Efficient quantum circuit synthesis for SAT-oracle with limited ancillary qubit

TL;DR

This paper introduces two efficient algorithms for synthesizing SAT-oracles in quantum computing, optimizing the use of ancillary qubits and circuit depth, which are crucial for resource-limited quantum hardware.

Contribution

The paper presents novel algorithms that significantly reduce ancillary qubits and circuit depth for SAT-oracle synthesis compared to prior methods.

Findings

Ancilla qubits reduced to 2√m with up to 8x circuit size increase

Ancilla qubits further reduced to 3 with quadratic circuit size increase

Circuit depth reduced to O(log m) using the second algorithm

Abstract

How to implement quantum oracle with limited resources raises concerns these days. We design two ancilla-adjustable and efficient algorithms to synthesize SAT-oracle, the key component in solving SAT problems. The previous work takes 2m-1 ancillary qubits and O(m) elementary gates to synthesize an m clauses oracle. The first algorithm reduces the number of ancillary qubits to 2\sqrt{m}, with at most an eightfold increase in circuit size. The number of ancillary qubits can be further reduced to 3 with a quadratic increase in circuit size. The second algorithm aims to reduce the circuit depth. By leveraging of the second algorithm, the circuit depth can be reduced to O(log m) with m ancillary qubits.