly, facilitating the integration of a filter of a corresponding frequency band in the process of quantum device manufacturing.

In an exemplary embodiment, after the TTM of the quantum noise process is extracted, a correlated noise between different quantum devices in the target quantum system may be further analyzed accordingly, to learn the source of the correlated noise. The process may include the following steps.

A quantum system may include a plurality of quantum devices. A qubit is the simplest quantum device, including only two quantum states. By using TTMs, a noise correlation between the plurality of quantum devices in the same quantum system can be completed. The following mainly describes a case where there are two quantum devices, and the same applies to other cases. For example, according to the method provided in this embodiment of this application, a noise correlation between any two quantum devices, or a noise correlation between any three or more quantum devices can also be determined.

Dynamical maps of any two quantum systems (or quantum devices) may be decomposed as follows: <MAT>
where εn,<NUM> represents a dynamical map of a first quantum device, εn,<NUM> represents a dynamical map of a second quantum device, and δεn is an unseparated part representing the influence of a correlated noise. In the foregoing decomposition of dynamical maps, a dynamical map εn → χn may be expressed in the form of Choi matrix, that is, χn is a Choi matrix being an equivalent representation of the dynamical map, and a trace of the Choi matrix is calculated as follows: <MAT>.

Then, a Choi matrix χn,i of a single quantum device is expressed back as a dynamical map εn,i. Dynamical maps εn of two quantum devices may both be obtained by performing joint QPT on the two quantum devices. δεn may be used for analyzing the correlated noise. In the case of second-order perturbation, a modulus of δεn is usually much less than that of εn. In a non-perturbative area, modulus values of δεn and εn may be equivalent, or even |δεn| is much greater than |εn|. Therefore, pure QPT can provide a preliminary determination on the strength of the correlated noise. However, it is rather difficult analyze the source of the correlated noise because all data is mixed together. Usually, sources of the correlated noise between two quantum devices include: (<NUM>) a correlated noise generated from direct coupling between the two quantum devices; (<NUM>) a correlated noise induced by a shared bath of the two quantum devices; or (<NUM>) a combination thereof.

An embodiment of this application provides a correlated noise analysis method based on a TTM. By this method, more information about a correlated noise may be obtained. First, a separable TTM is calculated according to εn : <MAT> and <MAT>.

For example, through QPT, a joint dynamical map εn of two quantum devices in the target quantum system may be obtained, a TTM Tn is further obtained, then εn,<NUM> and εn,<NUM> may be obtained by calculating traces for the two quantum devices according to εn respectively, and εn = εn,<NUM> ⊗ εn,<NUM>. Then, Tn is obtained through <MAT>. Finally, δTn = Tn - Tn = δLδtδn,<NUM> + δκnδt<NUM>.

Then, considering two different time steps δt and δt' : <MAT>
δL and δκn are calculated respectively.

To sum up, in the technical solution provided in this application, after the TTM of the quantum noise process is extracted, a correlated noise between different quantum devices in the target quantum system may be further analyzed accordingly, to learn the source of the correlated noise and design a corresponding solution to suppress the correlated noise.

To further verify the effectiveness of the technical solution of this application, numerical analysis is performed for a typical model. After this, on IBM Quantum Experience (which is a quantum computing cloud platform provided by IBM), an attempt is made to perform an experiment and observation on a real superconducting qubit and extract information about a noise process from the real superconducting qubit by using the technical solution of this application.

Results of numerical analysis for the typical model are as follows:.

Letting Hs = <NUM> z,Hsb = Bz(t) z,Czz (<NUM>) = = <NUM>, t = <NUM>, TTM results of a free evolution of a single qubit are as shown in <FIG>. Part (a) in <FIG> shows the variation of a Frobenius norm of the TTM over time. It may be seen from the figure that the TTM within a range t<NUM> → t<NUM> makes a non-trivial contribution, that is, non-Markov properties are demonstrated in the noise process. A line <NUM> in part (b) in <FIG> represents an evolution of a real part of a non-diagonal element of a density matrix corresponding to an initial state <MAT> over time. A line <NUM>, a line <NUM> and a line <NUM> respectively present prediction effects for the density matrix at different TTM lengths (that is, when K is <NUM>, <NUM>, and <NUM> respectively). It may be seen that when K is <NUM>, an evolution obtained through the TTM well coincides with an exact solution, and a long-term experimental evolution can be perfectly predicted.

