CN112418429A - Method and system for realizing CZ door - Google Patents
Method and system for realizing CZ door Download PDFInfo
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Abstract
A method and system for implementing a CZ door, comprising: s1, preparing a single quantum state of |00>, | 01>, |10>, |11> or a superposition state of a plurality of quantum states on two qubits, wherein at least one of the two qubits is provided with a Z-line; s2, defining a waveform function, and generating a voltage signal according to the waveform function, wherein the voltage signal is a voltage signal which enables quantum state |11> and quantum state |20> in two qubits to be aligned in energy level so as to realize the exchange probability of the quantum state |11> and the quantum state |20 >; s3, loading the voltage signal to the Z line to make the quantum state |11> the accumulated phase pi in the two quantum bits, and realizing the CZ gate; s4, measuring the fidelity of the CZ door, and adjusting the coefficient defining the wave function according to the measurement result to adjust the fidelity of the CZ door to be above a preset value. The method can realize the CZ gate with the fidelity of more than 99.5 percent, and the wave function definition method can improve the working efficiency of the quantum bit and realize the large-scale quantum computation.
Description
Technical Field
The invention relates to the field of quantum computers, in particular to a method and a system for realizing a CZ gate.
Background
The core of a quantum computing processor is a qubit. The performance of the processor is embodied in both the number of qubits and the performance of the qubits. The indicators of quantum-rate performance are the fidelity of a single-bit gate and the fidelity of a two-bit gate. Of the various two-bit door operations, the CZ door is one of particular importance. All qubit gate operations can be implemented with a combination of single-bit gates and two-bit CZ gates. In a practical qubit system, implementing a high fidelity CZ gate is one of the most important measurement control techniques. It is therefore particularly important to propose a method for realizing high fidelity CZ doors.
Disclosure of Invention
Technical problem to be solved
In view of the above technical problems, the present invention provides a method and system for implementing a CZ door, which is used to implement a CZ door with a fidelity higher than 99%.
(II) technical scheme
One aspect of the present invention provides a method for implementing a CZ door, comprising: s1, preparing two qubits, wherein at least one of the two qubits is provided with a Z-line; s2, defining a waveform function, and generating a voltage signal according to the waveform function, wherein the voltage signal is a voltage signal which makes the energy levels of quantum state |11> and quantum state |20> in two qubits align to realize the exchange probability of quantum state |11> and quantum state |20 >; and S3, loading the voltage signal to the Z line, and accumulating the quantum state |11> in the two quantum bits by the phase pi to realize the CZ gate.
Optionally, in step S2, defining the waveform function includes: the wave function is defined in terms of coefficients of the low frequency term and the double frequency term of the fourier function.
Optionally, the waveform function is defined by coefficients of low frequency terms with a number of selection terms not exceeding 5 and coefficients of low frequency terms and double frequency terms with a total number of low frequency terms and double frequency terms not exceeding 10.
Optionally, in step S1, a single quantum state of the four quantum states |00>, 01>, |10>, |11> or a superposition of multiple quantum states is prepared on the two qubits.
Optionally, the voltage signal is filtered by a low pass filter and then loaded onto the Z-line.
Optionally, after step S3, the method includes: s4, measuring the fidelity of the CZ door, and adjusting the coefficient defining the wave function according to the measurement result, thereby adjusting the fidelity of the CZ door to be above a preset value.
In another aspect, the present invention provides a system for implementing a CZ door, comprising: the quantum bit system comprises two quantum bits, wherein at least one of the two quantum bits is provided with a Z line, and the two quantum bits are provided with a single quantum state of |00>, 01>, |10>, |11> four quantum states or a superposition state of a plurality of quantum states; and the signal generator is used for outputting a voltage signal to the Z line according to the waveform function so as to enable the quantum state |11> in the two qubits to accumulate the phase pi and realize the CZ gate, wherein the voltage signal is the voltage signal which enables the energy levels of the quantum state |11> and the quantum state |20> in the two qubits to be aligned so as to realize the exchange probability of the quantum state |11> and the quantum state |20 >.
