LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach

TL;DR

LEAP is an incremental quantum circuit synthesis algorithm that enhances scalability and efficiency, enabling faster compilation and reduced gate counts for multi-qubit circuits by narrowing search spaces and re-optimizing iteratively.

Contribution

LEAP introduces an incremental approach to numerical optimization-based circuit synthesis, significantly improving scalability and performance over prior methods like QSearch.

Findings

LEAP compiles four-qubit unitaries up to 59x faster than QSearch.

LEAP reduces CNOT counts by up to 36x compared to CQC Tket.

LEAP generates optimal circuits for many known solutions despite heuristics.

Abstract

While showing great promise, circuit synthesis techniques that combine numerical optimization with search over circuit structures face scalability challenges due to a large number of parameters, exponential search spaces, and complex objective functions. The LEAP algorithm improves scaling across these dimensions using iterative circuit synthesis, incremental re-optimization, dimensionality reduction, and improved numerical optimization. LEAP draws on the design of the optimal synthesis algorithm QSearch by extending it with an incremental approach to determine constant prefix solutions for a circuit. By narrowing the search space, LEAP improves scalability from four to six qubit circuits. LEAP was evaluated with known quantum circuits such as QFT and physical simulation circuits like the VQE, TFIM, and QITE. LEAP can compile four qubit unitaries up to $59\times$ faster than QSearch and five and six qubit unitaries with up to $1.2\times$ fewer CNOTs compared to the QFAST package. LEAP can reduce the CNOT count by up to $36\times$, or $7\times$ on average, compared to the CQC Tket compiler. Despite its heuristics, LEAP has generated optimal circuits for many test cases with a priori known solutions. The techniques introduced by LEAP are applicable to other numerical-optimization-based synthesis approaches.