Thermalized state preparation method under quantum system, device and storage medium

A thermalized state preparation apparatus under a quantum system, comprising a memory for storing instructions and a processor for executing the instructions to:

• acquire a transformation process performed by a parameterized quantum circuit on an input quantum state of combined qubits, and then measure an output quantum state of the parameterized quantum circuit for n times to obtain n sets of measurement results, wherein
• the combined qubits include auxiliary qubits and system qubits of a target quantum system, and each set of measurement results includes:
• first measurement results corresponding to the system qubits, and
• second measurement results corresponding to the auxiliary qubits, wherein n is a positive integer and the first measurement results and the second measurement results are in a one-to-one mapping;
• process the second measurement results through a neural network to obtain weight parameters, wherein the weight parameters are used to characterize a probability in a mixed state of the target quantum system;
• compute a correlation function value of the mixed state of the target quantum system based on the weight parameters and the first measurement results;
• compute an expected value of an objective function based on the correlation function value of the mixed state;
• adjust variational parameters by taking an expected value convergence of the objective function as a goal, wherein the variational parameters include at least one of:
• parameters of the parameterized quantum circuit, or
• parameters of the neural network;
• and
• under a condition that the expected value of the objective function satisfies a convergence condition, the mixed state of the target quantum system to characterize a thermalized state of the target quantum system.

A thermalized state preparation system under a quantum system, comprising:

• a parameterized quantum circuit;
• and
• a computer device, wherein the parameterized quantum circuit is configured to perform a transformation process on an input quantum state of combined qubits to obtain an output quantum state of the parameterized quantum circuit, the combined qubits comprise auxiliary qubits and system qubits of a target quantum system, the computer device is configured to:
• acquire and measure the output quantum state of the parameterized quantum circuit for n times to obtain n sets of measurement results, wherein
• each set of measurement results comprises:
• first measurement results corresponding to the system qubits,
• second measurement results corresponding to the auxiliary qubits, wherein n is a positive integer and the first measurement results and the second measurement results are in a one-to-one mapping;
• process the second measurement results through a neural network to obtain weight parameters, wherein the weight parameters are used to characterize a probability in a mixed state of the target quantum system;
• compute a correlation function value of the mixed state of the target quantum system based on the weight parameters and the first measurement results;
• compute an expected value of an objective function based on the correlation function value of the mixed state;
• adjust variational parameters by taking an expected value convergence of the objective function as a goal;
• and
• acquire, under a condition that the expected value of the objective function satisfies a convergence condition, the mixed state of the target quantum system to characterize a thermalized state of the target quantum system, wherein the variational parameters comprise at least one of:
• parameters of the parameterized quantum circuit, or parameters of the neural network.