A quantum simulation information sensing method based on SSH model and measurement quenching

Abstract

The present invention relates to a quantum simulation information sensing method for an SSH model based on measurement quenching, comprising the following steps: constructing a one-dimensional SSH model chain, wherein the ground state of the one-dimensional SSH model chain has an even parity characteristic; measuring the spin x or spin y direction of any superconducting qubit on the one-dimensional SSH model chain, collapsing the entire one-dimensional SSH model chain from a stable ground state to an unstable semi-excited state, obtaining a time-varying curve of the expected value of the spin x or spin y direction of the superconducting qubit; and calibrating the energy spectrum of the one-dimensional SSH model chain by observing the frequency components corresponding to the time-domain evolution of the superconducting qubit. The present invention not only minimizes the introduction of decoherence but also simplifies the experimental process.

Description

Technical Field

[0001] The present invention relates to the field of quantum simulation technology, and in particular to a SSH model quantum simulation information sensing method based on measurement quenching. Background Art

[0002] Quantum simulation, a crucial component of the "Second Quantum Revolution," has garnered widespread attention. Currently, the most common approach to quantum simulation is to map the Hamiltonian of the simulated physical system onto a controllable quantum system. By performing the simulation on the controllable quantum system, the characteristics of the simulated physical system can be inferred. Unlike simulations using general quantum computing algorithms, this approach lacks the universality of digital simulation. However, it is more intuitive and, due to its greater tolerance to system noise and operational errors, is relatively easier to implement.

[0003] The process of quantum simulation involves preparing, manipulating, and reading the quantum state of one or more particles. While preparation and manipulation can be achieved through different means, reading is accomplished through measurement. A key step in quantum simulation is inducing the "correct" dynamics in the system. A common approach is quenching dynamics: inducing the temporal evolution of the system through abrupt changes in the Hamiltonian. This approach is widely used to address fundamental problems such as equilibrium and the emergence of highly entangled states, as well as practical applications such as creating long-distance entanglement. Experimentally, all of this relies on the use of macroscopic equipment, which can lead to decoherence and increase the complexity of the process. Furthermore, extracting information from a quantum simulation system using qubits typically involves measuring all qubits or designing an additional coupling structure when designing the quantum simulation system, using transmission or reflection spectra to extract information. However, such methods increase the complexity of the experimental measurement system and introduce new decoherence. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a SSH model quantum simulation information sensing method based on measurement quenching, which can not only minimize the introduction of decoherence but also simplify the experimental process.

[0005] The technical solution adopted by the present invention to solve the technical problem is to provide a SSH model quantum simulation information sensing method based on measurement quenching, comprising the following steps:

[0006] constructing a one-dimensional SSH model chain, wherein the ground state of the one-dimensional SSH model chain has an even parity property;

[0007] The spin x or spin y direction of any superconducting qubit on the one-dimensional SSH model chain is measured, and the entire one-dimensional SSH model chain is collapsed from a stable ground state to an unstable semi-excited state to obtain a curve of the expected value of the spin x or spin y direction of the superconducting qubit over time. The energy spectrum of the one-dimensional SSH model chain is calibrated by observing the frequency component corresponding to the time domain evolution of the superconducting qubit.

[0008] The one-dimensional SSH model chain includes an even number of superconducting qubits coupled in sequence. The superconducting qubits are divided into two categories according to their positions, wherein the superconducting qubits at odd positions are first-category superconducting qubits, and the superconducting qubits at even positions are second-category superconducting qubits; the superconducting qubits are provided with a readout resonant cavity and an XY control line.

[0009] One superconducting qubit of the first type and one superconducting qubit of the second type form a primitive cell, and the coupling strength within the primitive cell is the same, and the coupling strength between the primitive cells is the same.

[0010] The method comprises measuring the spin x or spin y direction of any superconducting qubit on the one-dimensional SSH model chain, collapsing the entire one-dimensional SSH model chain from a stable ground state to an unstable semi-excited state, and obtaining a curve of the expected value of the spin x or spin y direction of the superconducting qubit over time, specifically comprising:

[0011] preparing all the one-dimensional SSH model chains to the ground state;

[0012] Performing a measurement on any superconducting qubit in the one-dimensional SSH model chain in the spin x or spin y direction, projecting the superconducting qubit onto two eigenstates of spin x or spin y with equal probability, so that the system state of the one-dimensional SSH model chain is not in the spin z eigenstate, and performing time evolution;

[0013] Repeatedly measure the spin x or spin y direction of any superconducting quantum bit on the one-dimensional SSH model chain to obtain a curve of the expected value of the spin x or spin y direction of the superconducting quantum bit changing with time.