Additionally, <FIG> shows the variation of a Bloch volume over time, and the increase in the Bloch volume V(t) within a period of time (t<NUM>,t<NUM>,t<NUM>) clearly demonstrates non-Markov properties of the dynamical process, which proves the conclusion in <FIG> from another perspective.

Letting Hs = <NUM> z,Czz(<NUM>) = 〈Bz(t)Bz(<NUM>)〉 = <NUM>, t = <NUM>, and a frequency spectrum of a quantum noise process (equivalent to a bath noise spectrum) is obtained through a TTM method for a free evolution of a single qubit. Part (a) in <FIG> shows the variation of a noise correlation function Czz(t) over time in the case of weak coupling between the quantum system and the bath. A line <NUM> presents an accurate theoretical result of the noise correlation function, and each circle presents a numerical result obtained from a memory kernel under an assumption of K(t) K2 (t). It can be learned that in the case of weak coupling, an approximate second-order memory kernel obtained from TTM can well depict the quantum noise process.

In part (b) in <FIG>, let Hs =<NUM> z,Czz(<NUM>) (<NUM>,<NUM>), t=<NUM>. In the case of strong coupling between the quantum system and the bath, a noise correlation function at a special time point Czz(t = <NUM>δt) changes with a coupling strength Czz (<NUM>) =λ between the noise and the system. A line <NUM> is an accurate theoretical result. A line <NUM> presents a first numerical result: that is, directly assuming K(t) K<NUM>(t), it can be learned that in the case of strong coupling, there is a big difference between the first numerical result and a real noise spectrum. A line <NUM> presents a second numerical result: that is, directly assuming K(t) K<NUM>(t) + K<NUM>(t), even in the case of strong coupling under research, a memory kernel obtained from TTM can well reflect the real noise spectrum even for higher order.

Letting Hs = <NUM> z, Cxx (<NUM>) = <NUM>, t = <NUM>, a frequency spectrum of a quantum noise process (equivalent to a bath noise spectrum) is obtained through a TTM method for a free evolution of a single qubit. In this case, the noise is no longer a pure phase decoherence noise. As shown in <FIG>, a correlation function Cxx(t) = 〈Bx(t)Bx(<NUM>)〉 presented by a circle which is obtained from a memory kernel of a TTM well coincides with a real noise spectrum presented by a line <NUM>. This group of simulation indicates that when the influence of the bath noise exceeds that of pure dephasing, for example, Bx(t),By (t), the method of deducing a noise spectrum from a memory kernel of a TTM is still applicable.

Part (a) in <FIG> shows TTM results of free evolutions of two qubits coupled to each other in a direction z in a case that the two qubits are located in respective independent bath noises.

A correlation function is: <MAT>, t = <NUM>.

A line <NUM>, a line <NUM> and a line <NUM> represent a full TTM Tn, a separable TTM Tn and a correlated TTM δTn respectively. As shown in the figure, only the first item, that is, T<NUM>, in the correlated TTM is non-trivial. That is, the result indicates that in an independent noise bath, a correlated part of a TTM is almost Markovian. Further, it is learned through analysis that an entanglement of two qubits generated by Ls leads to a correlated decoherence effect even if noise sources are separated or independent of each other in sapce.

Part (b) in <FIG> shows TTM results of free evolutions of two qubits not directly coupled to each other in a case that the two qubits are located in correlated bath noises.

A line <NUM>, a line <NUM> and a line <NUM> represent a full TTM Tn, a separable TTM Tn and a correlated TTM δTn respectively. In this case, a plurality of Tn are non-trivial. It may be found through analysis that K(t<NUM>) is the main contributing factor of T<NUM>. Therefore, relative importance of different physical mechanisms that cause collective decoherence can be estimated directly according to the norm distribution of TTMs over time.

To investigate the importance of Tn, <FIG> presents a dynamical evolution of non-diagonal matrix elements of a density matrix of two qubits. Prediction results of TTMs whose lengths are (that is, K is) <NUM>, <NUM>, and <NUM> in a physical state are compared with a real dynamical simulation result. Two parts (a) and (b) in <FIG> respectively present prediction results for <MAT> based on a full TTM and a separable TTM in a first model. Two parts (c) and (d) in <FIG> respectively present prediction results for <MAT> based on a full TTM and a separable TTM in a second model. In both the two cases, the effect of collective decoherence cannot be described by using Tn alone. In <FIG>, Tn is very small, and has no influence. However, as can be seen from <FIG>, Tn still plays an important role in the prediction of the physical state. This further proves the complex characteristics of a highly non-Markovian system.

