A method and apparatus for locating a quantum phase transition point
By measuring evolution energy error using quantum circuits, the problem of inaccurate identification of quantum phase transition points in machine learning was solved, enabling accurate location of quantum phase transition points with limited quantum resources.
Patent Information
- Application Number
- CN202310843433.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-10
- Publication Date
- 2026-01-06
- Estimated Expiration
- 2043-07-10
AI Technical Summary
In existing technologies, when using machine learning to locate quantum phase transition points, it is difficult to obtain accurate ground state data, resulting in inaccurate identification of quantum phase transition points.
By designing quantum circuits and measuring the evolution energy error under two different evolution directions, the Hamiltonian parameter h that makes both evolution directions relatively fair can be found, thus locating the quantum phase transition point.
The quantum critical point can be accurately located without the need for precise ground-state data, reducing the use of quantum resources.
Smart Images
Figure CN116882507B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of quantum computing technology, and in particular to a method and apparatus for locating quantum phase transition points. Background Technology
[0002] Understanding quantum phase transitions in matter is a key topic in quantum many-body physics. The quantum phase transition points that distinguish different phases of matter become particularly interesting due to the novel physical properties of quantum phase transitions, such as the divergence of correlation lengths and violations of the area law of entanglement entropy. Describing quantum phase transition points requires solving for the ground state of the quantum system, which is difficult for classical computers due to the fermion sign problem. On the other hand, simulating quantum phase transition points using quantum computers can be efficient; however, existing methods for simulating quantum phase transition points using quantum computers require describing the quantum phase transition points with quantum circuitry, which is relatively complex and typically requires more quantum resources, even when using variational quantum algorithms designed specifically for implementation in recent quantum devices.
[0003] Existing technologies also utilize machine learning to locate quantum critical points. In this case, the location of quantum phase transition points is closely related to classification within the machine learning process, where some information may lead to the correct answer. Only certain descriptors of the quantum system, such as correlation functions or entanglement spectra, can identify different phases of matter, with quantum phase transition points standing out. Notably, quantum phase transition points can be identified as extreme points in machine learning through perplexity methods within unsupervised machine learning. However, these machine learning methods ultimately still require accurate ground-state data, such as measurements on real materials or quantum simulators, or data from numerical simulations using neural networks. In practice, obtaining accurate ground-state data is often difficult. Ideally, with infinite quantum resources, accurate ground-state data could be obtained, but this is clearly unrealistic given the limited quantum resources available in real-world applications. Therefore, quantum phase transition points identified through machine learning are often not accurate enough.
[0004] Therefore, overcoming the shortcomings of the existing technology is an urgent problem to be solved in this technical field. Summary of the Invention
[0005] The technical problem to be solved by this invention is that in the prior art, the measurement of quantum phase transition points is usually achieved using machine learning. However, machine learning often has difficulty obtaining accurate ground state data, resulting in the identification of quantum phase transition points being inaccurate.
[0006] The present invention adopts the following technical solution:
[0007] A method for locating a quantum phase transition point, the quantum circuit comprising a first circuit and a second circuit, including:
[0008] The first line is initialized to the eigenstate of the first initial Hamiltonian H0, and the first line is evolved to the eigenstate of the target Hamiltonian H and then back to the eigenstate of the first initial Hamiltonian H0. The evolution energy error ΔE0 of the first line is measured.
[0009] The second line is initialized to the eigenstate of the second initial Hamiltonian H1, and the second line is evolved so that the first line evolves to the eigenstate of the target Hamiltonian H and then returns to the eigenstate of the second initial Hamiltonian H1. The evolution energy error ΔE1 of the second line is measured.
[0010] The Hamiltonian parameter h corresponding to the same evolution energy error ΔE0 of the first line and the same evolution energy error ΔE1 of the second line is the phase transition point of the quantum computing problem.
