Method and system for measuring critical index of quantum phase change, medium and program product

Abstract

The invention relates to a quantum phase change critical index measuring method and system, a medium and a program product, and relates to the field of quantum calculation and quantum simulation. The method comprises the following steps: for each candidate value of a critical index, determining a plurality of value combinations of a change speed and a system size of a system parameter of a quantum system, so that the candidate value, the change speed and the system size meet a first condition; for each value combination of the change speed and the system size, linearly changing system parameters by the change speed to enable the quantum system to generate quantum phase change; measuring a first correlation function of the quantum system; performing scale transformation meeting a second condition on the first correlation function to obtain a second correlation function; for each candidate value, comparing differences between the second correlation functions; and selecting a candidate value that minimizes the difference as a measurement of the critical index. The method can overcome the problems of short coherence time and limited system size of a quantum system, and improves the measurement accuracy.

Description

Technical Field

[0001] The present disclosure relates to the fields of quantum computing and quantum simulation, and in particular to a method and system for measuring critical exponents in a phase transition process of a quantum system. Background Art

[0002] Quantum phase transition ( Quantum Phase Transition, QPT ) is a phase change caused by changing certain physical parameters under conditions of absolute temperature or near absolute temperature. Unlike classical thermal phase transitions, quantum phase transitions are mainly driven by quantum fluctuations. In quantum phase transitions, critical exponents are used to characterize the scaling behavior of quantum systems near critical points ( Scaling behavior ), reflecting the universal principle in quantum mechanics, that is, phase transitions under different microscopic mechanisms can have similar critical behaviors. Specifically, near the critical point of phase transition, the scaling behavior of the order parameter in the quantum system can be expressed by the critical exponent ( Critical exponent ). Measuring critical exponents by experimental means is of great significance for studying the nature of quantum phase transitions and the universality of the system, and can also provide guidance for practical applications such as quantum material design and quantum phase transition regulation. For example, some critical exponents describe how quickly the energy gap of a substance changes as the magnetic field or interaction intensity approaches the critical point. The success rate of the quantum annealing algorithm is very dependent on the size of the energy gap at the phase transition point. In this case, the measured critical exponent can be used to determine the time complexity of the algorithm.

[0003] However, the current measurement of the critical exponent of quantum phase transition faces the difficulties of short coherence time of quantum systems and limited system size, which leads to certain errors in the measurement results and low accuracy. Summary of the invention

[0004] The purpose of the present invention is to provide a method and system for measuring the critical index of quantum phase transition, which can overcome the problems of short coherence time and limited system size of quantum system and improve measurement accuracy.

[0005] According to one aspect of the present disclosure, the present disclosure provides a method for measuring a critical index of a quantum phase transition of a quantum system, comprising: for a critical index m Each candidate value of with me , determines the speed at which the system parameters of a quantum system change s and the system size of the quantum system L Multiple value combinations of with me , change speed s and system size L Satisfy the first condition; for changing speed s and system size L Each value combination of is used to measure the quantum phase change, including:s Linearly change the corresponding system size in the value combination L The system parameters of the quantum system g , so that the quantum system crosses the phase transition point from the disordered phase to the ordered phase; in the ordered phase, the local order parameters at two positions in the quantum system are measured with respect to the spatial distance between the two positions r The first correlation function G ; and for the first correlation function G Perform a scale transformation that satisfies the second condition and obtain the second correlation function G ' , wherein the first condition and the second condition are based on a first correlation function G The modified scaling law under finite system size is obtained; for each candidate value with me , compared to the change speed s and system size L The second correlation function under the multiple value combinations of G' and selecting the candidate value that minimizes the difference with me As the critical index m The measurement results.

[0006] According to another aspect of the present disclosure, a system for measuring a critical index of a quantum phase transition of a quantum system is provided, comprising: a processor; and a control device coupled to the processor, wherein the processor is configured to: for the critical index m Each candidate value of with me , determines the speed at which the system parameters of a quantum system change s and the system size of the quantum system L Multiple value combinations of with me , change speed s and system size L Satisfy the first condition; the control device is configured to: for changing the speed s and system size L Each value combination of is used to measure the quantum phase change, including: s Linearly change the corresponding system size in the value combination L The system parameters of the quantum system g , so that the quantum system enters the ordered phase from the disordered phase across the phase transition point; and in the ordered phase, measuring the local order parameters at two positions in the quantum system with respect to the spatial distance between the two positions. r The first correlation function G The processor is further configured to: for changing the speed s and system size L For each value combination ofG Perform a scale transformation that satisfies the second condition and obtain the second correlation function G' , wherein the first condition and the second condition are obtained according to the modified scaling law under the finite system size; for each candidate value with me , compared to the change speed s and system size L The second correlation function G under the multiple value combinations of ' and selecting a candidate value such that the difference satisfies a certain condition. with me As the critical index m The measurement results.

[0007] According to another aspect of the present disclosure, a computer-readable storage medium is provided, storing computer program instructions, which, when executed by one or more processors, cause the one or more processors to perform the aforementioned method.

[0008] According to another aspect of the present disclosure, a computer program product is provided, comprising computer executable instructions, which, when executed by one or more processors, cause the one or more processors to perform the aforementioned method.

[0009] Other features and advantages of the present invention will become more apparent from the following detailed description of exemplary embodiments of the present invention with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The accompanying drawings, which constitute a part of the specification, illustrate embodiments of the present disclosure and, together with the description, serve to explain the principles of the present disclosure.

[0011] The present disclosure may be more clearly understood from the following detailed description with reference to the accompanying drawings, in which: Figure 1 A method for measuring a critical exponent of a quantum phase transition of a quantum system according to some embodiments of the present disclosure is shown; Figure 2 A schematic diagram showing a one-dimensional blocking chain composed of Rydberg atoms according to some embodiments of the present disclosure; Figure 3 A more detailed flow chart showing quantum phase change measurement according to some embodiments of the present disclosure; Figure 4 The relationship between the ground state correlation length and the control parameters of a quantum system in some examples is shown; Figure 5 A schematic diagram of a second correlation function under different combinations of values ​​of change speed and system size in some examples is shown; Figure 6A schematic diagram showing the relationship between the difference between the second correlation functions and the candidate values ​​of the critical index in some examples; Figure 7 An exemplary system is shown that can be used to implement embodiments according to the present disclosure. DETAILED DESCRIPTION

[0012] Various exemplary embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. It should be noted that unless otherwise specifically stated, the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present disclosure.