Optionally, the signal generator outputs the voltage signal according to a wave function defined by coefficients of a low frequency term and a double frequency term of a fourier function.
Optionally, the waveform function is defined to select coefficients of low-frequency terms with the number of terms not exceeding 5 and coefficients of low-frequency terms and double-frequency terms with the total number of terms not exceeding 10.
Optionally, the system for implementing a CZ door further comprises: and the low-pass filter is connected with the Z line and used for filtering the voltage signal and loading the voltage signal to the Z line.
(III) advantageous effects
The invention provides a method and a system for realizing a CZ door, which have the beneficial effects that:
the method is characterized in that a quantum two-bit system with a Z line is adopted to prepare at least one quantum bit of a single quantum state with |00>, 01>, |10>, |11> four quantum states or a superposition state of a plurality of quantum states, a wave function is quickly defined according to coefficients of a low-frequency term and a frequency doubling term of a Fourier function, a voltage signal is generated and loaded onto the Z line, so that the quantum state |11> in the two quantum bits is accumulated in a phase pi, and the CZ gate with the fidelity of more than 99% can be realized. And the method for defining the wave function can improve the time efficiency of realizing the CZ gate by the wave, namely, the time for realizing the CZ gate is shortened, and the large-scale quantum computation is realized.
Drawings
FIG. 1 schematically illustrates a flow chart of a method of implementing a CZ door in accordance with an embodiment of the present invention.
Fig. 2 schematically illustrates a graph of the quantization energy levels of two qubits as a function of the Z-line in accordance with an embodiment of the present invention.
Fig. 3 is a graph schematically illustrating the probability of two qubits being in an energy eigenstate versus time according to an embodiment of the invention.
Fig. 4 schematically shows a path diagram of the evolution of quantum states of two qubits on a bloch sphere according to an embodiment of the present invention.
Fig. 5 schematically shows a waveform diagram defining a waveform function according to an embodiment of the present invention.
FIG. 6 schematically illustrates a pulse sequence chart for measuring CZ gate fidelity in accordance with an embodiment of the present invention
Fig. 7 is a diagram schematically illustrating an optimization process after coefficient fine tuning when 6 coefficients are adopted in the embodiment of the present invention.
FIG. 8 is a process diagram schematically illustrating the optimization of a CZ gate during the fine tuning of coefficients according to an embodiment of the present invention.
Fig. 9 is a waveform diagram schematically illustrating a waveform function after coefficient optimization according to an embodiment of the present invention.
Figure 10 schematically illustrates a graph of the actual effect of measuring the fidelity of a CZ door achieved by the method provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
An embodiment of the present invention provides a method for implementing a CZ door, where the CZ door has a fidelity of 99% or more, as shown in fig. 1, the method includes:
s1, preparing two qubits, wherein at least one of the two qubits is provided with a Z-line.
To implement a CZ gate, bits having an XY line and a Z line structure may be employed. Where the XY lines are capable of providing microwave photons. The Z-line can change the energy level of the qubit (i.e., the optimum frequency at which a photon can be absorbed). For operation of a CZ gate, at least one bit is required to have a Z line. In the above operation S1, a single quantum state of the four quantum states or a superposition state of multiple quantum states is prepared |00>, 01>, |10>, |11> on two qubits, at least one of the two qubits having a Z-line.
S2, defining a waveform function, and generating a voltage signal according to the waveform function, wherein the voltage signal is a voltage signal that aligns quantum state |11> and quantum state |20> in two qubits in energy level to achieve a probability of exchanging quantum state |11> with quantum state |20 >.
