Method for inducing kinetic quantum phase change by adopting chiral phase

Abstract

The invention discloses a method for inducing dynamic quantum phase change by adopting a chiral phase, and belongs to the technical field of dynamic quantum phase change methods, the chiral phase is introduced under the condition of reverse quenching in quantum superconducting bits, and the dynamic quantum phase change can be successfully observed from the chiral phase, which is not proposed by people at present. In the prior art, when quenching kinetics is constructed, the kinetics quantum phase change can be observed only by considering forward quenching, or the kinetics quantum phase change phenomenon cannot be observed by reverse quenching, and in the method, the kinetics quantum phase change is induced during reverse quenching in a phase introduction mode.

Description

Technical Field

[0001] The present invention relates to a method for dynamical quantum phase transition, in particular to a method for inducing dynamical quantum phase transition by chiral phase, and belongs to the technical field of methods for dynamical quantum phase transition. Background Art

[0002] Dynamical quantum phase transition is a newly emerging research direction in the field of quantum physics in recent years. It describes the non-analytical behavior that occurs in a quantum system during the time evolution due to sudden changes in parameters.

[0003] This concept can be traced back to the earliest study of quench dynamics. When the Hamiltonian of the system changes suddenly in a short time, the time evolution of the system may exhibit characteristics similar to equilibrium phase transitions. The occurrence of DQPT is usually closely related to the topological properties, quantum entanglement, and non-equilibrium dynamics of the system. For example, in some systems, the existence of DQPT can be revealed by analyzing the non-analytical points of the Loschmidt echo or the dynamical partition function. In addition, the research on DQPT is not limited to theoretical discussions and has also been preliminarily verified in some experimental platforms in recent years, such as the DQPT observed in optical lattices or superconducting qubit systems.

[0004] The Z3-symmetric Potts model is a spin interaction model that satisfies Z3 symmetry and is a generalization of the Ising model. It allows each spin to have multiple possible states and is usually used to study quantum phase transitions or topological phenomena. Mathematically, this model can be described as a spin system with discrete chiral symmetry, and its Hamiltonian exhibits a phase diagram including ferromagnetic and paramagnetic phases in the parameter space. The Potts model exhibits rich phase transition behaviors in different states. For example, when q = 2, the Potts model degenerates into the Ising model. For the case of q > 2, the phase transition properties of the model are more complex. In addition, the Potts model is also deeply related to problems such as graph coloring, knot theory, and percolation problems. In this model, introducing a chiral phase is equivalent to a chiral clock model.

[0005] In a superconducting qubit system, when performing quench dynamics on the Z3-symmetric Potts model, if it is from the paramagnetic phase to the ferromagnetic phase, then the phenomenon of dynamical quantum phase transition can be observed; however, for the reverse quench, that is, from the ferromagnetic phase to the paramagnetic phase, no dynamical quantum phase transition occurs.

[0006] In the prior art, generally, the environment is mutated within a short time in a superconducting qubit, so that the environment before and after the change is on both sides of the phase transition critical point, thereby observing the system quench dynamics. However, this technique has only successfully observed the dynamical quantum phase transition for the case of mutation from the paramagnetic phase to the ferromagnetic phase, and this phenomenon cannot be observed for reverse quenching, that is, from the ferromagnetic phase to the paramagnetic phase. Therefore, a method using chiral phase-induced dynamical quantum phase transition is designed to solve the above problems. Summary of the Invention

[0007] The main object of the present invention is to provide a method for inducing dynamical quantum phase transition by chiral phase.

[0008] The object of the present invention can be achieved by adopting the following technical solutions:

[0009] A method for inducing dynamical quantum phase transition by chiral phase, comprising the following steps:

[0010] Step 1: Cool the Transmon superconducting qubit chip to near absolute zero by a dilution refrigerator;

[0011] Step 2: Naturally relax for 50 microseconds under the condition of near absolute zero to prepare each qubit to the ground state;

[0012] Step 3: Combine single-qubit rotation operations to simulate the introduction of chiral phase in the evolution of the Potts model;

[0013] Step 4: After introducing the chiral phase, let the qubits perform dynamical evolution according to the Hamiltonian;

[0014] Step 5: When the qubits evolve to a predetermined time point, sample according to the actual performance of the superconducting qubit chip, and then perform reading;

[0015] Step 6: Obtain the rate function through the above steps. Observing the data, it is found that when the phase exp(-iπ / 6) is introduced, non-analytical points appear in the rate function, and then the dynamical quantum phase transition phenomenon in the dynamical evolution is observed.