Additionally, to verify the practicability of the technical solution of this application, tests have been conducted on IBM Quantum Experience. IBM Quantum Experience is a superconducting quantum computing cloud platform provided the IBM, and all computations are run on a real superconducting quantum computer. For a superconducting qubit, because the time for operating a quantum gate is too long (about <NUM> ns) relative to the correlation time of the bath and the noise process is not pure phase decoherence, the method of extracting a frequency spectrum based on dynamical decoupling of CPMG is inapplicable.

<FIG> shows research on TTMs of a free evolution of a single qubit on an IBM quantum computing cloud platform "IBM <NUM> Melbourne", where t = <NUM> s. Part (a) in <FIG> shows the norm distribution of TTMs over time. Part (b) in <FIG> shows a dynamical evolution of a state |<NUM>〉, and a line <NUM> is an experimental result. A line <NUM>, a line <NUM> and a line <NUM> are respective prediction results for an evolution of |<NUM>〉 when (<NUM>, <NUM>, and <NUM>) TTMs are taken respectively. It may be seen that the time scale of the memory kernel is in the order of magnitude of s, which is not short compared with the quantum gate time of <NUM>ns.

<FIG> shows the distribution of a Bloch volume V(t) of a single qubit over time. A transient increase demonstrates the non-Markov characteristics of the quantum system.

<FIG> shows a dynamic decoupling (DD) evolution of a single qubit on an IBM quantum computing cloud platform "IBM <NUM> Melbourne", where t = <NUM> s. Measurement results of four initial states (a) | (<NUM>)〉 = |<NUM>〉, (b) | (<NUM>)〉 = |<NUM>〉, (c) <MAT> and (d) <MAT> in three spinning directions under the XY<NUM>DD protocol are shown. Extension of quantum coherence may be observed.

<FIG> shows a dynamic decoupling (DD) evolution of a single qubit on an IBM quantum computing cloud platform "IBM <NUM> Melbourne", where t = <NUM> s. The norm distribution of TTMs over time under the XY<NUM>DD protocol is shown. An internal mechanism of extension of quantum coherence may be reflected by this TTM: an effective noise under the XY<NUM>DD protocol is more Markovian than a result of a free evolution.

<FIG> shows research on a TTM of a free evolution of two qubits on an IBM quantum computing cloud platform "IBM <NUM> Melbourne", where t = <NUM> s. The norm distribution of a full TTM |Tn|, a separable TTM |Tn|, and a correlated TTM I Tn| over time is shown. It may be seen that in this group of experiments, the TTMs are all non-trivial in a relatively long time scale, and have relatively strong non-Markov properties. With reference to the result of numerical simulation, it may be preliminarily considered that there are inter-bit coupling and a bath noise correlation between two neighboring bits on the IBM quantum cloud platform.

<FIG> shows research on TTMs of free evolutions of two qubits on an IBM quantum computing cloud platform "IBM <NUM> Melbourne", where t = <NUM> s. A black line with black dots is an experimental result of an evolution of a density matrix, and three lines represented with circles, triangles and squares are respectively results of predicting an evolution of a density matrix by selecting (<NUM>, <NUM>, and <NUM>) TTMs respectively. (a) and (b) in <FIG> respectively present prediction results based on a full TTM and a separable TTM in a case that the initial state is a non-entangled state <MAT>. (c) and (d) in <FIG> respectively present prediction results based on a full TTM and a separable TTM in a case that an initial state is an entangled state <MAT>. It can be learned that if no correlated TTM is included, the evolution cannot be accurately predicted either in the entangled state or in the non-entangled state. Through a further analysis of T<NUM>, it may be seen that Ls makes an important contribution, indicating that the two qubits are coupled to each other.

The following is an apparatus embodiment of this application, which can be used to execute the method embodiments of this application. For details that are not disclosed in the apparatus embodiments of this application, refer to the method embodiments of this application.

<FIG> is a block diagram of a quantum noise process analysis apparatus according to an embodiment of this application. The apparatus has functions of implementing the foregoing method embodiments. The functions may be implemented by hardware, or may be implemented by hardware executing corresponding software. The apparatus may be a computer device, or may be disposed in a computer device. The apparatus <NUM> may include: an obtaining module <NUM>, an extraction module <NUM>, and an analysis module <NUM>.