[0013] The following description of at least one exemplary embodiment is in fact merely illustrative and is in no way intended to limit the present disclosure and its application or use. That is, the structures and methods herein are shown in an exemplary manner to illustrate different embodiments of the structures and methods in the present disclosure. However, those skilled in the art will appreciate that they merely illustrate exemplary ways of the present disclosure that can be implemented, rather than exhaustive ways. In addition, the drawings need not be drawn to scale, and some features may be enlarged to illustrate the details of specific components.

[0014] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0015] On current artificial quantum platforms, the measurement of critical exponents of quantum phase transitions faces the difficulty of limited coherence time of quantum systems. The quantum Kibble-Zurek effect is used to measure critical exponents of quantum phase transitions, and the difficulty of short coherence time is solved through rapid dynamic evolution. The quantum Kibble-Zurek effect requires that the system parameters of the quantum system linearly cross the quantum phase transition point at a fixed change rate.

[0016] Near the phase transition point, the physical process satisfies various scaling laws, whose powers can be given by the dimensions of the physical quantity. r The dimension is 1, and the time scale t The dimension of z , and parameters g The dimension of -1 / u . Due to the speed of change of system parameters s is a system parameter g Divide by time t , whose dimension is -1 / y-z Its dimension is usually defined as - 1 / m ,get Scaling law refers to the scaling of physical quantities. , The behavior remains unchanged, where b is an arbitrary scaling factor, b The exponent of is the dimension of the corresponding physical quantity. In order to measure the critical exponent m , the two-point correlation function of a quantum system can be measured G , the two-point correlation function G It remains unchanged under scaling transformation. The two-point correlation function G is the joint correlation average function of the local order parameters measured at two locations in the quantum system. G is the spatial distance between two locations r and change speed s So we can get the function: Equation (1).

[0017] According to this scaling law, the critical exponent is measured m The method comprises the following steps: Step S01: Determine critical index m For each candidate value of s Different values ​​of ; Step S02: For changing speed s For each value of , quantum phase change measurements are performed, including: Sub-step (1): To change the speed s Linearly changing the system parameters of a quantum system g , so that the quantum system crosses the phase transition point from the disordered phase to the ordered phase; Sub-step (2): Measure the local order parameter at two locations in the quantum system in the ordered phase with respect to the spatial distance between the two locations r The two-point correlation function G(r) ; Sub-step (3): Correlation function between two points G(r) After scaling, we get G(s μ r) ; Step S03: For critical index m For each candidate value, calculate the change speed s Under different values ​​of G(s μ r) The difference between Step S04: Select a candidate value that satisfies certain conditions as the critical index m The measurement results.

[0018] However, the scaling law of the quantum Kibble-Zurek effect, Equation (1), is proposed when the system size is infinite. In actual measurements, the size of the quantum system is finite. L In finite time, the relationship in equation (1) above will no longer be accurate and can be used to measure m This will introduce errors and result in inaccurate critical index measurements.

[0019] Some embodiments of the present disclosure are based on the following new understanding: for a finite size system, the system size L It should also be a two-point correlation function G The independent variable needs to satisfy In order to ensure the two-point correlation function G unchanged, that is, the correlation function between the two points at this time G Satisfies the modified scaling law for finite system size: Equation (2).

[0020] Therefore, changing the speed s When the system size should be changed accordingly L , in order to obtain the correct scaling law. According to the above equation (2), the embodiment of the present disclosure proposes that for the critical index m For each possible candidate value of L and s ,but s μ L Fixed as a constant, measure the correlation function of two points at the rescaled distance G(s μ r) The difference between the two makes the candidate value that satisfies certain conditions as the critical index m The measurement results are more accurate at this time.

[0021] It can be seen that the quantum phase transition critical index measurement method disclosed in the present invention also adopts a dynamic measurement method based on the quantum Kibble-Zurek effect, but takes into account the influence of the finite system size on the scale invariance. Under the finite system size, the traditional scaling law needs to be corrected to obtain the scaling law under the finite system size. Specifically, when the rate of change of the system parameters changes, the system size also needs to change accordingly to obtain the correct scaling law. Designing the measurement process based on the corrected scaling law can reduce the error of the measured critical index.

[0022] Combine the following Figure 1 A method for measuring a critical exponent of a quantum phase transition of a quantum system according to some embodiments of the present disclosure is specifically introduced.

[0023] The measurement method 100 starts at step 110. In step 110, for a critical index m Each candidate value of with me , determines the speed at which the system parameters of a quantum system change s and the system size of the quantum system L Multiple value combinations of with me , change speed s and system size L The first condition is met.

[0024] In the present disclosure, a quantum system refers to a multi-body system that operates based on the principles of quantum mechanics, and its behavior is characterized by quantum phenomena such as quantum states, quantum superposition, quantum entanglement, and quantum decoherence. In a quantum system, the states of microscopic particles (such as electrons, photons, atoms, etc.) can be described by quantum states, and these states can be manipulated by quantum operations. Quantum systems can be implemented according to different underlying physical mechanisms. In some embodiments, a quantum system may include any one of a superconducting quantum system, an ion trap quantum system, a photon quantum system, a neutral atom quantum system, or a semiconductor quantum system. The measurement method disclosed in the present disclosure can be applied to quantum platforms of various technical routes. The quantum system disclosed in the present disclosure is a quantum system that can be applied to fields such as quantum computing, quantum communication, quantum sensing, and quantum simulation.