[0016] Preferably, in Step 1, the external control system is connected to the input and output ports of the readout port of the Transmon qubit.

[0017] Preferably, in Step 2, the system corresponds to the ferromagnetic ground state, that is, the ground state of the Potts model corresponding to J = 1, f = 0.

[0018] Preferably, in Step 3, for the unitary operator τ acting on a monomer, the additional phase required is exp(-iπ / 6), while for the Hermitian conjugate of τ, the additional phase required is exp(iπ / 6);

[0019] Through Ramsey interference measurement, we know that the required frequencies for the transitions of this system are: ω01 = 2π * 5.355 GHz, ω12 = 2π * 5.127 GHz;

[0020] Meanwhile, single qubit rotation also needs to be realized. The specific pulse signals required can be calculated from the following formula:

[0021]

[0022] Where:

[0023] R is a rotation operation operator;

[0024] is the Pauli operator;

[0025] θ, φ are specific parameters, depending on m and n as follows:

[0026] m, n refer to the quantum state numbers before and after the transition from 1 to 3;

[0027] When (m,n) = (1,3) or (2,1) or (3,2), θ = π, φ = -π / 6;

[0028] When (m,n) = (1,2) or (2,3) or (3,1), θ = π, φ = π / 6;

[0029] In other cases, θ = φ = 0.

[0030] Preferably, step three further includes applying the above microwave pulse sequence to the Transmon qubit by precisely controlling the signal in the input channel, and these pulse sequences can introduce a chiral phase during the evolution of the qubit;

[0031] If a comparison is needed, in another experiment without introducing this phase, the phenomenon of dynamical quantum phase transition will not occur.

[0032] Preferably, in step four under the above settings, this evolution process occurs naturally and is jointly determined by the Hamiltonian of the qubit and the applied microwave pulse sequence.

[0033] Preferably, in step five, the dispersive readout method is used, that is, the state of the Transmon qubit is utilized to cause a small frequency shift in the resonance frequency of the coupled resonator;

[0034] The specific operation is to apply a microwave probe signal to the resonator, whose frequency is close to but not equal to the resonance frequency of the resonator;

[0035] This probe signal interacts with the resonator and is affected by the state of the qubit. Due to the different states of the qubit, the resonant frequency of the resonator will have different offsets. Based on this offset, the specific value can be read out, thereby obtaining the magnitude of the inner product of the wave function at the current moment and the initial moment. Repeat the above evolution and measurement processes multiple times according to the sampling plan to obtain sufficient data.

[0036] Advantageous technical effects of the present invention:

[0037] A method for inducing dynamical quantum phase transition by chiral phase provided by the present invention. For the case of no dynamical quantum phase transition in the quench from ferromagnetic system to paramagnetic, an implementation scheme for inducing dynamical quantum phase transition in the superconducting qubit system by introducing the chiral phase is proposed. Brief description of the drawings

[0038] Figure 1 (a) In the Potts model, the coefficient J determines the interaction strength, and the coefficient f determines the paramagnetic term strength. (b) Schematic diagram after introducing the chiral phase into the system. Among them, the direction of the arrow points to the spin direction of the lattice point, and here only one possible state of the system is shown. The dotted line represents the nearest-neighbor interaction with strength J, and the right side shows that each local lattice point can be divided into three states. (a) and (b) respectively represent the changes in the paramagnetic strength before and after introducing the phase angle.

[0039] Figure 2 Schematic diagram of the phase diagram of the Potts model with introduced phase and the quench direction. Among them, it is assumed that the interaction strength J = 1 - f. The a1 direction represents the general reverse quench, and no dynamical quantum phase transition phenomenon can be observed. However, if the phase is introduced, that is, quenched along the a2 direction, the dynamical quantum phase transition phenomenon can be observed.

[0040] Figure 3 Schematic diagram of the connection of the experimental device. Detailed implementation manners

[0041] To make the technical solutions of the present invention clearer and more definite to those skilled in the art, the present invention will be further described in detail below with reference to the embodiments and the accompanying drawings. However, the implementation manners of the present invention are not limited thereto.