[0011] Preferably, the evolution of the first line specifically includes:
[0012] Perform Hamiltonian time evolution on the first path until it evolves to the eigenstate of the target Hamiltonian H;
[0013] It acts on the first line after the evolution of time. Make in Under the influence of , the first path reverts to the eigenstate of the first initial Hamiltonian H0; where,
[0014] Preferably, the evolution of the second line specifically includes:
[0015] The Hamiltonian time evolution of the second path is performed until it evolves to the eigenstate of the target Hamiltonian H;
[0016] It acts on the second line after time evolution. Make in Under the influence of this, the second path reverts to the eigenstate of the second initial Hamiltonian H1; among which,
[0017] Preferably, the measurement of the evolution energy error ΔE0 of the first line specifically includes:
[0018] The energy E before the evolution of the first initial Hamiltonian H0 of the first circuit is measured. z The energy E0 of the first initial Hamiltonian H0 after the first line evolves is measured, and the energy E before evolution is used as the starting energy. z The difference between the evolved energy E0 and the evolved energy E0 is taken as the evolutionary energy error ΔE0.
[0019] Preferably, the quantum circuit further includes a third circuit, wherein the energy E of the first initial Hamiltonian H0 before the evolution of the first circuit is measured. z Specifically, it includes:
[0020] The eigenstate of the first initial Hamiltonian H0 applied to the third circuit, the energy E before evolution z This was obtained by measuring the third line.
[0021] Preferably, the measurement of the evolution energy error ΔE1 of the second circuit specifically includes:
[0022] The energy E before the evolution of the second initial Hamiltonian H1 before the second circuit evolves is measured. x The evolved energy E1 of the second initial Hamiltonian H1 after the second circuit evolves is measured, with the energy E before evolution as the starting point. x The difference between the evolved energy E1 and the energy E1 is taken as the evolution energy error ΔE1.
[0023] Preferably, the quantum circuit further includes a fourth circuit, wherein the energy E of the second initial Hamiltonian H1 before the second circuit evolves is measured. x Specifically, it includes:
[0024] The eigenstate of the first initial Hamiltonian H1 applied to the fourth line, the energy E before evolution x This was obtained by measuring the fourth line.
[0025] Preferably, before initializing the first circuit to the eigenstate of the first initial Hamiltonian H0, the method further includes: obtaining the first initial Hamiltonian H0 and the second initial Hamiltonian H1 of the quantum computing problem.
[0026] Preferably, obtaining the first initial Hamiltonian H0 and the second initial Hamiltonian H1 for the quantum computing problem specifically includes:
[0027] When locating the phase transition point in the transverse-field Ising model, the Hamiltonian is calculated based on the transverse-field Ising model.
[0028]
[0029] Let H TFIM (h) = H0 + hH1, thus obtaining the first initial Hamiltonian. Second initial Hamiltonian
[0030] When locating the phase transition point of the spin XZ model, the Hamiltonian is calculated based on the spin XZ model.
[0031] Let Hxz (h) = H0 + hH1, thus obtaining the first initial Hamiltonian. Second initial Hamiltonian
[0032] In a second aspect, the present invention also provides a quantum phase transition point positioning device for implementing the quantum phase transition point positioning method described in the first aspect, the device comprising:
[0033] At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor for performing the quantum phase transition point localization method described in the first aspect.
[0034] Thirdly, the present invention also provides a non-volatile computer storage medium storing computer-executable instructions that are executed by one or more processors to perform the quantum phase transition point localization method described in the first aspect.
[0035] This invention designs a quantum circuit and measures the evolution energy error under two different evolution directions. It then uses the evolution energy error to find the Hamiltonian parameter h that makes the two evolution directions relatively fair. The position of the Hamiltonian parameter h is the phase transition point of the quantum computing problem. Therefore, it is not necessary to accurately obtain the ground state data of the quantum critical point. The quantum critical point can be accurately located with less quantum resources, and the quantum resources used are also reduced. Attached Figure Description
[0036] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.
[0037] Figure 1 This is a flowchart illustrating a method for locating quantum phase transition points provided in an embodiment of the present invention;
[0038] Figure 2 This is a flowchart illustrating another method for locating quantum phase transition points provided in an embodiment of the present invention;
[0039] Figure 3 This is a flowchart illustrating another method for locating quantum phase transition points provided in an embodiment of the present invention;
[0040] Figure 4 This is a schematic diagram of the quantum circuit in a quantum phase transition point location method provided in an embodiment of the present invention;
[0041] Figure 5 This is a flowchart illustrating another method for locating quantum phase transition points provided in an embodiment of the present invention;
[0042] Figure 6 This is a circuit diagram of a three-qubit GHZ state provided in an embodiment of the present invention;
[0043] Figure 7 This is a schematic diagram illustrating the application of a quantum phase transition point location method provided by an embodiment of the present invention to the transverse field Ising model;
[0044] Figure 8 This is a schematic diagram illustrating the application of a quantum phase transition point location method provided in an embodiment of the present invention to a spin XZ model;
[0045] Figure 9 This is a schematic diagram of the architecture of a quantum phase transition point positioning device provided in an embodiment of the present invention. Detailed Implementation
[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0047] In the description of this invention, the terms "left," "right," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and are not intended to require the invention to be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the invention.