[0025] In the present disclosure, quantum phase transition refers to a phase transition phenomenon occurring at absolute zero (or close to absolute zero). Unlike classical phase transitions that achieve phase transitions by changing temperature, quantum phase transitions are achieved by changing system parameters at absolute temperature. Quantum phase transitions describe the sudden change in the ground state of a multi-body system due to quantum fluctuations. In some embodiments, according to the principle of universality, quantum phase transitions may include various types of second-order quantum phase transitions. In some embodiments, the critical properties of quantum phase transitions can be studied using various lattice statistical models. Common lattice statistical models include, but are not limited to, the Ising model, the XY model, or the Bose-Hubbard model.

[0026] In the present disclosure, the critical exponent of a quantum phase transition reflects the power-law relationship of the change in order parameter with the rate of change of system parameters near the phase transition point. Near the critical point of the quantum phase transition, quantum fluctuations drive the correlation length of the quantum system to diverge. Therefore, for different length scales, the quantum system satisfies a unified power-law relationship, and its critical exponent remains unchanged. The quantum phase transition is characterized by the change in the order parameter. The order parameter of the same quantum phase transition process is the same. In some cases, the same quantum phase transition process corresponds to a unique system parameter. That is, the quantum phase transition process can only be achieved by changing the unique system parameter. In other cases, the same quantum phase transition process corresponds to different system parameters. That is, the same quantum phase transition process can be achieved by changing different system parameters. Different system parameters are changed, and different critical exponents may exist. The critical exponent to be measured in the present disclosure is a critical exponent related to the rate of change of the system parameters, that is, the dynamic critical exponent of the system parameters (the critical exponent described above). m ), rather than the static critical index of the system parameter itself (the critical index described above u ).

[0027] Different quantum systems or quantum phase transition processes can have different system parameters and order parameters. For example, for a quantum system that satisfies the two-dimensional Bose-Hubbard model, its quantum phase transition process can be to change the relative size of the tunneling and interaction of particles (bosons) in the lattice, so that the system undergoes a quantum phase transition from the Mott insulating phase to the superfluid phase. The system parameters can be the tunneling amplitude or interaction strength of the bosons. The order parameter is the density of the superfluid condensate.

[0028] In some embodiments, the quantum system includes a Rydberg atom array. A Rydberg atom array is a quantum system based on Rydberg atoms, in which atoms are excited to an excited state (Rydberg state) in which the principal quantum number of electrons is high (the principal quantum number n is much greater than 1, for example, 50, 60, 70, 80, 90 or other values), and are arranged in optical tweezers or optical lattices to form an array. Rydberg atoms have strong interactions and long lifetimes. When the distance between two Rydberg atoms is close enough, the excitation of one atom prevents the excitation of the other atom, a phenomenon called Rydberg blockade. In a Rydberg atom array, a highly programmable quantum bit array can be achieved by precisely controlling the position and excitation state of atoms. Depending on the spatial arrangement of the optical tweezers or optical lattices, the Rydberg atom array can be a one-dimensional, two-dimensional, or three-dimensional array.

[0029] The atoms in the Rydberg atom array may be selected from alkali metal atoms (such as rubidium atoms, cesium atoms, etc.) or alkaline earth metal atoms (such as strontium atoms and ytterbium atoms, etc.).

[0030] In some further embodiments, the quantum system is a one-dimensional blocking chain composed of Rydberg atoms. A one-dimensional blocking chain is a special array of Rydberg atoms. In a one-dimensional blocking chain, the distances between adjacent atoms can be equal or unequal. The distance between adjacent atoms is smaller than the Rydberg blocking radius, but the distance between two atoms separated by one atom is larger than the Rydberg blocking radius. Therefore, it is impossible for adjacent atoms to appear in Rydberg excited states at the same time, that is, the simultaneous excitation of two adjacent atoms is "blocked". The atoms in the chain show an alternating distribution pattern of "ground state", "Rydberg state", "ground state", "Rydberg state"..., such as Figure 2 shown.

[0031] In the present disclosure, a system parameter is any physical parameter that can be changed to make a quantum system cross the critical point of quantum phase transition. In some embodiments, when the quantum system is a Rydberg atom array, the system parameter may include the frequency of the excitation light applied to the quantum system. The Rydberg atom array can be regarded as a two-level multi-body system. Excitation light is applied to the system, and the photons interact with the atoms to drive the energy level transition of each atom in the system. Set a suitable laser intensity, and adjust the excitation light frequency so that the frequency detuning amount between the excitation light frequency and the energy level difference (corresponding frequency) between the two energy levels of the two-level system changes. When the detuning amount changes from a negative value (red detuning) to a positive value (blue detuning), the multi-body system crosses the phase transition point from a disordered phase (all atoms are in the ground state) to an ordered phase (for example, a state where "ground state" and "Rydberg state" are staggered in a one-dimensional blocking chain).

[0032] In addition to directly selecting the frequency of the excitation light, in some embodiments, the overall system parameters may also include other physical quantities related to the frequency, such as the detuning amount of the frequency of the excitation light.

[0033] The speed at which system parameters change s The variable that represents the system parameter per unit time. For example, if the system parameter is frequency or frequency detuning, then the change speed s It is the change of frequency or frequency detuning per unit time.

[0034] System Dimensions L Represents the linear length of a quantum system. For example, in a one-dimensional atomic array system, the system size L It can be the macroscopic length of the atomic array. However, since the number of atoms is proportional to the length, in some cases, the number of atoms can also be used N As system size L For a two-dimensional or three-dimensional atomic array system, the system size LIt can be any physical quantity that represents the linear length, such as the length, width, height, or diagonal length of the atomic array. Similarly, the number of atoms in the corresponding dimension can also be used. N In some cases, the number of qubits in a quantum system can also be used to characterize the size of the system. L For example, in a superconducting quantum system, the number of quantum bits can be used to characterize the size of the system, where each quantum bit corresponds to a Josephson junction.

[0035] The first condition is obtained from the modified scaling law for finite system size. The modified scaling law for finite system size is described by equation (2) above. According to this equation, to satisfy the scale invariance, the speed s and system size L Need to meet: s μ L=C , Equation (3) in C is a constant.