[0042] The evolution process of the entire system can be summarized as Figure 2 shown. By adjusting the initial state of each qubit to the quantum state corresponding to the starting point of the arrow, and then, when setting the system evolution, adjusting to add an additional phase to each qubit, and then letting the system perform time evolution and measure the rate function to observe whether a dynamical quantum phase transition occurs.

[0043] The instruments required for the present invention are the Transmon experimental device, which mainly consists of the following modules:

[0044] The Transmon qubit, as the core of the device, consists of a Josephson junction in parallel with a large capacitor and is used to store and process quantum information.

[0045] The readout port, microwave cavity, and microwave transmission line are used to connect different qubits, read the states, and apply microwave signals to the qubits for manipulation.

[0046] The superconducting quantum interference device (SQUID) adjusts the operating frequency of the Transmon qubit by applying an external magnetic field.

[0047] The qubit drive line is used to apply microwave drive pulses to the qubit.

[0048] The dilution refrigerator can reduce the influence of thermal noise on the qubit. The Transmon qubit needs to work at extremely low temperatures, usually around 10 mK.

[0049] The external control system includes a microwave source, circulator, mixer, amplifier, etc., and is used to generate and process microwave signals.

[0050] Experimental preparation: First, the dilution refrigerator is needed to cool down. The specific principle of this device is to use the dilution process of the mixture of helium-3 (³He) and helium-4 (⁴He) to achieve refrigeration. At extremely low temperatures, the mixture of ³He and ⁴He will undergo phase separation, forming a concentrated phase and a dilute phase. When ³He diffuses from the concentrated phase to the dilute phase, it absorbs heat, thereby reducing the temperature. Through the dilution refrigerator, the temperature of the Transmon superconducting qubit chip is reduced to near absolute zero (generally 8 - 12 mK), reducing the influence of thermal noise; the external control system is connected to the input and output ports of the readout port of the Transmon qubit to ensure stable signal transmission.

[0051] Initializing the qubit: Naturally relax for 50 microseconds under conditions close to absolute zero to prepare each qubit to the ground state (1, 0, 0). At this time, the system can correspond to the ferromagnetic ground state, that is, the ground state of the Potts model corresponding to J = 1, f = 0, also known as the fully ferromagnetic state.

[0052] Introducing the chiral phase: Specifically, for the unitary operator τ acting on a single body, the additional phase needed is exp(-iπ / 6), while for the Hermitian conjugate of τ, the additional phase needed is exp(iπ / 6). Through Ramsey interference measurement, we know that the required frequencies for the transitions of this system are: ω01 = 2π * 5.355 GHz, ω12 = 2π * 5.127 GHz. At the same time, single qubit rotation also needs to be achieved, and the specific pulse signals required can be calculated from the following formula:

[0053]

[0054] Wherein:

[0055] R is a rotation operation operator;

[0056] is the Pauli operator;

[0057] θ, φ are specific parameters, depending on m and n as follows;

[0058] m, n refer to the quantum state numbers before and after the transition (from 1 to 3);

[0059] When (m, n) = (1, 3) or (2, 1) or (3, 2), θ = π, φ = -π / 6;

[0060] When (m, n) = (1, 2) or (2, 3) or (3, 1), θ = π, φ = π / 6;

[0061] In other cases, θ = φ = 0.

[0062] Combining these single-qubit rotation operations can simulate the introduction of the chiral phase in the evolution of the Potts model. By precisely controlling the signals in the input channels to apply the above microwave pulse sequences to the Transmon qubits, these pulse sequences can introduce the chiral phase during the evolution of the qubits. If a comparison is needed, an experiment can be conducted without introducing this phase in another experiment, and then the phenomenon of dynamical quantum phase transition will not occur.

[0063] Evolution of the qubit: After introducing the chiral phase, let the qubit perform dynamical evolution according to the Hamiltonian. Under the above settings, this evolution process occurs naturally and is jointly determined by the Hamiltonian of the qubit and the applied microwave pulse sequences.

[0064] Measurement of the qubit: When the qubit evolves to a predetermined time point, sampling is performed according to the actual performance of the superconducting qubit chip, and then the reading is taken. Here, the dispersive readout method is mainly used, that is, the state of the Transmon qubit causes a small frequency shift in the resonant frequency of the coupled resonator. The specific operation is to apply a microwave probe signal to the resonator, whose frequency is close to but not equal to the resonant frequency of the resonator. This probe signal will interact with the resonator and be affected by the state of the qubit. Due to different qubit states, the resonant frequency of the resonator will have different shifts. According to this shift, the specific value can be read out, so as to obtain the magnitude of the inner product of the wave function at the current moment and the initial moment. The measurement process should be fast to ensure that the state of the qubit can be accurately captured. Repeat the above evolution and measurement processes multiple times according to the sampling plan to obtain sufficient data.

