Decomposition of Multi-Qubit Gates for Circuit Cutting

Abstract

A large-scale quantum circuit can be partitioned into multiple subcircuits through circuit cutting, where each subcircuit is executed multiple times and the expectation value of the original circuit is reconstructed by classical post-processing from their measurement (sampling) results. In this process, appropriate cut locations are identified after the user-designed quantum circuit, including multi-qubit gates that act on three or more qubits, has been decomposed into single-qubit gates and two-qubit gates such as the CNOT gate. Here, we present a method for reducing the sampling overhead, which refers to the increase in the number of samples required due to the cutting process, by modifying the decomposition strategy of multi-qubit gates. Using MCX and CCCX gates as representatives of multi-qubit gates, we demonstrate that the proposed decomposition method, which introduces a small number of ancilla qubits according to the identified cut locations, effectively decreases the sampling overhead.

Figures (12)

• Figure 1: Circuit cutting. A quantum circuit is partitioned into independently executable subcircuits along red line.
• Figure 2: Procedure for partitioning a quantum circuit and executing its subcircuits
• Figure 3: Conventional decomposition of CCCX gate
• Figure 4: Decomposition of CCCX gate using one ancilla qubit ($a$)
• Figure 5: Decomposition of CCCX gate using two ancilla qubits ($a_0$ and $a_1$) (dec2A)