[0036] For critical index m Each candidate value of with me , C A constant means the speed of change s and system size L The values ​​of are related to each other. s When the system size changes L It also needs to change accordingly, which forms the speed of change s and system size L For each value combination, change the speed s has a certain value, and the system size L has a corresponding value. For the critical index of the same quantum system m Different candidate values ​​for with me , C is also the same constant. In some embodiments, C It can be any number between 1 and 10. C It reflects the distance of the quantum system from the phase transition point. C The smaller the value, the faster the change s The smaller the value of is, the closer it is to the adiabatic state, and the closer the quantum system is to the phase transition point. For different quantum systems or quantum phase transition processes, the constant C The values ​​of can be the same or different. Different quantum systems here refer to quantum systems based on different physical technology routes, such as the superconducting quantum system, ion trap quantum system, photon quantum system, semiconductor quantum system, neutral atom quantum system, etc. mentioned above.

[0037] In step 120, for changing the speed s and system size L The quantum phase change measurement is performed for each value combination of . The quantum phase change measurement adopts the dynamic measurement method based on the quantum Kibble-Zurek effect introduced above. Specifically, it includes: In sub-step 121, the speed is changed s Linear change has the corresponding system size in the value combination L The system parameters of the quantum system g , which causes the quantum system to cross the phase transition point from the disordered phase to the ordered phase.

[0038] Changing the system parameters linearly at a changing speed means that the system parameters change uniformly over time. The value interval formed by the initial value and the end value of the system parameters covers the critical point of the phase transition of the quantum system.

[0039] When changing speed s When the system size changes L also changes, for example, it may change from L 1 Changes to L 2 At this time, the system size of the quantum system needs to be reduced from L 1 Change to L 2 In some embodiments, sub-step 121 includes changing the speed s and system size L The system size in each value combination of L Prepare quantum systems. For example, the new system size can be changed L 2 Prepare a quantum system. Take the quantum system as an example, Rydberg atom array. L 2 < L 1 , that is, the system size is reduced, then the corresponding number of atoms can be discarded from the atomic array. For example, the optical tweezers or optical lattice where these atoms are located can be turned off so that the atoms are no longer trapped in the optical potential well. L 2 > L 1 , that is, the size of the system increases, then the corresponding number of atoms can be added according to the original atomic spacing of the atomic array, so that the size of the system is enlarged in a corresponding proportion. For example, the corresponding optical tweezers or optical lattices can be added in proportion to the original arrangement of the optical tweezers or optical lattices, so that the corresponding number of supplementary atoms can be captured in them.

[0040] The disordered phase of a quantum system refers to a state in which the arrangement of microscopic particles or the state of the quantum system is relatively chaotic and there is no long-range regularity. In the disordered phase, the symmetry of the system is not spontaneously broken. In the case where the quantum system is a Rydberg atomic array, the disordered phase of the multi-body system can be that all atoms in the atomic array are in the ground state.

[0041] The ordered phase of a quantum system is a state in which the arrangement or state of microscopic particles in the quantum system shows a certain regularity on a macroscopic scale. In the ordered phase, the symmetry of the system is spontaneously broken.

[0042] The order parameter is used to describe the degree of order of the system. In the ordered phase, the order parameter is not zero, and in the disordered phase, the order parameter is zero. Therefore, the order parameter can be detected to determine whether the quantum system undergoes a phase transition into an ordered phase. In some quantum systems, such as the Rydberg atom array system, it is possible to select whether the atoms at a specific position in the system (such as the array lattice formed by optical tweezers or optical lattices) are in the ground state or in the Rydberg state as the local order parameter. For example, fluorescence detection technology can be used to detect whether the atoms at a specific position are in the ground state or the excited state, thereby determining the local order parameter. Atoms in an excited state will return to a lower energy level or the ground state within a certain period of time, and at the same time release photons and emit fluorescence. The state of the atom is determined by detecting the intensity, wavelength or distribution of the photons released by the atom, thereby determining the local order parameter. After determining the local order parameter, the local order parameters at each position in the system are combined to serve as the overall order parameter of the system. For example, first detect whether the atoms at each position are in the ground state or in the excited state. Then, for a multi-body system, if the atoms at each position are in the ground state, the corresponding order parameter is zero. However, if there are atoms at specific positions that are not in the ground state, the corresponding overall order parameter is non-zero. In other quantum systems, the local order parameter measured at any position is directly used as the overall order parameter. For example, for a quantum system that conforms to the Bose-Hubbard model, the density of the superfluid condensate at any position can be directly measured as the order parameter or local order parameter.

[0043] In sub-step 122, the local order parameter at two locations in the quantum system is measured in the ordered phase with respect to the spatial distance between the two locations. r The first correlation function G .

[0044] First correlation function G It is the joint statistical average function of the local order parameter at the first position of the two positions taking the first specific value and the local order parameter at the second position taking the second specific value. The first correlation function G Spatial distance from two locations r is related, so it can also be expressed as G(r) In a Rydberg atomic array, if the distance between atoms is constant d, then the spatial distance r The value of can be 0 , d , 2d , 3d wait.

[0045] Each detection of the local order parameter is equivalent to a destructive measurement of the collapse of the wave function, that is, the superposition state of the quantum system will collapse to a certain eigenstate corresponding to the measurement result. Each detection of the atom at a certain position is recorded as, for example, "-1" in the ground state, and as, for example, "+1" in the excited state. By performing multiple detections, the calculation of any two positions (for example i Location and j position)-1 and 1 appear in a certain combination of correlation average, that is, <Z i Z j > ,in Z i is i A random variable with a value of -1 or +1 at a point, Z j is j A random variable with a value of -1 or +1 at a point. The angle brackets <*> represent the statistical mean.

[0046] Therefore, sub-step 122 may include: step 122a, measuring the values ​​of the local order parameters at two positions in the quantum system in the ordered phase for multiple times; and step 122b, calculating the joint correlation average for one of the combinations of the measured values ​​of the local order parameters to obtain a first correlation function. Since each measurement of the local order parameter will cause the state of the quantum system to collapse, in order to perform multiple measurements, it is necessary to maintain the current change speed after each measurement. s and system size L If the phase change is unchanged, step 121 is executed. That is, the first correlation function can be calculated only after multiple cycles of "phase change-measurement-...-phase change-measurement".