[0065] Finally, the rate function can be obtained from the above experimental results. It is observed from the data that when the phase exp(-iπ / 6) is introduced, non-analytical points appear in the rate function, which means that dynamical quantum phase transition phenomena will occur in the dynamical evolution of the system.

[0066] As described above, the above are only further embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the scope disclosed by the present invention, according to the technical solution and its concept of the present invention, makes equivalent substitutions or changes, all belong to the protection scope of the present invention.

Claims

1. A method for inducing dynamic quantum phase transition using chiral phase, characterized in that: The steps include: Step 1: Cool the Transmon superconducting quantum bit chip to near absolute zero using a dilution refrigerator; Step 2: Naturally relax for 50 microseconds at near absolute zero to prepare each quantum bit to the ground state; Step 3: Combine the single-qubit rotation operations to simulate the introduction of chiral phases in the evolution of the Potts model; Step 4: After introducing the chiral phase, let the quantum bit evolve dynamically according to the Hamiltonian; Step 5: When the quantum bit evolves to a predetermined time point, sampling is performed based on the actual performance of the superconducting quantum bit chip, and then reading is performed; Step 6: The rate function is obtained through the above steps. By observing the data, it is found that when the exp(-iπ / 6) phase is introduced, non-analytical points appear in the rate function, and the dynamical quantum phase transition phenomenon in the dynamical evolution is observed.

2. The method of inducing dynamic quantum phase transition using chiral phase according to claim 1, characterized in that: In step one, the external control system is connected to the readout port input and output port of the Transmon quantum bit.

3. The method of inducing dynamic quantum phase transition using chiral phase according to claim 2, characterized in that: In step 2, the system corresponds to a ferromagnetic ground state, that is, the Potts model ground state corresponding to J=1, f=0.

4. The method of inducing dynamic quantum phase transition using chiral phase according to claim 3, characterized in that: In step 3, for the unitary operator τ acting on the monomer, the additional phase required is exp(-iπ / 6), while for the Hermitian conjugate of τ, the additional phase required is exp(iπ / 6); Through Ramsey interferometry, we know that the required frequencies for the transition of this system are: ω01 = 2π*5.355GHz, ω12 = 2π*5.127GHz; At the same time, it is also necessary to realize the rotation of a single quantum bit. The specific pulse signal required can be calculated by the following formula: in: R is a rotation operator; is the Pauli operator; θ, φ are specific parameters, depending on m and n as follows: m, n refers to the quantum state numbers before and after the transition from 1 to 3; When (m,n)=(1,3) or (2,1) or (3,2), θ=π, φ=-π / 6; When (m,n)=(1,2) or (2,3) or (3,1), θ=π, φ=π / 6; In other cases, θ=φ=0.

5. The method of inducing dynamic quantum phase transition using chiral phase according to claim 4, characterized in that: Step three also includes applying the above microwave pulse sequence to the Transmon qubit by precisely controlling the signal entering the channel. These pulse sequences can introduce chiral phases during the evolution of the qubit. If a control is needed, the dynamical quantum phase transition phenomenon will not occur if this phase is not introduced in other experiments.

6. The method of inducing dynamic quantum phase transition using chiral phase according to claim 5, characterized in that: In step 4, under the above settings, this evolution process occurs naturally and is determined by the Hamiltonian of the quantum bit and the applied microwave pulse sequence.

7. The method of inducing dynamic quantum phase transition using chiral phase according to claim 6, characterized in that: In step 5, the dispersion readout method is used, that is, the state of the Transmon quantum bit is used to produce a small frequency shift on the resonant frequency of the coupled resonant cavity; The specific operation is to apply a microwave probe signal to the resonant cavity, whose frequency is close to but not equal to the resonant frequency of the resonant cavity; This probe signal will interact with the resonant cavity and be affected by the state of the quantum bit. Due to the different states of the quantum bit, the resonant frequency of the resonant cavity will shift differently. The specific value can be read out based on the shift to obtain the inner product size of the wave function at the current moment and the initial moment. The above evolution and measurement process is repeated multiple times according to the sampling plan to obtain sufficient data.

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