[0048] In this invention, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.
[0049] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
[0050] Example 1:
[0051] Embodiment 1 of the present invention provides a method for locating a quantum phase transition point. The quantum circuit includes a first circuit and a second circuit, such as... Figure 1 As shown, it includes:
[0052] In step 201, the first circuit is initialized to the eigenstate of the first initial Hamiltonian H0, and the first circuit is evolved to the eigenstate of the target Hamiltonian H and then back to the eigenstate of the first initial Hamiltonian H0. The evolution energy error ΔE0 of the first circuit is measured.
[0053] In step 202, the second line is initialized to the eigenstate of the second initial Hamiltonian H1, and the second line is evolved so that the first line evolves to the eigenstate of the target Hamiltonian H and then returns to the eigenstate of the second initial Hamiltonian H1. The evolution energy error ΔE1 of the second line is measured. The relationship between the first initial Hamiltonian H0, the second initial Hamiltonian H1 and the target Hamiltonian H is: H = H0 + hH1, that is, the target Hamiltonian H is obtained by evolving from the first initial Hamiltonian H0 and the second initial Hamiltonian H1.
[0054] It should be noted that in the actual evolution process, the first initial Hamiltonian H0 and the second initial Hamiltonian H1 change continuously. In this embodiment, the terms "first initial Hamiltonian H0 before the first line evolves," "first initial Hamiltonian H0 after the first line evolves," "second initial Hamiltonian H1 before the second line evolves," and "second initial Hamiltonian H1 after the second line evolves" are used to distinguish the evolution before and after. For the sake of brevity, in this embodiment, unless otherwise specified, "first initial Hamiltonian H0" is used to refer to the first initial Hamiltonian H0 before the first line evolves, and "second initial Hamiltonian H1" is used to refer to the second initial Hamiltonian H1 before the second line evolves.
[0055] It is important to emphasize that, due to the inherent errors in quantum circuits, the return to the eigenstate of the first initial Hamiltonian H0 does not refer to a complete return to the eigenstate of the first initial Hamiltonian H0. Rather, it refers to a return to the state closest to the eigenstate of the first initial Hamiltonian H0, or a return to a state where the energy difference between the first initial Hamiltonian H0 and its eigenstate is within a predetermined range. This predetermined range is determined by those skilled in the art based on experience. The evolution energy error ΔE0 of the first circuit is the error between the first initial Hamiltonian H0 before and after the evolution of the first circuit.
[0056] Similarly, the return to the eigenstate of the second initial Hamiltonian H1 does not refer to a complete return to the eigenstate of the second initial Hamiltonian H1, but rather a return to the state closest to the eigenstate of the second initial Hamiltonian H1, or a return to a state where the energy difference between the eigenstate and the eigenstate of the second initial Hamiltonian H1 is within a preset range. The evolution energy error ΔE1 of the second circuit is the error between the second initial Hamiltonian H1 before and after the second circuit evolves.
[0057] In step 203, the Hamiltonian parameter h corresponding to the same evolution energy error ΔE0 of the first circuit and the same evolution energy error ΔE1 of the second circuit is found, which is the phase transition point of the quantum computing problem.
[0058] Here, the Hamiltonian parameter h is an adjustable parameter in quantum computing problems, and its meaning may differ in different quantum computing problems. When the evolution energy error ΔE0 of the first path is the same as the evolution energy error ΔE1 of the second path, the evolution of the two different evolution directions of the first and second paths is considered to be the most fair, thus obtaining the phase transition point.
[0059] In practical applications, steps 201-203 are typically performed as follows: multiple Hamiltonian parameters h are preset, and steps 201 and 202 are executed under multiple Hamiltonian parameters h respectively. The h that is closest to the evolution energy error ΔE0 of the first circuit and the evolution energy error ΔE1 of the second circuit is taken as the phase transition point of the quantum computing problem.