[0047] Next, in sub-step 123, the first correlation function G Perform a scale transformation that satisfies the second condition and obtain the second correlation function G' .

[0048] The second condition is obtained according to the modified scaling law under finite system size. In some embodiments, the second condition includes determining G(r) about s μ' r According to equation (2) above, for the critical index m Each candidate value of with me , when changing speeds and system size L When the first correlation function is obtained each time G(r) Perform a scale transformation on the independent variable while maintaining G(r) and r When the mapping relationship between them remains unchanged, the independent variable r Transformed to s μ' r get G(r) about s μ' r The change law of is expressed as the second correlation function G'(s μ' r) .

[0049] According to the modified scaling law, if the candidate value with me is the true critical index, then the different change speeds s and system size L The combination of G'(s μ' r) Theoretically, they should be equal. Therefore, the critical index m It should be to make different change speeds s and system size L under the combination of G'(s μ' r) The candidate value with the smallest difference between with me .

[0050] Figure 3 A more detailed flow chart of step 120 is shown, which takes into account the process of re-preparing the quantum system and realizing the phase transition due to state collapse caused by measurement. Steps 301 to 303 are repeated for a predetermined number of times. In each repetition (i.e., one cycle), in step 301, the system size is first re-prepared according to the system size. L The current value of prepares the quantum system, and then in step 302 changes the speed s The current value of changes the control parameter g , so that the quantum system undergoes a quantum phase transition, and then the value of the local order parameter in the ordered phase is measured in step 303. In response to determining that the predetermined number of repetitions has been made, the loop is exited and step 304 is entered. Since multiple values ​​of local order parameters have been obtained at this time, the first correlation function can be calculated based on the local order parameter, and then the second correlation function is obtained in step 305 based on the first correlation function. Steps 302, 303, 304 and 305 correspond to steps 121, 122a, 122b and 123 introduced above, respectively, and the relevant contents are not repeated here.

[0051] Back to Figure 1 In step 130, for each candidate value with me , compared to the change speed s and system size L The second correlation function under multiple value combinations of G' The difference between.

[0052] For example, for each candidate value with me , change speed s and system size L Multiple value combinations of can be [ s 1 , L 1 ]、[ s 2 , L 2 ]……[ s m , L m ],in m is an integer greater than 1, then for each combination [ s i , L i ], 1≤ i ≤ m , the second correlation function can be measured G i ' , and compare multiple G i ' The difference between.

[0053] There are many ways to compare the differences between multiple functions. As a non-limiting example, when the function is a continuous function, each function is drawn into a continuous curve, and the ordinate differences of multiple curves under the same horizontal coordinate are compared. Statistical analysis is performed on the differences in multiple ordinates to obtain differences. For example, one way is to add the ordinate differences corresponding to all horizontal coordinates. Other ways may include averaging or finding variances, etc. As another non-limiting example, when the function is a discrete value (data point), the discrete data points can be converted into a continuous function by curve fitting, and then the above method is used. As another non-limiting example, when the function is a discrete value (data point), the horizontal coordinates of the data points of different functions can be made consistent by interpolating the data points of multiple functions, so as to facilitate the comparison of the vertical coordinate differences. Specifically, the horizontal coordinate of a data point of a function is obtained by interpolation, and the data point corresponding to the horizontal coordinate of another function is obtained. Various other methods known in the art can also be used to compare differences, which will not be repeated here.

[0054] In step 140, the candidate value that minimizes the difference is selected. with me As a critical index m The measurement results are as follows. Thus, the measurement of the critical index of the quantum phase transition of the quantum system has been achieved.

[0055] The advantage of the embodiments disclosed herein is that, in the process of dynamically measuring the critical exponent of quantum phase transition according to the quantum Kibble-Zurek effect, the influence of the finite system size on the scale invariance is taken into account. Under the finite system size, the traditional scaling law needs to be corrected to obtain the scaling law under the finite system size. Specifically, when the rate of change of the system parameters changes, the system size also needs to change accordingly to obtain the correct scaling law. Designing the measurement process based on the corrected scaling law can reduce the error of the measured critical exponent.

[0056] In addition, for the previous Kibble-Zurek measurement method (as described in steps S01-S04 above), the system parameters g The speed of change s There are great limitations, it cannot be too fast or too slow. If it is too slow, it will enter the adiabatic region (equilibrium state), and it will take a long time to wait. The coherence time of the current quantum system cannot meet it, resulting in large errors in the measurement results. The measurement method according to the embodiment of the present disclosure overcomes the finite size effect to a certain extent and is insensitive to the adiabatic region. Therefore, it can still obtain good measurement accuracy when the change speed s is low.

[0057] It should be appreciated that the above advantages need not all be realized in one or some specific embodiments, but may be partially dispersed in different embodiments according to the present disclosure. Embodiments according to the present disclosure may have one or some of the above advantages, or may alternatively or additionally have other advantages.

[0058] The measurement method according to some embodiments of the present disclosure is described below through numerical simulation.

[0059] The selected quantum system is a one-dimensional blocking chain composed of Rydberg atoms. Control parameters g is the frequency detuning of the excitation light. The quantum phase transition at this time belongs to the universal class of Ising phase transition. g Related critical index u = 1. Relativistic z =1, that is, the scales of space and time are the same. According to the derivation of the dimensions in the previous article, we can get the value of the change speed. s Related critical index .