The obtaining module <NUM> is configured to perform quantum process tomography (QPT) on a quantum noise process of a target quantum system, to obtain dynamical maps of the quantum noise process.

The extraction module <NUM> is configured to extract TTMs of the quantum noise process from the dynamical maps, the TTMs being used for representing a dynamical evolution of the quantum noise process.

The analysis module <NUM> is configured to analyze the quantum noise process according to the TTMs.

In some possible designs, the dynamical maps include dynamical maps of the quantum noise process at K time points, K being a positive integer; and
the extraction module <NUM> is configured to calculate TTMs of the quantum noise process at the K time points according to the dynamical maps of the quantum noise process at the K time points.

In some possible designs, the extraction module <NUM> is configured to calculate a TTM Tn of the quantum noise process at an nth time point according to the following formula: <MAT>
where T<NUM> = ε<NUM>, εn represents a dynamical map of the quantum noise process at the nth time point, εm represents a dynamical map of the quantum noise process at an mth time point, and Tn-m represents a TTM of the quantum noise process at an (n-m)th time point, both n and m being positive integers.

In some possible designs, as shown in <FIG>, the analysis module <NUM> includes a Markov determination sub-module <NUM>.

The Markov determination sub-module <NUM> is configured to:.

In some possible designs, as shown in <FIG>, the analysis module <NUM> includes a state evolution prediction sub-module <NUM>.

The state evolution prediction sub-module <NUM> is configured to predict a state evolution of the quantum noise process within a subsequent time according to the TTMs at the K time points.

In some possible designs, the state evolution prediction sub-module <NUM> is configured to calculate a quantum state ρ(tn) of the quantum noise process at an nth time point tn according to the following formula: <MAT>
where Tm represents a TTM at an mth time point, and ρ(tn-m) represents a quantum state at an (n-m)th time point tn-m, both n and m being positive integers.

In some possible designs, as shown in <FIG>, the analysis module <NUM> includes:.

In some possible designs, the memory kernel extraction sub-module <NUM> is configured to: select N different parameters, perform an experiment on the quantum noise process, and extract memory kernels respectively corresponding to the N different parameters from the experiment; and perform calculation according to the memory kernels respectively corresponding to the N different parameters, to obtain the second-order memory kernel of the quantum noise process.

In some possible designs, the correlation function calculation sub-module <NUM> is configured to numerically extract the correlation function Cαα' of the quantum noise process according to the following formula: <MAT>
where κ<NUM> represents the second-order memory kernel of the quantum noise process, tn represents the nth time point, κexp is a second-order correlation function at the nth time point, κexp represents an approximate second-order memory kernel obtained through an experiment, δtn,t<NUM> represents an interval between the nth time point and an initial moment, λn is an adjustable parameter, and Caa'(tn-<NUM>) is a second-order correlation function at an (n-<NUM>)th time point tn-<NUM>.

In some possible designs, as shown in <FIG>, the analysis module <NUM> includes a correlated noise analysis sub-module <NUM>.

The correlated noise analysis sub-module <NUM> is configured to calculate, for s quantum devices included in the target quantum system, a correlated TTM among the s quantum devices according to TTMs respectively corresponding to the s quantum devices, s being an integer greater than <NUM>; and analyze a source of a correlated noise among the s quantum devices according to the correlated TTM.

When the apparatus provided in the foregoing embodiments implements its functions, a description is given only by using the foregoing division of function modules as an example. In actual applications, the functions may be allocated to and implemented by different function modules according to the requirements, that is, the internal structure of the device may be divided into different function modules, to implement all or some of the functions described above. In addition, the apparatus and method embodiments provided in the foregoing embodiments belong to the same conception. For the specific implementation process, refer to the method embodiments, so the details are not described herein again.

<FIG> is a schematic structural diagram of a computer device according to an embodiment of this application. The computer device is configured to implement the quantum noise process analysis method provided in the foregoing embodiments. Specifically:.

The computer device <NUM> includes a central processing unit (CPU) <NUM>, a system memory <NUM> including a random access memory (RAM) <NUM> and a read-only memory (ROM) <NUM>, and a system bus <NUM> connecting the system memory <NUM> and the CPU <NUM>. The computer device <NUM> further includes a basic input/output system (I/O system) <NUM> configured to transmit information between components in the computer, and a mass storage device <NUM> configured to store an operating system <NUM>, an application program <NUM>, and other program module <NUM>.