[0060] This embodiment designs a quantum circuit and measures the evolution energy error under two different evolution directions. The Hamiltonian parameter h that makes the two evolution directions relatively fair is found by the evolution energy error. The position of the Hamiltonian parameter h is the phase transition point of the quantum computing problem. Therefore, it is not necessary to accurately obtain the ground state data of the quantum critical point. The quantum critical point can be accurately located with less quantum resources, and the quantum resources used are also reduced.
[0061] In an optional implementation, the evolution of the first line is as follows: Figure 2 As shown, it specifically includes:
[0062] In step 301, the Hamiltonian time evolution is performed on the first line until it evolves to the eigenstate of the target Hamiltonian H.
[0063] In step 302, the action is performed on the first line after time evolution. Make in Under the influence of , the first path reverts to the eigenstate of the first initial Hamiltonian H0; where, i is an imaginary number, and α and β are the parameters trained in the parametric quantum circuit.
[0064] The evolution of the second line, such as Figure 3 As shown, it specifically includes:
[0065] In step 401, the Hamiltonian time evolution is performed on the second line until it evolves to the eigenstate of the target Hamiltonian H.
[0066] In step 402, the action is performed on the second line after time evolution. Make in Under the influence of this, the second path reverts to the eigenstate of the second initial Hamiltonian H1; among which, i is an imaginary number, and α and β are the parameters trained in the parametric quantum circuit.
[0067] In specific application scenarios, the measurement of the evolution energy error ΔE0 of the first line specifically includes:
[0068] The energy E before the evolution of the first initial Hamiltonian H0 of the first circuit is measured. z The energy E0 of the first initial Hamiltonian H0 after the first line evolves is measured, and the energy E before evolution is used as the starting energy. z The difference between the evolved energy E0 and the evolved energy E0 is taken as the evolutionary energy error ΔE0.
[0069] The measurement of the evolution energy error ΔE1 of the second line specifically includes:
[0070] The energy E before the evolution of the second initial Hamiltonian H1 before the second circuit evolves is measured. x The evolved energy E1 of the second initial Hamiltonian H1 after the second circuit evolves is measured, with the energy E before evolution as the starting point. x The difference between the evolved energy E1 and the energy E1 is taken as the evolution energy error ΔE1.
[0071] This embodiment also provides the following optional implementation: the quantum circuit further includes a third circuit, wherein the energy E of the first initial Hamiltonian H0 before the evolution of the first circuit is measured. z Specifically, it includes:
[0072] The third circuit is initialized to the eigenstate of the first initial Hamiltonian H0, where the pre-evolution energy E z This was obtained by measuring the third line.
[0073] The quantum circuit also includes a fourth circuit, which measures the energy E of the second initial Hamiltonian H1 before its evolution in the second circuit. x Specifically, it includes:
[0074] The fourth circuit is initialized to the eigenstate of the first initial Hamiltonian H1, where the pre-evolution energy E x This was obtained by measuring the fourth line.
[0075] Before initializing the first circuit to the eigenstate of the first initial Hamiltonian H0, the method further includes: obtaining the first initial Hamiltonian H0 and the second initial Hamiltonian H1 of the quantum computing problem.
[0076] Depending on the specific quantum computing problem, the first initial Hamiltonian H0 and the second initial Hamiltonian H1 may also be different.
[0077] In specific application scenarios, obtaining the first initial Hamiltonian H0 and the second initial Hamiltonian H1 for a quantum computing problem specifically includes:
[0078] When locating the phase transition point in the transverse-field Ising model, the Hamiltonian is calculated based on the transverse-field Ising model.
[0079] Let H TFIM (h) = H0 + hH1, thus obtaining the first initial Hamiltonian. Second initial Hamiltonian
[0080] When locating the phase transition point of the spin XZ model, the Hamiltonian is calculated based on the spin XZ model. Let H xz (h) = H0 + hH1, thus obtaining the first initial Hamiltonian. Second initial Hamiltonian
[0081] Example 2:
[0082] Based on the method described in Embodiment 1, this invention combines specific application scenarios and uses technical descriptions in relevant scenarios to illustrate the implementation process of the features of this invention in those scenarios.