[0060] Figure 4The relationship between the ground state correlation length and the control parameters of the quantum system in this example is shown. Figure 4-5 The number of atoms in the atomic array system N Characterizing system dimensions L If the system size of the quantum system L is infinite, the corresponding number of atoms N is also infinite, then the ground state correlation length of the multi-body system is x In the control parameters g When the value of is close to the critical value (when the frequency detuning amount is 0), it tends to diverge. L When it is a finite value, the corresponding number of atoms N is also a finite value. The ground state correlation length ξ no longer tends to diverge near the critical value, but reaches a finite maximum value, and the ground state correlation length x Relative to the control parameters g It seems that scale invariance is no longer satisfied. However, if a scale transformation is performed, Figure 4 As you can see from the small picture in the upper right corner, ξ / N Relative to g·N 1 / υ It still satisfies scale invariance, that is, ξ / N=F(g·N 1 / υ ) , where F( ) is a function that satisfies the invariance of scale transformation. This means that when N When changes occur, the corresponding g and x The proportions also change, so the curves in the figure are separated. However, if the scale is transformed, ξ / N Relative to g·N 1 / υ The same power law relationship is maintained for different system sizes, so the three curves coincide. This shows that for finite system sizes L For quantum systems, the scaling law still holds, but needs to be corrected.

[0061] The dynamic numerical simulation of the quantum system is performed according to the method 100 disclosed in the present invention. Figure 5 It shows that when the critical index m Candidate value of with me When it is taken as 0.5, at different change speed s and system size L The second correlation function obtained under the combination of values G' ,in s and L satisfy s μ' L=C , C is a constant. It can be seen that at this time the three groups G' The curves have smaller differences and higher overlap.

[0062] Figure 6 The second correlation function is shown G' The difference between the candidate values with me It can be seen that when with me When the value is 0.524, the second correlation function G' The difference between them is the smallest, that is, the second correlation function G' It can best maintain scale invariance, so the with me The value of m The measurement results.

[0063] System Parameters g The final state value in the ordered phase will also affect the scaling law. The modified scaling law of equation (2) above applies to the system parameters g When the final state value is infinite. When the final state value is finite, the modified scaling law of equation (2) needs to be further adjusted to obtain: Equation (4).

[0064] Except for s and L satisfy s μ L=C , C In addition to being a constant, it also needs to satisfy: g υ L=D , D Accordingly, some steps in method 100 need to be further restricted.

[0065] In some cases, the relativistic nature of quantum systems z is known, then by with me Another critical index can be calculated u Candidate value of u' , and according to g υ L=D Correspondingly determine the final value of the system parameter g g e .

[0066] In other cases, relativistic z is unknown. At this time, step 110 includes: for each candidate value with me and another critical index u Each other candidate value of u' , determine the speed of change s 、System size L and final value g eMultiple value combinations of with me , change speed s and system size L The first condition is met, and another candidate value u' , final state value g e and system size L The third condition is satisfied, and the third condition is obtained by further adjusting the scaling law according to the modified scaling law under finite system size.

[0067] Critical Index m With changing speed s is associated with another critical index u With system parameters g The final value of g e The modified scaling law under finite system size is further adjusted to express the scaling law as shown in the above equation (4). In some embodiments, the third condition includes g e υ' L=D , D is a constant.

[0068] For critical index u Each candidate value of u' , D A constant means the final value g e and system size L The values ​​of are related to each other. L When changing, the final value g e Also needs to change accordingly. According to the first condition, when the speed is changed s When the system size changes L It also needs to change accordingly, which forms the speed of change s 、System size L and final value g e When the candidate value with me and candidate values u' When they are specific values, for each value combination, the change speed s has a certain value, and the system size L and final value g e has a corresponding value. For the critical index of the same quantum system u Each candidate value of u' , D is also the same constant. In some embodiments, D It can be any number between 1 and 10.D It reflects the distance of the quantum system from the phase transition point. D The smaller the value, the closer the quantum system is to the phase transition point. For different quantum systems or quantum phase transition processes, the constant D The values ​​of can be the same or different. Different quantum systems here refer to quantum systems based on different physical technology routes, such as the superconducting quantum system, ion trap quantum system, photon quantum system, semiconductor quantum system, neutral atom quantum system, etc. mentioned above.

[0069] Step 120 includes: s 、System size L and final value g e The quantum phase change measurement here still includes steps 121 to 123, but it should be noted that the end point of the quantum phase change is limited. Specifically, in step 121, the control parameter is changed g After the quantum system undergoes a phase transition, the parameters in the ordered phase are controlled g The value of g e .

[0070] Step 130 includes: for each candidate value with me and each candidate value u' The combination of s 、System size L and final value g e The difference between the second correlation functions under multiple value combinations of . Each candidate value with me Can correspond to multiple candidate values u' , and for with me and u' For each combination of , a series of second correlation functions can be obtained and the differences between them can be compared.

[0071] Step 140 includes: selecting the candidate value that minimizes the difference with me and candidate values u' Candidate values ​​in the combination of with me As a critical index m The measurement results.

[0072] Figure 7 1 shows a block diagram of a system 700 according to an embodiment of the present disclosure. The system 700 can be used to perform a method for measuring a critical index of a quantum phase transition according to an embodiment of the present disclosure, such as the method 100. Figure 7 As shown, the system 700 may include a processor 701 and a control device 702 .

[0073] The control device 702 is used to perform various controls on the subsystem to be measured and to measure / monitor it. The control device 702 may include, but is not limited to, a CPU, a hardware microprocessor, a hardware processor, a multi-core processor, a single-core processor, a microcontroller, an application-specific integrated circuit (ASIC), a DSP, or other similar processing devices, and can execute any type of instructions, algorithms, or software for the operations and functions of controlling and measuring the quantum system according to the embodiments described in the present disclosure. The control device 702 may be various implementations of a digital circuit system, an analog circuit system, or a mixed signal (a combination of analog and digital) circuit system that performs functions in a computing system. The control device 702 may include, for example, an integrated circuit (IC), a portion or circuit of a separate processor core, an entire processor core, a separate processor, a programmable hardware device such as a field programmable gate array (FPGA), and / or a system including multiple processors. In order to cooperate in realizing the control and / or measurement functions of the quantum system, the control device 702 may be communicatively coupled to the quantum system through various actuators and / or sensors, so that the quantum system can ultimately be controlled or measured by the control device 702. For example, when the quantum system is a Rydberg atomic array, the control device 702 can control optical tweezers or an optical lattice to achieve the capture and / or manipulation of atoms; and / or the control device 702 can control the radiation of the excitation light beam, including intensity, frequency, duration, etc.; and / or the control device 702 can control the fluorescence detection system to take pictures of the atomic array, etc.

