Decoding-based method for quantum circuit optimization

A computing system for optimizing a quantum circuit, comprising:

• a memory device that stores a first digital form of an initial quantum circuit expressed as a sequence of CNOT and RZ gates;
• a processor device that obtains and analyzes the first digital form to determine an ordered set or vector of phase coefficients and to specify a linear permutation;
• the processor device determines a sequence of CNOT and RZ gates using the set of phase coefficients and the linear permutation, such that the number of RZ gates is reduced;
• the processor device subsequently computes a second digital form of a new quantum circuit;
• and
• the memory devices stores the second digital form.

A process of producing a quantum circuit, comprising:

• obtaining a digital form of an initial n-qubit quantum circuit expressed over CNOT and RZ gates;
• a computer analyzing the digital form of the initial quantum circuit to obtain a set of phase coefficients and a linear permutation;
• the computer determining a sequence of CNOT and RZ gates using the set of phase coefficients and the linear permutation, and computing a digital form of a new n-qubit quantum circuit from the sequence having a reduced number of RZ gates compared to the initial quantum circuit, and the new quantum circuit performing the same function as the initial quantum circuit;
• and
• executing physical CNOT and RZ transformations in a quantum computer in accordance with the digital form of the new quantum circuit.

A system of producing a quantum circuit, comprising:

• a binary computer in data communication with a quantum computer;
• the binary computer comprising a memory device that stores a digital form of an initial n-qubit quantum circuit expressed over CNOT and RZ gates;
• the binary computer comprising a processor device to:
• analyze the digital form of the initial quantum circuit to obtain a set of phase coefficients and a linear permutation;
• determine a sequence of CNOT and RZ gates using the set of phase coefficients and the linear permutation, and compute a digital form of a new n-qubit quantum circuit from the sequence having a reduced number of RZ gates compared to the initial quantum circuit, and the new quantum circuit performing the same function as the initial quantum circuit;
• the binary computer further comprising a communication device to transmit the digital form of the new quantum circuit to the quantum computer;
• the quantum computer comprising a communication device to receive the digital form of the new quantum circuit;
• and
• the quantum computer comprising devices to execute physical CNOT and RZ transformations in the quantum computer in accordance with the digital form of the new quantum circuit.