[0083] The quantum circuit used in this embodiment is as follows: Figure 4 As shown. Figure 4 The execution steps of the quantum circuit shown are as follows Figure 5 As shown, this includes initial state preparation, dynamic evolution, and locating the quantum phase transition point. The circuit is read from left to right, with each line representing a connection in the quantum circuit. These connections do not necessarily correspond to physical connections; they may correspond to time periods or physical particles, such as photons, moving from one place in space to another. Any quantum unitary operation can be decomposed into a combination of single-qubit gates and CNOT gates. The quantum circuit is implemented using multiple easily implemented single-qubit gates and CNOT gates. It should be noted that this embodiment provides... Figure 4 In the case of the quantum circuit diagram shown, those skilled in the art can easily implement the scheme through the quantum circuit diagram without having to focus on the implementation of each single-bit gate and CNOT gate. Therefore, the fact that this embodiment does not provide the specific number of single-bit gates and CNOT gates and the circuit diagram composed of them should not be taken as a lack of clarity in the disclosure of this embodiment.
[0084] like Figure 6 The diagram shown is a circuit diagram of a three-qubit GHZ (Greenberger–Horne–Zeilinger, maximally entangled state) used in quantum circuits. It includes the initial quantum state |000>, the single-qubit H-gate, and the two-qubit CNOT-gate. Under the action of these gates, the quantum state is constructed: A measurement gate is a measurement of a quantum state on its computational basis vectors. After the measurement, the quantum state collapses into a substate. For example... After measurement, The probability of obtaining a state |000> is given. The probability of obtaining the state is |111>.
[0085] Specifically, the initial state preparation includes:
[0086] It has the same effect on the first and third lines. It has the same effect on the second and fourth lines. This involves initializing the quantum circuit. and It relates to the Hamiltonian of the problem, for example, H = H0 + hH1. These are eigenstates of H0. H1 is an eigenstate of H1, where H is the target Hamiltonian, H0 is the first initial Hamiltonian, H1 is the second initial Hamiltonian, and h is the system Hamiltonian parameter.
[0087] The dynamic evolution specifically includes:
[0088] The ground-state energy of the target Hamiltonian H is directly measured for the third line (during the measurement, since the target Hamiltonian of this line only contains the first initial Hamiltonian H0 before evolution, the energy of the first initial Hamiltonian H0 is actually measured), and E is obtained. z ; it first acts on the first line It is the Hamiltonian time evolution of the target Hamiltonian H, which directly evolves to the eigenstates of H, and then through... in, QAOA (Quantum Approximate Optimization Algorithm) involves the alternating evolution of parametric quantum circuits, causing the quantum state to return to its previous state. Because quantum circuits have errors, it is practically impossible for us to completely revert to quantum mechanics. Then H0 is measured to obtain E0, ΔE0=|E0-E zSimilarly, the ground-state energy of H is directly measured for the second line (during the measurement, since the target Hamiltonian of this line only contains the second initial Hamiltonian H0 before evolution, the energy of the second initial Hamiltonian H1 is actually measured), yielding E. x The fourth line is primarily affected. The Hamiltonian time evolution of H directly evolves into the eigenstates of H, and then through... in, The alternating evolution of the QAOA parametric quantum circuit allows the quantum state to return to... Because quantum circuits have errors, it is practically impossible for us to completely revert to quantum mechanics. Then H1 is measured to obtain E1, ΔE1=|E1-E x |
[0089] The specific method for locating the quantum phase transition point involves comparing ΔE0 and ΔE1 to determine which phase the material is in, where ΔE0 = ΔE1 at the quantum phase transition point. If ΔE0 < ΔE1, the system is in a phase where h < 1; if ΔE0 > ΔE1, the system is in a phase where h > 1. This allows for the determination of the material's phase and the utilization of the specific physical properties of that phase.
[0090] In this embodiment, the variable quantum algorithm is used to locate the quantum phase transition point. Based on the principle of dynamic evolution and combined with QAOA Ansatz (quantum circuit), the error property of the variable quantum algorithm is used to locate the quantum phase transition point and determine the phase of the material.
[0091] Example 3:
[0092] This embodiment uses the horizontal field Ising model as a specific application scenario, and uses the technical descriptions in the relevant scenario to illustrate the implementation process of the characteristics of the present invention in the scenario.
[0093] The transverse-field Ising model is the standard model for studying quantum phase transitions. The Hamiltonian operator of the transverse-field Ising model can be described as follows:
[0094]
[0095] The transverse field Ising model belongs to Symmetric, and in σ z to -σ z Keep it unchanged. To use the HVA assumption, we let H... TFIM (h)=H zz +hH x ,in The two reference states are respectively selected as H zz and Hx ground state, and in Note that there is another option. It still violates Z2 symmetry.
