WO2023142386A1 - Quantum bit frequency arrangement method - Google Patents

Abstract

Provided in the present disclosure is a quantum bit frequency arrangement method. A quantum bit operating frequency is set in a superconducting quantum bit system to realize a high-fidelity alternating-current CZ gate, and the superconducting quantum bit system comprises a plurality of quantum bits and quantum coupling units which are located between adjacent quantum bits. The quantum bit frequency arrangement method comprises: obtaining energy level structure parameters of superconducting quantum bits according to formant information of quantum bits; constructing an assessment function by means of the energy level structure parameters, so as to quantitatively assess advantages and disadvantages of a quantum bit energy level arrangement solution during multi-bit expansion; and determining, according to the assessment function, a bit operating frequency which avoids a frequency conflict.

Description

Quantum bit frequency arrangement method technical field

The disclosure belongs to the technical field of quantum computing, and in particular relates to a qubit frequency arrangement method, which realizes a high-fidelity AC CZ (Controlled-Z) gate by setting the qubit operating frequency in a superconducting qubit.

Background technique

Today is the initial stage of the development of quantum computer technology. How to realize the precise control of quantum systems is the focus of the development of quantum computing. Superconducting quantum chips realized by superconducting qubits are currently one of the most effective physical platforms for quantum computing. How to use electrical pulses to achieve high-precision regulation of superconducting quantum chips is the core technology and challenge to improve the precision of quantum manipulation.

In the method of realizing the CZ gate by applying AC microwave on the quantum coupler, due to the nonlinear characteristics of the magnetic flux change and the coupling strength change of the coupler, multiple frequency components other than the driving frequency will be generated. These frequency components may be on some unnecessary resonance levels, causing a decrease in quantum fidelity. Therefore, how to reasonably arrange and set the operating frequency of superconducting qubits, so that superconducting qubits can realize high-fidelity CZ gates, is an urgent technical issue to be solved.

Contents of the invention

The present disclosure provides a method for arranging qubit frequency. The qubit operating frequency is set in a superconducting qubit system to realize a high-fidelity AC CZ gate. The superconducting qubit system includes a plurality of qubits and is located between adjacent qubits. The qubit frequency arrangement method includes: obtaining the energy level structure parameters of the superconducting qubit according to the resonant peak information of the qubit; constructing an evaluation function through the energy level structure parameters to quantitatively evaluate the qubit energy when multi-bit expansion The advantages and disadvantages of the level arrangement scheme; and determine the bit operating frequency to avoid frequency conflicts according to the evaluation function.

Optionally, the energy level structure parameters include anharmonicity parameters; and an adjustment curve of the coupling strength varying with the magnetic flux of the superconducting quantum interferometer loop in the coupling unit.

Optionally, the expression of the anharmonicity parameter η is: η=f ₁₂ -f ₀₁ ;

Among them, f ₁₂ is the eigenfrequency difference between qubit |1> state and |2> state, and f ₀₁ is the eigenfrequency difference between qubit |0> state and |1> state.

Optionally, the adjustment curve is expressed as g(t)/2π, then g(t)/2π=h(Φ _p (t)/Φ ₀ );

Among them, Φ _P (t)/Φ ₀ is the amount of change in magnetic flux, and h is the mapping relationship between coupling strength and magnetic flux.

Optionally, the evaluation function is expressed as:

Among them, Δ=f _{01, Q1} -f _{01, Q2} , ω _target =η±Δ,

Δ is the frequency difference between |01> and |10>; ω _target is the frequency difference between |11> and |20> or |11> and |02>; Δ _Lea is the frequency difference between |11> and |02> or |11> and The frequency difference of |20＞;

Indicates the error caused by the proximity of |11> and |20> or |11> and |02>,

is the error estimate introduced by the interaction of |01>, |10>,

is the error estimate introduced by the interaction between |11> and |02> or |11> and |20>; a ₁ , a ₂ , and a ₃ are weight coefficients respectively; when the microwave pulse of ω _target is applied in the quantum coupler , due to the nonlinear relationship between the flux change and the equivalent coupling strength, the equivalent coupling strength g/2π will have a frequency component of nω _target , n is a natural number, and C _n is the equivalent coupling versus time curve g(t) The driving strength of /2π at the nω _target frequency is determined by the adjustment curve of the quantum coupler and the duration of the AC CZ gate.

Optionally, the choice of the sign of F _± depends on whether ω _target is η+Δ or η+Δ; F ₊ corresponds to the case of ω _target =η+Δ, and F ₋ corresponds to the case of ω _target =η-Δ.