The basic I/O system <NUM> includes a display <NUM> configured to display information and an input device <NUM> configured for a user to input information, such as a mouse or a keyboard. The display <NUM> and the input device <NUM> are both connected to the CPU <NUM> by an input/output controller <NUM> connected to the system bus <NUM>. The basic I/O system <NUM> may further include the input/output controller <NUM>, to receive and process inputs from multiple other devices, such as a keyboard, a mouse, or an electronic stylus. Similarly, the input/output controller <NUM> further provides an output to a display screen, a printer, or other type of output device.

The mass storage device <NUM> is connected to the CPU <NUM> by a mass storage controller (not shown) connected to the system bus <NUM>. The mass storage device <NUM> and an associated computer-readable medium provide non-volatile storage for the computer device <NUM>. That is, the mass storage device <NUM> may include a computer-readable medium (not shown), such as a hard disk or a CD-ROM drive.

Without loss of generality, the computer-readable medium may include a computer storage medium and a communication medium. The computer storage medium includes volatile and non-volatile, removable and non-removable media implemented by using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. The computer storage medium includes a RAM, a ROM, an EPROM, an EEPROM, a flash memory, or other solid-state storage technique, a CD-ROM, a DVD, or other optical storage, a magnetic cassette, a magnetic tape, a magnetic disk storage, or other magnetic storage device. Certainly, it is known to a person skilled in the art that the computer storage medium is not limited to the foregoing types. The system memory <NUM> and the mass storage device <NUM> may be collectively referred to as a memory.

According to the embodiments of this application, the computer device <NUM> may further be connected, through a network such as the Internet, to a remote computer on the network. That is, the computer device <NUM> may be connected to a network <NUM> by a network interface unit <NUM> connected to the system bus <NUM>, or may be connected to another type of network or remote computer system (not shown) by a network interface unit <NUM>.

The memory stores at least one instruction, at least one section of program, a code set or an instruction set, and the at least one instruction, the at least one section of program, the code set or the instruction set is configured to be executed by one or more processors to implement the quantum noise process analysis method provided in the foregoing embodiments.

In an exemplary embodiment, a computer-readable storage medium is further provided, the storage medium storing at least one instruction, at least one program, a code set or an instruction set, the at least one instruction, the at least one program, the code set or the instruction set being executed by a processor of a computer device to implement the quantum noise process analysis method provided in the foregoing embodiments. In an exemplary embodiment, the computer-readable storage medium may be a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, or an optical data storage device.

In an exemplary embodiment, a computer program product is provided. When executed, the computer program product is configured to implement the quantum noise process analysis method provided in the foregoing embodiments.

Claim 1:
A quantum noise process analysis method, applicable to a computer device, the method comprises:
performing (<NUM>) quantum process tomography, QPT, on a quantum noise process of a target quantum system, to obtain dynamical maps of the quantum noise process;
extracting (<NUM>) transfer tensor maps, TTMs, of the quantum noise process from the dynamical maps, the TTMs being maps recursively extracted from dynamical maps of the quantum noise process, the maps encoding a memory kernel of the target quantum system, and being used for predicting a dynamical evolution of the quantum noise process and determining properties of noise; and
analyzing (<NUM>) the quantum noise process according to the TTMs,
wherein the dynamical maps comprise dynamical maps of the quantum noise process at K time points, K being a positive integer,
wherein the extracting (<NUM>) the TTMs of the quantum noise process from the dynamical maps comprises calculating the TTMs of the quantum noise process at the K time points according to the dynamical maps of the quantum noise process at the K time points,
characterized in that analyzing (<NUM>) the quantum noise process according to the TTMs comprises:
determining that the quantum noise process is a Markov process in a case that each of moduli of TTMs of the quantum noise process at first time points is less than a preset threshold, the first time points being time points other than the foremost time point of the K time points; and
determining that the quantum noise process is a non-Markov process in a case that a modulus of a TTM of the quantum noise process at a second time point is greater than the preset threshold, the second time point being at least one time point other than the foremost time point of the K time points, and
wherein the method further comprises:
determining a respective noise suppression solution according to the determination of the quantum noise process being a Markov process or a non-Markov process.