[0014] The calibrating the energy spectrum of the one-dimensional SSH model chain by viewing the frequency components corresponding to the time-domain evolution of the superconducting quantum bit specifically includes:

[0015] Based on the even-parity property of the ground state of the one-dimensional SSH model chain and the measurement projection effect, the superconducting quantum bit chain system is subjected to non-equilibrium evolution, and the time evolution of the expected value of the superconducting quantum bit spin x or spin y direction is tracked;

[0016] The expected value curve is Fourier transformed to obtain a spectrum corresponding to the time-domain evolution, and the energy spectrum of the one-dimensional SSH model chain is calibrated by viewing the frequency components corresponding to the time-domain evolution of the superconducting quantum bit.

[0017] Beneficial effects

[0018] Due to the adoption of the above-mentioned technical solution, the present invention has the following advantages and positive effects compared to existing technologies: the entire perception process of the present invention relies on measurement to achieve perturbations of the ground state system, and also relies on measurement to extract energy level and boundary transmission characteristics. The entire process involves very few operations and measurements, and even only requires a single superconducting qubit to achieve perception of the entire system information. This method not only minimizes the introduction of decoherence, but also simplifies the experimental process, opening up new possibilities for simulating large-scale topological systems using superconducting qubits, while significantly reducing the corresponding costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the structure of a one-dimensional SSH model chain in an embodiment of the present invention;

[0020] Figure 2 This is a schematic diagram of the quantum simulation measurement principle of the one-dimensional SSH model chain in an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of the SSH model measuring the dynamic evolution of quenching and the frequency domain evolution of the first quantum bit;

[0022] Figure 4 It is the energy level information diagram of the measured quenching-aware SSH model;

[0023] Figure 5 This is a diagram showing the boundary transmission characteristics of the SSH model after measured quenching. DETAILED DESCRIPTION

[0024] Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiments are only used to illustrate the present invention and are not used in limiting the scope of the present invention.In addition, should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall equally within the scope limited by the appended claims of the application.

[0025] An embodiment of the present invention relates to an SSH model quantum simulation information sensing method based on measurement quenching, comprising the following steps: constructing a one-dimensional SSH model chain, wherein the ground state of the one-dimensional SSH model chain has an even parity characteristic; measuring the spin x or spin y direction of any superconducting quantum bit on the one-dimensional SSH model chain, collapsing the entire one-dimensional SSH model chain from a stable ground state to an unstable semi-excited state, obtaining a curve of the expected value of the spin x or spin y direction of the superconducting quantum bit over time, and calibrating the energy spectrum of the one-dimensional SSH model chain by observing the frequency components corresponding to the time-domain evolution of the superconducting quantum bit.

[0026] This implementation exploits the unique characteristics of quantum measurement—in quantum mechanics, measurements can significantly alter the state of a system, leading to an ecological collapse. When a measurement is made on a quantum system, the system's wave function immediately "collapses" to a specific state. This "collapse" can be considered a perturbation to the system; through interactions between qubits, the perturbation propagates throughout the entire qubit chain. Simulations demonstrate that measurement quenching can effectively detect the energy spectrum and boundary transmission characteristics of the SSH model.

[0027] The main structure of the SSH model in this embodiment is composed of a series of superconducting qubits composed of Josephson junctions and capacitors, wherein a one-dimensional SSH model chain consisting of 10 superconducting qubits is shown in FIG. Figure 1 As shown. Superconducting qubits are divided into two categories, A and B, according to their positions. The ones at odd positions are type A superconducting qubits (solid), and the ones at even positions are type B superconducting qubits (hollow). A type A superconducting qubit and a type B superconducting qubit form a unit cell (UNIT CELL), and the entire one-dimensional SSH model chain can also be regarded as an arrangement of five units. The coupling between superconducting qubits can use a variety of coupling schemes such as capacitance, inductance, Josephson junction or resonant cavity. The scheme shown in the figure is the one using capacitive coupling. Different coupling strengths can be achieved depending on the size of the selected coupling capacitor. At this time, the coupling strength between the two superconducting qubits can be expressed as: Among them, C1, C2, C 12 , ω1 and ω2 are the capacitance of the first superconducting qubit, the capacitance of the second superconducting qubit, the coupling capacitance between the two superconducting qubits, the operating frequency of the first superconducting qubit, and the operating frequency of the second superconducting qubit, respectively. Coupling can be divided into intra-cell coupling and inter-cell coupling. In the SSH model, the coupling strength within all cells is the same, and the coupling strength between cells is also the same. Define the interaction strength within the cell as J1 and the interaction strength between cells as J2. Figure 1 The system presented has a Hamiltonian and |2i,1> refer to the states of the electron at the 2i-1 and 2i lattice points in the SSH model, respectively. By introducing a superconducting qubit readout resonant cavity and XY control lines, a readout operation can be performed on the superconducting qubit to achieve a measurement quenching operation.

