Expectation value estimation method and apparatus in quantum system, device, and system

An expectation value estimation apparatus for a quantum system, comprising:

• a processor and a memory, the memory storing a computer program, the computer program being loaded and executed by the processor to implement:
• acquiring an output quantum state of n qubits, the output quantum states of the n qubits being obtained by an input quantum state of the n qubits through a noisy parameterized quantum circuit (PQC), n being a positive integer;
• acquiring a measurement result corresponding to the output quantum state of the n qubits, the measurement result comprising a plurality of bit strings obtained by measuring the n qubits in measurement bases corresponding to respective Pauli strings of a decomposition of a target function;
• and
• performing quantum error mitigation (QEM) on noise of the PQC, comprising:
• post-processing the measurement result by using a neural network configured to output, for each Pauli string of the decomposition, a corresponding estimated expectation value, to obtain expectation values of a plurality of Pauli strings, the plurality of Pauli strings being obtained by decomposing the target function;
• calculating an expectation value of the target function under the output quantum state of the n qubits according to the expectation values of the plurality of Pauli strings;
• adjusting a parameter of a target object until the expectation value of the target function converges, the target object comprising the neural network, wherein while adjusting parameters of the neural network, no additional executions of the PQC are performed and the same recorded measurement result is re-used before and after the parameter adjustment;
• and
• acquiring, when the expectation value of the target function satisfies a convergence condition, a convergent expectation value of the target function, the convergent expectation value being an expectation value that satisfies the convergence condition.

A non-transitory computer-readable storage medium, storing a computer program, the computer program being loaded and executed by a processor to implement:

• acquiring an output quantum state of n qubits, the output quantum states of the n qubits being obtained by an input quantum state of the n qubits through a noisy parameterized quantum circuit (PQC), n being a positive integer;
• acquiring a measurement result corresponding to the output quantum state of the n qubits, the measurement result comprising a plurality of bit strings obtained by measuring the n qubits in measurement bases corresponding to respective Pauli strings of a decomposition of a target function;
• and
• performing quantum error mitigation (QEM) on noise of the PQC, comprising:
• post-processing the measurement result by using a neural network configured to output, for each Pauli string of the decomposition, a corresponding estimated expectation value, to obtain expectation values of a plurality of Pauli strings, the plurality of Pauli strings being obtained by decomposing the target function;
• calculating an expectation value of the target function under the output quantum state of the n qubits according to the expectation values of the plurality of Pauli strings;
• adjusting a parameter of a target object until the expectation value of the target function converges, the target object comprising the neural network, wherein while adjusting parameters of the neural network, no additional executions of the PQC are performed and the same recorded measurement result is re-used before and after the parameter adjustment;
• and
• acquiring, when the expectation value of the target function satisfies a convergence condition, a convergent expectation value of the target function, the convergent expectation value being an expectation value that satisfies the convergence condition.