[0074] The processor 701 is used to receive data from the control device 702, perform data processing operations, and transmit parameters required for controlling the quantum system to the control device 702. The processor 701 can be any type of processor for performing classical computing, and can include but is not limited to one or more general-purpose processors or special-purpose processors (such as special-purpose processing chips).

[0075] The processor 701 and the control device 702 can cooperate to execute instructions to implement the various methods (including method 100) or steps and processes thereof described above according to the embodiments of the present disclosure. Specifically, the processor 701 can be configured to execute step 110, sub-step 123 in step 120, and steps 130-140; the control device 702 can be configured to execute sub-steps 121-122 in step 120. It should be recognized that the functions or operations of the processor 701 and the control device 702 can also be partially or completely combined in any one of the processor 701 or the control device 702.

[0076] The system 700 may also include or be connected to a memory 703, which may be any non-transitory storage device that can implement data storage, and may include but is not limited to a disk drive, an optical storage device, a solid-state memory, a floppy disk, a flexible disk, a hard disk, a magnetic tape or any other magnetic medium, a compressed disk or any other optical medium, a cache memory and / or any other storage chip or module, and / or any other medium from which a computer can read data, instructions and / or codes. The memory 703 may store various dynamic and static instructions and / or data for the processor 701 and / or the control device 702 to read and / or execute.

[0077] The processor 701 and the control device 702 may be physically separated from each other but coupled to each other by wired or wireless communication, or they may exist as different modules or components of the same physical device. In the latter case, the processor 701 and the control device 702 may each be connected or communicated with the bus 704 via one or more interfaces. The bus 704 may include, but is not limited to, an Industry Standard Architecture (ISA) bus, a Micro Channel Architecture (MCA) bus, an Enhanced ISA (EISA) bus, a Video Electronics Standards Association (VESA) local bus, and a PCI bus or a PCI-e bus, etc.

[0078] The system 700 may also include I / O devices and / or network interfaces connected or in communication with the bus 704. Examples of I / O devices may include, but are not limited to, keyboards, touch pads, mice, joysticks or other pointing devices, microphones, speakers, displays, or printers, etc. A network interface may be any type of device or system capable of enabling communication with an external device and / or a network, and may include, but are not limited to, a modem, a network card, an infrared communication device, a wireless communication device, and / or a chipset (such as a Bluetooth™ device, a WiFi device, a WiMax device, a cellular communication facility, etc.). The I / O devices and / or network interfaces may also be communicatively coupled to the processor 701 and / or the control device 702 and / or the memory 703 via the bus.

[0079] The present disclosure may be implemented as any combination of an apparatus, a system, an integrated circuit, and a computer program on a non-transitory computer-readable medium or a computer program product. One or more processors or control devices may be implemented as an integrated circuit (IC), an application specific integrated circuit (ASIC), or a large-scale integrated circuit (LSI), a system LSI, a super LSI, or a super LSI component that performs some or all of the functions described in the present disclosure.

[0080] The present disclosure includes the use of software, applications, computer programs, or algorithms. The software, applications, computer programs, or algorithms may be stored on a non-transitory computer-readable medium or computer program product to enable a computer such as one or more processors to perform the above steps and the steps described in the accompanying drawings. For example, one or more memories store the software or algorithm in executable instructions, and one or more processors may associate a set of instructions to execute the software or algorithm to provide various functions according to the embodiments described in the present disclosure.

[0081] Software and computer programs (which may also be referred to as programs, software applications, applications, components or code) include machine instructions for a programmable processor and may be implemented in a high-level procedural language, an object-oriented programming language, a functional programming language, a logic programming language, or an assembly language or machine language. The term "computer-readable medium" refers to any computer program product, apparatus or device for providing machine instructions or data to a programmable data processor, such as magnetic disks, optical disks, solid-state storage devices, memories and programmable logic devices (PLDs), including computer-readable media that receive machine instructions as computer-readable signals.

[0082] For example, a computer readable medium may include a dynamic random access memory (DRAM), a random access memory (RAM), a read-only memory (ROM), an electrically erasable read-only memory (EEPROM), a compact disk read-only memory (CD-ROM) or other optical disk storage device, a magnetic disk storage device or other magnetic storage device, or any other medium that can be used to carry or store the desired computer readable program code in the form of instructions or data structures and can be accessed by a general or special-purpose computer or a general or special-purpose processor. As used herein, a disk or disc includes a compact disc (CD), a laser disc, an optical disc, a digital versatile disc (DVD), a floppy disk, and a Blu-ray disc, wherein a disk typically copies data magnetically, while a disc copies data optically by a laser. Combinations of the above are also included within the scope of computer readable media.

[0083] The subject matter of the present disclosure is provided as an example of devices, systems, methods and programs for performing the features described in the present disclosure. However, in addition to the above-mentioned features, other features or variations may also be expected. It is expected that the implementation of the components and functions of the present disclosure may be completed with any emerging technology that may replace any of the above-mentioned implementation technologies.

[0084] In addition, the above description provides examples, but does not limit the scope, applicability or configuration set forth in each embodiment of the present disclosure. Without departing from the spirit and scope of the present disclosure, the function and arrangement of the elements discussed can be changed. Various embodiments can appropriately omit, replace or add various processes or parts. For example, the features described in certain embodiments can be combined in other embodiments.

[0085] Similarly, while operations are depicted in a particular order in the drawings, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed to achieve desired results. In certain circumstances, multitasking and parallel processing can be advantageous.