[0028] This implementation is achieved by measuring the perturbation system and tracking the impact of this perturbation on the system. The key point is that it is necessary to use measurement methods to collapse the entire SSH model quantum simulation system from a stable ground state to an unstable semi-excited state. For an SSH model system composed of 10 superconducting quantum bits, the basic steps of measuring quenching are as follows: Figure 2 As shown. First, the entire one-dimensional SSH model chain is prepared to the ground state. At this time, under the condition of ignoring the on-site energy, its energy is 0, and the state of the entire chain is written as Perform a σ on the first qubit x or σ y Measurement in the direction (this measurement can be for any quantum bit. For the convenience of discussion, we take the measurement of the first quantum bit as an example and select the measurement direction σ x ), the first qubit will be projected onto or The specific state to which the projection is made depends on the measurement result. Taking the projection to the |↑1> state as an example, the state of the entire one-dimensional SSH model chain is At this time, the system state is not in the eigenstate, and the system will evolve over time. Among them, E n and |E n > represents the nth eigenenergy and eigenstate of the system.

[0029] In order to fully realize the measurement quenching quantum simulation information perception, it is necessary to continuously measure the first superconducting quantum bit in σ x The component in the direction is measured, and this measurement needs to be averaged multiple times. Multiple measurements can obtain the σ of the first superconducting quantum bit. x The expected value of the curve changes with time, the basic formula is Using the complete relation I = ∑ n |E n > <E n |, the expected formula can be written as Since the Hamiltonian of the SSH model composed of superconducting quantum bits commutes with the parity operator, the ground state of the system will maintain a certain parity during the evolution. For the one-dimensional SSH model chain of this embodiment, its ground state has even parity. xThe measurement in the direction will produce the |↑> state or |↓> state with equal probability. Based on this characteristic, the first superconducting quantum bit σ x The evolution of the directional expectation value can be written as Perform Fourier transform on it The spectrum corresponding to the time domain evolution can be written as The spectrum shows that the frequency components corresponding to the time-domain evolution of the first qubit correspond exactly to the energy difference between the system's intrinsic energy state and its ground state. Since the system's ground state energy is 0, the system's energy spectrum can be uniquely calibrated by examining the frequency components corresponding to the time-domain evolution of the first qubit.

[0030] The SSH model structure consisting of 10 superconducting quantum bits was simulated using QuTiP. By comparing the energy spectrum of the system with The frequency components of the measured quenching perception SSH model can verify the accuracy of the quantum simulation information, and by observing the σ of the quantum bits at the left and right ends of the chain structure z The directional component is expected to vary with time, verifying the boundary state transmission characteristics under the SSH model exhibited by the measured quenching.

[0031] The simulation parameters used were J1 = θJ2 and J2 = 5 Hz, where θ is a variable. Ten values of θ were chosen: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, and 1.8. This selection of multiple values is based on the fact that the finite-length SSH model undergoes a phase transition at θ = 1 under open boundary conditions. As θ increases, the system transitions from a topological phase with topological edge states to a trivial phase without topological edge states. This multi-point selection facilitates the universality of the proposed scheme. In the simulations, a time scale of 10,000 s was considered, and a total of 100,000 evolutionary steps were considered in the numerical calculations. The choice of coupling strength, time scale, and number of evolutionary steps is closely related. Longer time scales inevitably require more evolutionary steps, and the extra steps in the numerical simulations accumulate computational errors. However, as the coupling strength increases, shorter time scales are sufficient to fully describe the system evolution. The results demonstrate that the simulation parameters selected are appropriate and efficient.

