Method for reducing quantum circuit depth for amplitude estimation

A quantum computing system configured to perform a quantum computational task, the quantum computing system comprising:

• a quantum computer comprising:
• an array of qubits;
• at least one quantum circuit comprising one or more quantum gates configured to act on the qubits to generate processed qubits;
• and
• at least one measuring device configured to determine states of the processed qubits to generate measurement data;
• and
• a classical computing system in communication with the quantum computer, the classical computing system comprising a non-transitory memory configured to store specific computer-executable instructions and a hardware processor in communication with the non-transitory memory, wherein the hardware processor is configured to execute the specific computer-executable instructions to at least:
• receive input data,
• prepare the array of qubits based at least in part on the input data;
• configure the at least one quantum circuit, based at least in part on the input data, to execute at least a series of quantum operations on the array of qubits to generate final processed qubits;
• perform at least a first variational approximation after at least a first sequence of quantum operations of the series of quantum operations, to generate a first variational quantum state based at least in part on the measurement data generated after the first sequence of quantum operations;
• execute, using at least the first variational quantum state, at least a second sequence of quantum operations of the series of quantum operations to generate the final processed qubits;
• and
• generate output data using the final processed qubits;
• wherein performing the first variational approximation reduces quantum noise arising from performing the quantum computational task and generating the output data compared to quantum noise arising from performing the quantum computational task and generating the output data without performing the first variational approximation.