[0096] With H TFIM (h) is the target Hamiltonian, H zz As the first initial Hamiltonian, H x As the second initial Hamiltonian, the quantum circuit described in Example 2 is used to locate the phase transition point. To facilitate illustrating the relationship between the evolution energy error ΔE0 of the first circuit and the evolution energy error ΔE1 of the second circuit, this embodiment also uses... Figure 4 The evolution energy error ΔE0 of the first circuit and the evolution energy error ΔE1 of the second circuit are obtained in the quantum circuit shown, and are expressed as follows: Figure 7 The diagram shows the curves, where the dashed line with dots represents ΔE0, and the other curve represents ΔE1. These represent the measured evolutionary energy error ΔE0 of the first path and the measured evolutionary energy error ΔE1 of the second path, respectively. Figure 7 As shown, the horizontal axis represents the external magnetic field strength, and the vertical axis represents the energy. It can be seen that the intersection of the two curves corresponds to the position of the quantum phase transition point (ignoring the first point where h=0). ΔE0=ΔE1 occurs at the position where h=1, so the quantum phase transition point is located at h=1, which is consistent with the actual quantum phase transition point of the horizontal field Ising model. Furthermore, it can be seen that symmetry breaking occurs when h<1.
[0097] Example 4:
[0098] This embodiment uses the spin XZ model as a specific application scenario, and uses the technical descriptions in the relevant scenario to illustrate the implementation process of the characteristics of the present invention in the scenario.
[0099] The spin XZ model exhibits a symmetry-breaking quantum phase transition, distinct from the transverse field Ising model, and its Hamiltonian is:
[0100]
[0101] The quantum phase transition point is located at h=1. Unlike the transverse-field Ising model, which only exhibits symmetry breaking on one side of the quantum phase transition point, the spin XZ model has symmetry-breaking phases on both sides. However, these two symmetry-breaking phases break different symmetries. Let us... It is represented as symmetric. σ y →-σ y ,σ z →-σ z (σ y →-σ y ,σx →-σ x Then, H xz (h<1)(H xz The ground state of (h>1) is destroyed. But it was retained. symmetry.
[0102] The spin XZ model can be written as H xz (h)=H zz +hH xx ,in The two reference states are respectively and It is a symmetry-broken state.
[0103] With H xz (h) is the target Hamiltonian, H zz As the first initial Hamiltonian, H xx As a second initial Hamiltonian, under the influence of multiple different external magnetic field strengths h (i.e., the Hamiltonian parameter h in Example 1), the quantum circuit described in Example 2 is used to locate the phase transition point. To facilitate illustrating the relationship between the evolution energy error ΔE0 of the first circuit and the evolution energy error ΔE1 of the second circuit, this embodiment also uses... Figure 4 The evolution energy error ΔE0 of the first circuit and the evolution energy error ΔE1 of the second circuit are obtained in the quantum circuit shown, and are expressed as follows: Figure 8 The diagram shows the curves, where the dashed line with dots represents ΔE0, and the other curve represents ΔE1, representing the measured evolution energy error ΔE0 of the first path and the measured evolution energy error ΔE1 of the second path, respectively. Figure 8 As shown, the horizontal axis represents the external magnetic field strength, and the vertical axis represents the energy. It can be seen that the intersection of the two curves corresponds to the position of the quantum phase transition point (ignoring the first point h=0). ΔE0=ΔE1 occurs at the position h=1, which means that the quantum phase transition point is located at h=1, which is consistent with the actual quantum phase transition point of the spin XZ model. Furthermore, it can be seen that symmetry breaking occurs at h<1.
[0104] Example 5:
[0105] like Figure 9 The diagram shown is a schematic representation of the architecture of a quantum phase transition point positioning device according to an embodiment of the present invention. The quantum phase transition point positioning device of this embodiment includes one or more processors 21 and a memory 22. Figure 9 Take a processor 21 as an example.
[0106] Processor 21 and memory 22 can be connected via a bus or other means. Figure 9 Taking the example of a connection between China and Israel via a bus.