Optionally, F=min(F ₊ , F ₋ ) is selected as the final evaluation function of different bit frequency arrangement schemes.

Optionally, by optimizing the frequencies of all qubits, all accumulations can be made to obtain the minimum double-bit gate evaluation function F _2Q =∑F _CZ,i , where F _CZ,i is the evaluation function of the i-th CZ gate, and i takes all The CZ gate realizes the optimization of the qubit operating frequency distribution of the AC double-bit gate, and finally obtains the bit frequency arrangement.

The qubit frequency arrangement method disclosed in the present disclosure can quantitatively evaluate the influence of two bit frequency differences on a double-bit gate (AC CZ gate); it can quantitatively evaluate the impact of different frequency distribution schemes on two-dimensional network qubit arrays in a two-dimensional network qubit array. The comprehensive influence of all the AC CZ gates in the dimensional grid qubit array; the goal of optimizing the performance of the AC CZ gates can be achieved, so that all the AC CZ gates in the two-dimensional grid can work efficiently and accurately.

Description of drawings

FIG. 1 is a flowchart of a qubit frequency arrangement method according to an embodiment of the present disclosure;

2 is a schematic diagram of the energy level structure and interaction of a superconducting qubit according to an embodiment of the present disclosure;

FIG. 3 is a schematic diagram of the relationship between magnetic flux and equivalent coupling strength with time in the coupler according to an embodiment of the disclosure;

4 is a schematic diagram of the frequency domain component of the equivalent coupling strength and the magnetic flux of the quantum coupler according to an embodiment of the present disclosure; wherein the solid line on the left is the frequency domain component of the equivalent coupling strength, and the dotted line on the right is the frequency of the magnetic flux of the quantum coupler. Domain component;

FIG. 5 is a schematic diagram of potential frequency conflicts during application of an AC CZ gate according to an embodiment of the present disclosure;

FIG. 6 is a schematic diagram of a two-dimensional grid array qubit according to an embodiment of the present disclosure.

Detailed ways

This disclosure provides a qubit frequency arrangement method. According to the energy level structure characteristics of superconducting qubits, the qubit frequency arrangement method is proposed to avoid the potential frequency in the process of implementing CZ gates by applying AC microwaves through quantum couplers. Conflict issues. In a two-dimensional qubit array, how to set and distribute the frequency of each qubit is one of the technical problems to ensure the effective operation of the double-bit quantum gate. The energy level arrangement scheme proposed in the present disclosure can well solve this problem and improve the performance of parallel AC CZ gates in a two-dimensional qubit array.

Embodiments of the present disclosure will be further described below in conjunction with the accompanying drawings.

Fig. 1 is a flowchart of a qubit frequency arrangement method in an embodiment of the disclosure; Fig. 2 is a schematic diagram of the energy level structure and interaction of a superconducting qubit in an embodiment of the disclosure; Fig. 3 is a schematic diagram of a coupler in an embodiment of the disclosure A schematic diagram of the relationship between the magnetic flux and the equivalent coupling strength with time; FIG. 4 is a schematic diagram of the frequency domain components of the equivalent coupling strength and the quantum coupler magnetic flux of the embodiment of the present disclosure; The frequency domain component, the dotted line on the right is the frequency domain component of the magnetic flux of the quantum coupler; FIG. 5 is a schematic diagram of the potential frequency conflict of the AC CZ gate in the application process of the embodiment of the present disclosure; FIG. 6 is the two-dimensional network of the embodiment of the disclosure Schematic diagram of a lattice array qubit.

As shown in Figure 1 and Figure 2, the present disclosure provides a qubit frequency arrangement method, in which the operating frequency of the qubit is set in the superconducting qubit system to realize a high-fidelity AC CZ gate, and the superconducting qubit system includes multiple qubits Bits and quantum coupling units located between adjacent qubits, the qubit frequency arrangement method includes:

Operation S1: Obtain the energy level structure parameters of the superconducting qubit according to the resonant peak information of the qubit;

Operation S2: constructing an evaluation function through energy level structure parameters to quantitatively evaluate the pros and cons of the qubit energy level arrangement scheme during multi-bit expansion; and

Operation S3: Determine a bit operating frequency that avoids frequency conflicts according to the evaluation function.