[0032] Figure 3 It is shown that under 10 different θ, each superconducting quantum bit in the system <σ x >, and the inset shows the first superconducting quantum bit When θ = 0, the excitation of the first superconducting qubit caused by the measurement is turned off due to coupling and cannot be transmitted to other superconducting qubits. Once θ is no longer 0, for example 0.2, J1 also becomes non-zero, opening the coupling channel between the first and second superconducting qubits. <σ x> begins to oscillate over time, and as θ increases, its oscillation frequency also increases. It is worth noting that <σ x > does not evolve over time and remains at 0. When checking <σ y >, the source of this result becomes clear, since the superconducting qubits at even positions have y The first superconducting qubit evolves in the direction of the superconducting qubit, while the superconducting qubits at odd positions do not evolve with time. The spectrum clearly shows five discrete frequency quantities, corresponding to the five energy levels above the Fermi level. Figure 4 The left y-axis and the lower x-axis show the evolution of the system energy level as θ changes. The square and circle lines represent the first superconducting quantum bit when θ = 1.0 and θ = 2.0, respectively. The spectrum of the SSH model is matched. Measuring quenching can realize the perception of the energy level information of the SSH model. Figure 5 For each superconducting quantum bit in the bit chain <σ z >Time tracking shows the information transmission between boundary bits.

[0033] It is not difficult to find that the SSH model quantum simulation information sensing method based on measurement quenching proposed in the present invention relies on measurement to achieve perturbations to the ground state system, and also relies on measurement to extract energy level and boundary transmission characteristics. The entire process involves very few operations and measurements, and even only requires a single superconducting quantum bit to achieve perception of the entire system information. This method can not only minimize the introduction of decoherence, but also simplify the experimental process, and the energy spectrum simulation demonstrated above can be easily realized in experiments using a superconducting quantum bit chain system with a decoherence time of 60μs and an inter-cell coupling strength J2 of approximately 100MHz. The method of the present invention opens up new possibilities for simulating large-scale topological systems using superconducting quantum bits, while significantly reducing the corresponding costs.

Claims

1. A quantum simulation information sensing method of the SSH model based on measurement quenching, characterized in that: The following steps are involved: constructing a one-dimensional SSH model chain, wherein the ground state of the one-dimensional SSH model chain has an even parity property; Measure the spin x or spin y direction of any superconducting quantum bit on the one-dimensional SSH model chain, collapse the entire one-dimensional SSH model chain from a stable ground state to an unstable semi-excited state, and obtain a curve of the expected value of the superconducting quantum bit spin x or spin y direction over time. Calibrate the energy spectrum of the one-dimensional SSH model chain by observing the frequency component corresponding to the time domain evolution of the superconducting quantum bit, wherein, The method comprises measuring the spin x or spin y direction of any superconducting qubit on the one-dimensional SSH model chain, collapsing the entire one-dimensional SSH model chain from a stable ground state to an unstable semi-excited state, and obtaining a curve of the expected value of the spin x or spin y direction of the superconducting qubit over time, specifically comprising: preparing all the one-dimensional SSH model chains to the ground state; Performing a measurement on any superconducting qubit in the one-dimensional SSH model chain in the spin x or spin y direction, projecting the superconducting qubit onto two eigenstates of spin x or spin y with equal probability, so that the system state of the one-dimensional SSH model chain is not in the spin z eigenstate, and performing time evolution; Repeatedly measuring the spin x or spin y direction of any superconducting qubit on the one-dimensional SSH model chain to obtain a curve of the expected value of the spin x or spin y direction of the superconducting qubit over time; The calibrating the energy spectrum of the one-dimensional SSH model chain by viewing the frequency components corresponding to the time-domain evolution of the superconducting quantum bit specifically includes: Based on the even-parity property of the ground state of the one-dimensional SSH model chain and the measurement projection effect, the superconducting quantum bit chain system is subjected to non-equilibrium evolution, and the time evolution of the expected value of the superconducting quantum bit spin x or spin y direction is tracked; The expected value curve is Fourier transformed to obtain a spectrum corresponding to the time-domain evolution, and the energy spectrum of the one-dimensional SSH model chain is calibrated by viewing the frequency components corresponding to the time-domain evolution of the superconducting quantum bit.

2. The SSH model quantum simulation information sensing method based on measurement quenching according to claim 1 is characterized in that: The one-dimensional SSH model chain includes an even number of superconducting qubits coupled in sequence. The superconducting qubits are divided into two categories according to their positions, wherein the superconducting qubits at odd positions are first-category superconducting qubits, and the superconducting qubits at even positions are second-category superconducting qubits; the superconducting qubits are provided with a readout resonant cavity and an XY control line.

3. The SSH model quantum simulation information sensing method based on measurement quenching according to claim 2 is characterized in that: One superconducting qubit of the first type and one superconducting qubit of the second type form a primitive cell, and the coupling strength within the primitive cell is the same, and the coupling strength between the primitive cells is the same.

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