[0107] The memory 22, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs and non-volatile computer-executable programs, such as the quantum phase transition point location method in Embodiment 1. The processor 21 executes the quantum phase transition point location method by running the non-volatile software program and instructions stored in the memory 22.
[0108] Memory 22 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, memory 22 may optionally include memory remotely located relative to processor 21, which can be connected to processor 21 via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.
[0109] The program instructions / modules are stored in the memory 22 and, when executed by one or more processors 21, execute the quantum phase transition point location method in Embodiment 1 above.
[0110] It is worth noting that the information interaction and execution process between the modules and units in the above-mentioned device and system are based on the same concept as the processing method embodiment of the present invention. For details, please refer to the description in the method embodiment of the present invention, and will not be repeated here.
[0111] Those skilled in the art will understand that all or part of the steps in the various methods of the embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include: read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, etc.
[0112] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method of locating a quantum phase transition point, characterized in that, The quantum circuit comprises a first circuit and a second circuit, comprising: initializing a first circuit to an eigenstate of a first initial Hamiltonian and evolving the first circuit such that the first circuit evolves to an eigenstate of a target Hamiltonian H and then back to an eigenstate of the first initial Hamiltonian and measuring an evolution energy error of the first circuit ; initializing a second circuit to an eigenstate of a second initial Hamiltonian and evolving the second circuit such that the first circuit evolves to an eigenstate of a target Hamiltonian H and then back to an eigenstate of the second initial Hamiltonian and measuring an evolution energy error of the second circuit ; finding the evolution energy error of the first circuit finding the evolution energy error of the second circuit the hamiltonian parameter h corresponding to the same time is the phase point of the quantum computing problem; The measurement first line evolution energy error , specifically comprising: measuring the first initial Hamiltonian evolution before energy , measuring the first initial Hamiltonian evolution after energy , taking the difference between the evolution before energy and the evolution after energy as the evolution energy error ; the quantum circuit further comprises a third line, the measurement first line evolution before energy of the first initial Hamiltonian , specifically comprising: initializing the third line to the eigenstate of the first initial Hamiltonian , the evolution before energy is obtained by measuring the third line; The evolution energy error of the second line is measured. Specifically, this includes: measuring the second initial Hamiltonian before the second line evolves. Pre-evolutionary energy The second initial Hamiltonian after the evolution of the second circuit is measured. Energy after evolution , with pre-evolutionary energy With post-evolutionary energy The difference between them is used as the evolutionary energy error. The quantum circuit also includes a fourth circuit, which measures the second initial Hamiltonian before the second circuit evolves. Pre-evolutionary energy Specifically, this includes: initializing the fourth line to the first initial Hamiltonian. In the eigenstates, the pre-evolutionary energy This was obtained by measuring the fourth line.
2. The method of locating a quantum phase transition point of claim 1, wherein, The evolution of the first circuit comprises: Hamiltonian time evolution is performed on the first circuit until evolution into an eigenstate of the target Hamiltonian H is achieved; It acts on the first line after the evolution of time. , making in Under its influence, the first path reverts to the first initial Hamiltonian. The eigenstates; among which, .
3. The method of claim 1, wherein, The evolution of the second circuit comprises: Hamiltonian time evolution is performed on the second circuit until evolution into an eigenstate of the target Hamiltonian H is achieved; acting on the second line after time evolution causes the second line to return to the eigenstate of the second initial Hamiltonian under the action of ; wherein .
4. The method of locating a quantum phase transition point according to any one of claims 1 to 3, wherein prior to said initializing the first circuit to an eigenstate of a first initial Hamiltonian the method further comprises obtaining a first initial Hamiltonian and a second initial Hamiltonian of a quantum computing problem.
5. The method for locating the quantum phase transition point according to claim 4, characterized in that, The first initial Hamiltonian of the quantum computing problem is obtained and the second initial Hamiltonian , specifically comprising: When locating the phase transition point of the transverse field Ising model, the Hamiltonian is calculated based on the transverse field Ising model ; Let , a first initial Hamiltonian , a second initial Hamiltonian ; When locating the phase transition point of the spin XZ model, the Hamiltonian is calculated based on the spin XZ model ; Let , a first initial Hamiltonian , a second initial Hamiltonian .
6. A quantum phase transition point locating device, characterized in that, The device comprises: At least one processor; and a memory connected to the at least one processor in communication; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the processor to execute the positioning method of the quantum phase transition point according to any one of claims 1-5.