[Paper Review] LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach

Ethan Smith, Marc Davis+4 more|arXiv (Cornell University)|Jun 21, 2021

Quantum Computing Algorithms and Architecture54 references42 citations

TL;DR

LEAP introduces an incremental, scalable approach to numerical optimization-based quantum circuit synthesis by combining prefix-based search, incremental re-synthesis, dimensionality reduction, and multistart optimization. It accelerates four-qubit unitary compilation up to 59× compared to QSearch and reduces CNOT counts by up to 36× compared to Tket, while achieving optimal or near-optimal depth for circuits up to six qubits on NISQ devices.

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 $59 imes$ faster than QSearch and five and six qubit unitaries with up to $1.2 imes$ fewer CNOTs compared to the QFAST package. LEAP can reduce the CNOT count by up to $36 imes$, or $7 imes$ 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.

Motivation & Objective

• To address scalability challenges in numerical optimization-based quantum circuit synthesis, particularly for NISQ-era devices with limited qubit coherence and gate fidelity.
• To reduce the exponential search space and high-dimensional parameter optimization inherent in circuit structure and function synthesis.
• To improve solution quality and runtime efficiency by integrating incremental re-synthesis, dimensionality reduction, and multistart numerical optimization.
• To enable synthesis of circuits up to six qubits with optimal or near-optimal depth and CNOT count, surpassing existing tools like QSearch, QFAST, and Tket.

Proposed method

• Employs an iterative, prefix-based search strategy that limits backtracking depth and coarsens search granularity, pruning the solution space using execution-driven heuristics.
• Applies incremental re-synthesis by re-optimizing disjoint sub-circuits and recombining them to explore new configurations, improving global solution quality.
• Implements dimensionality reduction by identifying and removing non-contributing parameterized gates (e.g., U3), reducing optimization complexity and critical path length.
• Uses multistart numerical optimization to enhance success rate and avoid local minima, increasing convergence to high-quality solutions despite complex objective functions.
• Extends the QSearch algorithm with a branch-and-bound framework that monitors progress and dynamically selects promising partial solutions.
• Integrates all techniques into a unified pipeline within the BQSkit toolkit, enabling application to real-world circuits like QFT, VQE, TFIM, and QITE.

Experimental results

Research questions

• RQ1 Can an incremental, prefix-based approach significantly reduce the search space in numerical optimization-based quantum circuit synthesis without sacrificing solution quality?
• RQ2 To what extent can incremental re-synthesis improve circuit depth and CNOT count by recombining optimized sub-circuits?
• RQ3 How effective is dimensionality reduction in eliminating redundant parameters and improving optimization efficiency in quantum circuit synthesis?
• RQ4 Can multistart optimization substantially increase the success rate of numerical optimizers in high-dimensional, non-convex quantum circuit landscapes?
• RQ5 How does LEAP’s performance compare to state-of-the-art tools like QSearch, QFAST, Tket, and Qiskit-synth in terms of runtime, circuit depth, and CNOT count for benchmark circuits?

Key findings

• LEAP compiles four-qubit unitaries up to 59× faster than QSearch, significantly improving runtime scalability.
• For five- and six-qubit circuits, LEAP reduces CNOT count by up to 1.19× on average compared to QFAST, with a 3.55× performance penalty in runtime.
• LEAP reduces CNOT count by up to 36× and 7× on average compared to the CQC Tket compiler, demonstrating superior circuit optimization.
• Multistart optimization increases the success rate of numerical optimizers from 15% to 99%, drastically improving reliability.
• Dimensionality reduction eliminates up to 40% of U3 gates, shortening the critical path and reducing optimization complexity.
• LEAP generates optimal or near-optimal depth circuits for known benchmarks like QFT, VQE, TFIM, and QITE, even with heuristic-driven search.