Claims

1. A method for measuring the critical exponent of a quantum phase transition of a quantum system, characterized in that The method comprises: For critical index μ Each candidate value of μ' , determines the speed at which the system parameters of a quantum system change s and the system size of the quantum system L Multiple value combinations of μ' , change speed s and system size L The first condition is met; For changing speed s and system size L Each value combination of is used to measure the quantum phase change, including: At the speed of change s Linearly change the corresponding system size in the value combination L The system parameters of the quantum system g , which makes the quantum system go from the disordered phase to the ordered phase across the phase transition point; Measuring the local order parameters at two locations in the quantum system in the ordered phase with respect to the spatial distance between the two locations r The first correlation function G ;as well as The first correlation function G Perform a scale transformation that satisfies the second condition and obtain the second correlation function G' , wherein the first condition and the second condition are based on a first correlation function G The modified scaling law for finite system size is obtained; For each candidate value μ' , compared to the change speed s and system size L The second correlation function under the multiple value combinations of G' the differences between Select the candidate value that minimizes the difference μ' As the critical index μ The measurement results.

2. The method according to claim 1, characterized in that The first condition is s μ' L=C , C is a constant, for the first correlation function G Performing a scale transformation that satisfies the second condition includes: determining a first correlation function G Relative to s μ' r The law of change.

3. The method according to claim 1, characterized in that System Parameters g The final state value in the ordered phase is an infinite value.

4. The method according to claim 1, characterized in that The final state value of the system parameter g in the ordered phase is a finite value g e , Among them, for the critical index μ Each candidate value of μ' , determines the speed at which the system parameters of a quantum system change s and the system size of the quantum system L Multiple value combinations of μ' , change speed s and system size L The first condition is met, including: For each candidate value μ' and another critical index υ Each other candidate value of υ' , determine the speed of change s 、System size L and final value g e Multiple value combinations of μ' , change speed s and system size L The first condition is met, and another candidate value υ' , final state value g e and system size L The third condition is satisfied, wherein the third condition is obtained according to a scaling law adjusted on the basis of a modified scaling law under a finite system size, Among them, for the change speed s and system size L Each value combination of quantum phase change measurement includes: For the change speed s, system size L and final value g e Each value combination of is used to measure the quantum phase change, Among them, for each candidate value μ' , compared to the change speed s and system size L The second correlation function under the multiple value combinations of G' The differences between For each candidate value μ' and each candidate value υ' , compared to the change speed s 、System size L and final value g e The second correlation function under the multiple value combinations of G' The difference between Among them, select the candidate value that minimizes the difference μ' As the critical index μ The measurement results include: Select the candidate value that minimizes the difference μ' and candidate values υ' Candidate values ​​in the combination of μ' As the critical index μ The measurement results.

5. The method according to claim 4, characterized in that The third condition is g e υ' L=D , D is a constant.

6. The method according to claim 1, characterized in that The quantum system is any one of a superconducting quantum system, an ion trap quantum system, a photon quantum system, a neutral atom quantum system or a semiconductor quantum system.

7. The method according to claim 1, characterized in that The quantum system includes a Rydberg atom array, the system parameters include the frequency of the excitation light applied to the quantum system, the local order parameter includes a representation of whether the atoms at each lattice point in the Rydberg atom array are in a ground state or a Rydberg state, and in the disordered phase all the atoms in the quantum system are in the ground state.

8. The method according to claim 1, characterized in that Measuring the local order parameters at two locations in the quantum system in the ordered phase with respect to the spatial distance between the two locations r The first correlation function G include: measuring the values ​​of the local order parameters at the two positions in the quantum system in the ordered phase multiple times; and Calculate the joint correlation average for one of the combinations of the values ​​of the measured local order parameter to obtain the first correlation function G .

9. The method according to claim 1, characterized in that: Compare the change speed s and system size L The second correlation function under the multiple value combinations of G' The differences include: The second correlation function G' Plotted as a continuous curve; and The vertical coordinate differences of the continuous curves corresponding to the multiple value combinations under the same horizontal coordinate are compared.

10. The method according to claim 1, characterized in that For changing speed s and system size L Each value combination of is used to measure the quantum phase change, and also includes: According to the system size in each value combination L The quantum system is prepared.

11. A system for measuring a critical exponent of a quantum phase transition of a quantum system, characterized in that The system comprises: Processor; and a control device coupled to the processor, Wherein, the processor is configured to: For critical index μ Each candidate value of μ' , determines the speed at which the system parameters of a quantum system change s and the system size of the quantum system L Multiple value combinations of μ' , change speed s and system size L The first condition is met; The control device is configured to: For changing speed s and system size L Each value combination of is used to measure the quantum phase change, including: At the speed of change s Linearly change the corresponding system size in the value combination L The system parameters of the quantum system g , so that the quantum system crosses the phase transition point from the disordered phase to the ordered phase; and Measuring the local order parameters at two locations in the quantum system in the ordered phase with respect to the spatial distance between the two locations r The first correlation function G , The processor is further configured to: For changing speed s and system size L For each value combination of G Perform a scale transformation that satisfies the second condition and obtain the second correlation function G' , wherein the first condition and the second condition are obtained according to a modified scaling law under a finite system size; For each candidate value μ' , compared to the change speed s and system size L The second correlation function under the multiple value combinations of G' the differences between Select the candidate value that minimizes the difference μ' As the critical index μ The measurement results.

12. The system according to claim 11, characterized in that The first condition is s μ' L=C , C is a constant, for the first correlation function G Performing a scale transformation that satisfies the second condition includes: determining a first correlation function G Relative to s μ' r The law of change.

13. The system according to claim 11, characterized in that The quantum system is any one of a superconducting quantum system, an ion trap quantum system, a photon quantum system, a neutral atom quantum system or a semiconductor quantum system.

14. The system according to claim 11, characterized in that The quantum system includes a Rydberg atom array, the system parameters include the frequency of the excitation light applied to the quantum system, the local order parameter includes a representation of whether the atoms at each lattice point in the Rydberg atom array are in a ground state or a Rydberg state, and in the disordered phase all the atoms in the quantum system are in the ground state.

15. A computer-readable storage medium storing computer program instructions, characterized in that: The computer program instructions, when executed by one or more processors, cause the one or more processors to perform the method according to any one of claims 1-10.

16. A computer program product comprising computer executable instructions, characterized in that: The computer executable instructions, when executed by one or more processors, cause the one or more processors to perform the method according to any one of claims 1-10.

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