To implement the CZ gate, the two qubits prepared in step S1 are subjected to non-adiabatic evolution, as shown in fig. 2, where the stress state low and stress state high represent the high-energy and low-energy eigenstates for the formation of the two quantum states involved in the interaction. Non-adiabatic evolution refers to the quantum system always being in an eigenstate when the voltage signal applied on the Z line changes the energy level slowly enough. In one embodiment of the present invention, to implement a CZ gate, a voltage signal corresponding to that shown in fig. 3 is applied to the Z line. The quantum system now undergoes a non-adiabatic process, i.e., the quantum state proceeds from the |11> state along the dashed line. If an appropriate voltage signal can be applied to the Z-line, the quantum state undergoes quantum evolution near the intersection of the two dashed lines and a pi phase is obtained, and the |11> quantum state evolves on the bloch sphere as shown in fig. 4.
The voltage signal is output by the signal generator according to a defined waveform function, in an embodiment of the invention, the waveform function is defined according to the low-frequency item and the double-frequency item of the Fourier function, the low-frequency item coefficient with the item number not more than 5 and the low-frequency item and the double-frequency item coefficient with the total item number not more than 10 are selected to define the waveform function, so that the voltage signal output by the signal generator according to the waveform function is an appropriate voltage signal, two qubits can be subjected to non-adiabatic evolution, the energy levels of a quantum state |11> and a quantum state |20> in the two qubits are aligned, the energy levels of the quantum state |11> and the quantum state |20> pass through an alignment point for multiple times, the probability of exchanging the quantum state |11> and the quantum state |20> is realized, and the CZ gate is realized. The waveform of the defined waveform function is shown in fig. 5, and the probability of two qubits being in the energy eigenstate varies with time is shown in fig. 3. The coefficient may be any number, and may be a complex number within 10 without loss of generality. The method for defining the wave function can improve the time efficiency of realizing the CZ gate by the wave and realize the large-scale quantum computation.
And S3, loading the voltage signal to the Z line, and accumulating the quantum state |11> in the two quantum bits by the phase pi to realize the CZ gate.
In operation S3, after the voltage signal is outputted by the signal generator according to the defined waveform function, the voltage signal is filtered by the low-pass filter and then loaded onto the Z-line, at this time, the quantum state |11> in two qubits is accumulated in the phase pi, and the other quantum states are not affected, so as to adjust the bit back to the original operating point, which is the voltage value with the bit frequency equal to the idle and the single-bit gate time frequency, to implement the CZ gate.
S4, measuring the fidelity of the CZ door, and adjusting the coefficient defining the wave function according to the measurement result, thereby adjusting the fidelity of the CZ door to be above a preset value.
The pulse sequence shown in fig. 6 is used to measure the fidelity of the CZ gate, and according to the measurement results, the coefficients defining the wave function are fine-tuned by using the expected effects shown in fig. 7 and 8, and the wave function is optimized, until the CZ fidelity reaches the expected value, the values of 1 or several parameters can be fine-tuned, the final result of the optimized wave function is shown in fig. 9, and the length of the wave function in fig. 9 is 40 ns. In practical physical devices, the voltage pulse often has a rising edge and a falling edge, and the 2ns rising edge and falling edge in fig. 9 do not affect the effectiveness of the CZ gate.
Fig. 10 is a graph showing the actual effect of accurately measuring the fidelity of a CZ door implemented by the method provided in the embodiment of the present invention, and it can be seen from the graph that the fidelity of a CZ door reaches more than 99.5%.
An embodiment of the present invention provides a system for implementing a CZ door, including:
a qubit system includes two qubits, wherein at least one of the two qubits has a Z-line, and the two qubits are prepared with a single quantum state of four quantum states of |00>, 01>, |10>, |11> or a superposition state of multiple quantum states.
And the signal generator is used for outputting a voltage signal to the Z line according to the waveform function so as to enable the quantum state |11> in the two qubits to accumulate the phase pi and realize the CZ gate, wherein the voltage signal is the voltage signal which enables the energy levels of the quantum state |11> and the quantum state |20> in the two qubits to be aligned so as to realize the exchange probability of the quantum state |11> and the quantum state |20 >. In one embodiment of the invention, the signal generator outputs the voltage signal according to a wave function defined by coefficients of a low frequency term and a double frequency term of a fourier function. And defining the coefficients of the low-frequency terms of which the number of terms selected by the waveform function does not exceed 5 and the coefficients of the low-frequency terms and the frequency doubling terms of which the total number of terms is not more than 10. The signal generator is an arbitrary waveform generator, and in one embodiment of the present invention, the waveform generator is a digital signal generator capable of digital frequency modulation and amplitude modulation.