In superconducting qubits, it is necessary to utilize the |2> energy level of the qubit to realize the CZ gate. In the experiment, the disclosure can obtain the anharmonicity and coupling strength of the qubit with the adjustment curve of the loop magnetic flux of the superconducting quantum interferometer of the coupling unit (collectively referred to as the energy of the superconducting qubit and the coupling unit) through the formant information of the qubit. level structure parameters). Among them, the anharmonicity of qubit is expressed as: η=f ₁₂ -f ₀₁ ; among them, f ₀₁ is the eigenfrequency difference between qubit |0> state and |1> state, and f ₁₂ is qubit |1> The eigenfrequency difference between the state and the |2> state.

The energy level frequency f _{01 of a qubit, Qi} (i=0, 1, 2...) is adjustable, and for two bits (defined as Q1 and Q2), the frequency difference is defined as Δ=f _{01, Q1} − f _{01, Q2} , ω _target = η±Δ,

Where Δ is the frequency difference between |01> and |10>; ω _target is the frequency difference between |11> and |20> or |11> and |02>; Δ _Lea is |11> and |02> or |11> The frequency difference with |20>; as shown in Figure 2, |11> and |20>, |11> and |02>, |01> and |10> will interact and potential frequency conflict.

The adjustment curve of the coupling strength with the loop magnetic flux of the superconducting quantum interferometer of the coupling unit is expressed as:

g(t)/2π＝h(Φ _p (t)/Φ ₀ );

Among them, g(t)/2π represents the coupling strength, h represents the mapping relationship between the coupling strength and the magnetic flux, Φ _P (t)/Φ ₀ represents the flux change, and the magnetic flux change Φ _P (t)/Φ ₀ Under the action, the coupling strength g/2π will also change with time. An example of the relationship between Φ _P (t)/Φ ₀ and g(t)/2π is shown in Figure 3. The solid line in the figure represents the coupling strength change curve, and the dotted line Indicates the flux change curve.

According to the embodiment of the present disclosure, when the sine wave of ω _target is applied in the quantum coupler, due to the nonlinear relationship between the amount of magnetic flux change and the equivalent coupling strength g/2π, g/2π will have a frequency component of nω _target , n =0, 1, 2, 3..., as shown in Figure 3, the solid line is the change of the equivalent coupling strength g(t)/2π with time, and the dotted line is the quantum coupler magnetic flux φ _p (t) with time The change. As shown in Figure 4, the solid line on the left is the frequency domain component of the equivalent coupling strength, and the dotted line on the right is the frequency domain component of the magnetic flux of the quantum coupler.

Select the qubit energy level frequency arrangement f _{01, Qi} , and calculate the corresponding frequency difference Δ, there are two optional ω _targets , and the frequency conflict of each ω _target is Δ=0, Δ _Lea =0, ω _target =0, n|ω _target |−|Δ|=0, n|ω _target |−|Δ _Lea |=0. It can be seen from the data in Figure 5 that when avoiding these frequency conflicts, it is relatively easy to realize a CZ gate with a fidelity higher than 99.99% in simulation.

In order to quantitatively evaluate the pros and cons of the qubit energy level arrangement scheme during multi-bit expansion, it is necessary to introduce an evaluation function for evaluating frequency conflicts to evaluate the pros and cons of the selection of the current operating point Δ.

in,

Indicates the error caused by |11>, |20> (or |11>, |02>) close to the frequency, a ₁ is the weight coefficient;

is the error estimate introduced by the interaction of |01>, |10>, a ₂ is the weight coefficient;

is the error estimate introduced by the interaction of |11>, |02> (or |11>, |20>); a ₃ is the weight coefficient; C _n is the equivalent coupling versus time curve g(t)/2π at The driving strength of the nω _target frequency is determined by the adjustment curve of the quantum coupler and the duration of the AC CZ gate. The choice of the sign of F _± depends on whether ω _target is η+Δ or η+Δ; F ₊ corresponds to the case of ω _target = η+Δ, and F _- corresponds to the case of ω _target = η-Δ. This disclosure selects F=min(F ₊ , F ₋ ) as the final evaluation function of different bit frequency arrangement schemes.

In the two-dimensional grid array bits shown in Figure 6, any two connected bits will generate a

Q _i and Q _j represent different bits. By optimizing the frequency of all qubits, the accumulation of all F can obtain the double-bit gate evaluation function

The smallest one can realize the optimization of the qubit operating frequency distribution of the AC double-bit gate, and finally obtain the bit frequency arrangement f _01,Qi .