And the low-pass filter is connected with the Z line and used for filtering the voltage signal and loading the voltage signal to the Z line.
The actual effect of the fidelity measurement of a CZ door implemented by this system is shown in fig. 10, from which it can be seen that the achieved CZ door has a fidelity of above 99.5%.
In summary, the present invention provides a method and a system for implementing a CZ gate, which employ a quantum two-bit system in which at least one qubit of a single quantum state or a superposition state of multiple quantum states with |00>, 01>, |10>, |11> four quantum states has a Z line, and rapidly define a waveform function according to coefficients of a low frequency term and a frequency doubling term of a fourier function, generate a voltage signal to be loaded onto the Z line, so that the quantum state |11> in the two quantum bits is accumulated in a phase pi, thereby implementing a CZ gate with a fidelity of 99.5% or more. And the method for defining the wave function can improve the time efficiency of realizing the CZ gate by the wave and realize the large-scale quantum computation.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A method of implementing a CZ door, comprising:
s1, preparing two qubits, wherein at least one of the two qubits is provided with a Z-line;
s2, defining a waveform function, and generating a voltage signal according to the waveform function, wherein the voltage signal is the voltage signal which enables quantum state |11> and quantum state |20> in the two qubits to be aligned in energy level so as to realize the exchange probability of quantum state |11> and quantum state |20 >;
and S3, loading the voltage signal to the Z line, and enabling a quantum state |11> in the two quantum bits to accumulate a phase pi to realize the CZ gate.
2. The method of claim 1, wherein in step S2, defining a wave function comprises:
the wave function is defined in terms of coefficients of the low frequency term and the double frequency term of the fourier function.
3. The method of claim 2, wherein said waveshape function is defined by coefficients of said low frequency terms having a number of selected terms not exceeding 5 and coefficients of said low frequency terms and double frequency terms having a total number of terms not exceeding 10.
4. The method of claim 1, wherein in step S1, a single quantum state of four quantum states |00>, 01>, |10>, |11> or a superposition of multiple quantum states is prepared on two qubits.
5. The method of claim 1, wherein the voltage signal is filtered by a low pass filter and then loaded onto the Z line.
6. The method of implementing a CZ door of claim 2, comprising, after step S3:
s4, measuring the fidelity of the CZ door, and adjusting the coefficient defining the wave function according to the measurement result, thereby adjusting the fidelity of the CZ door to be above a preset value.
7. A system for implementing a CZ door, comprising:
the quantum bit system comprises two quantum bits, wherein at least one of the two quantum bits is provided with a Z line, and a single quantum state of four quantum states of |00>, 01>, |10>, |11> or a superposition state of a plurality of quantum states is prepared on the two quantum bits;
and the signal generator is used for outputting a voltage signal to the Z line according to a waveform function so as to enable a quantum state |11> in the two qubits to accumulate a phase pi and realize a CZ gate, wherein the voltage signal is the voltage signal which enables the quantum state |11> and the quantum state |20> in the two qubits to be aligned in energy level so as to realize the exchange probability of the quantum state |11> and the quantum state |20 >.
8. The system of claim 7, wherein the signal generator outputs the voltage signal according to a wave function defined by coefficients of a low frequency term and a double frequency term of a Fourier function.
9. The system of claim 8, wherein said waveform function is defined to select coefficients for said low frequency terms having a number of terms not exceeding 5 and coefficients for said low frequency terms and double frequency terms having a total number of terms not exceeding 10.
10. The system of claim 7, wherein the system of implementing a CZ door further comprises:
and the low-pass filter is connected with the Z line and used for filtering the voltage signal and loading the voltage signal to the Z line.
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