In actual operation, the influence of single-bit gate or decoherence will also be considered. At this time, it is only necessary to accumulate other evaluation functions and double-bit gate evaluation functions to obtain a comprehensive evaluation function, and comprehensively optimize the frequency distribution of qubits so that the overall performance of qubits best.

In summary, the present disclosure provides a qubit frequency arrangement method, which can quantitatively evaluate the influence of two bit frequency differences on a double-bit gate (AC CZ gate), and quantitatively evaluate the qubit array in a two-dimensional network. , the combined effect of different frequency distribution schemes on all ac CZ gates in a 2D grid qubit array. The goal of optimizing the performance of AC CZ gates is achieved by optimizing the frequency distribution of qubits in the array, so that all AC CZ gates in the two-dimensional grid can work efficiently and accurately.

The specific implementation manners of the present disclosure described above are not intended to limit the protection scope of the present disclosure. Any other corresponding changes and modifications made according to the technical concepts of the present disclosure shall be included in the protection scope of the claims of the present disclosure.

Claims (8)

1. A qubit frequency arrangement method, the qubit operating frequency is set in a superconducting qubit system to achieve high-fidelity AC CZ gates, the superconducting qubit system includes a plurality of qubits and adjacent qubits Quantum coupling unit, the qubit frequency arrangement method includes:

   According to the resonant peak information of the qubit, the energy level structure parameters of the superconducting qubit are obtained;

   Constructing an evaluation function through the energy level structure parameters to quantitatively evaluate the pros and cons of the qubit energy level arrangement scheme during multi-bit expansion; and

   A bit operating frequency that avoids frequency conflicts is determined according to the evaluation function.
2. According to the qubit frequency arrangement method according to claim 1, the energy level structure parameters include:

   anharmonicity parameter; and

   Tuning curves of coupling strength as a function of flux in the superconducting quantum interferometer loop in the coupling cell.
3. According to the qubit frequency arrangement method according to claim 2, the expression of the anharmonicity parameter n is:

   η=f ₁₂ -f ₀₁ ;

   Among them, f ₁₂ is the eigenfrequency difference between qubit |1> state and |2> state, and f ₀₁ is the eigenfrequency difference between qubit |0> state and |1> state.
4. According to the qubit frequency arrangement method according to claim 2, the adjustment curve is expressed as g(t)/2π:

   g(t)/2π＝h(Φ _p (t)/Φ ₀ );

   Among them, Φ _P (t)/Φ ₀ is the amount of change in magnetic flux, and h is the mapping relationship between coupling strength and magnetic flux.
5. According to the qubit frequency arrangement method according to claim 1, the evaluation function is expressed as:

   

   Among them, Δ=f _{01, Q1} -f _{01, Q2} , ω _target =η±Δ,

   

   Δ is the frequency difference between |01> and |10>; ω _target is the frequency difference between |11> and |20> or |11> and |02>; Δ _Lea is the frequency difference between |11> and |02> or |11> and The frequency difference of |20＞;

   

   Indicates the error caused by the proximity of |11> and |20> or |11> and |02>,

   

   is the error estimate introduced by the interaction of |01>, |10>,

   

   is the error estimate introduced by the interaction between |11> and |02> or |11> and |20>; a ₁ , a ₂ , and a ₃ are weight coefficients respectively; when the microwave pulse of ω _target is applied in the quantum coupler , due to the nonlinear relationship between the flux change and the equivalent coupling strength, the equivalent coupling strength g/2π will have a frequency component of nω _target , n is a natural number, and C _n is the equivalent coupling versus time curve g(t) The driving strength of /2π at the nω _target frequency is determined by the adjustment curve of the quantum coupler and the duration of the AC CZ gate.
6. According to the quantum bit frequency arrangement _method described _in claim 5, the sign selection of F _± depends on ω _target being η+ _Δ or η+Δ; Take the case of ω _target =η-Δ.
7. According to the qubit frequency arrangement method according to claim 6, F=min(F ₊ , F ₋ ) is selected as the final evaluation function of different bit frequency arrangement schemes.
8. According to the qubit frequency arrangement method described in any one of claims 1-7, by optimizing the frequency of all qubits, all accumulations are obtained to obtain a double-bit gate evaluation function F _2Q =∑ F _{CZ, i is} the smallest, where F _{CZ, i} is the evaluation function of the i-th CZ gate, i takes all the CZ gates, realizes the optimization of the qubit operating frequency distribution of the AC double-bit gate, and finally obtains the bit frequency arrangement.

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