[Paper Review] QFAST: Conflating Search and Numerical Optimization for Scalable Quantum Circuit Synthesis

Ed Younis, Koushik Sen+2 more|arXiv (Cornell University)|Mar 12, 2021

Quantum Computing Algorithms and Architecture4 citations

TL;DR

QFAST is a scalable quantum circuit synthesis algorithm that replaces exhaustive search over circuit structures with efficient numerical optimization by encoding circuit topology and unitary transformations in generic gates. It achieves near-optimal circuit depth—1.19× longer than optimal for up to four qubits—while accelerating compilation by 3.55×, and scales to seven qubits, producing circuits up to 331× shorter than Qiskit’s rule-based methods.

ABSTRACT

We present a quantum synthesis algorithm designed to produce short circuits and to scale well in practice. The main contribution is a novel representation of circuits able to encode placement and topology using generic "gates", which allows the QFAST algorithm to replace expensive searches over circuit structures with few steps of numerical optimization. When compared against optimal depth, search based state-of-the-art techniques, QFAST produces comparable results: 1.19x longer circuits up to four qubits, with an increase in compilation speed of 3.6x. In addition, QFAST scales up to seven qubits. When compared with the state-of-the-art "rule" based decomposition techniques in Qiskit, QFAST produces circuits shorter by up to two orders of magnitude (331x), albeit 5.6x slower. We also demonstrate the composability with other techniques and the tunability of our formulation in terms of circuit depth and running time.

Motivation & Objective

• To address the scalability limitations of search-based quantum circuit synthesis algorithms for NISQ-era devices.
• To reduce circuit depth and compilation time by replacing combinatorial search with numerical optimization over a compact, topology-aware gate representation.
• To enable composability with existing native gate synthesis tools and tunability between circuit depth and runtime.
• To scale quantum circuit synthesis beyond four qubits while maintaining high-quality approximations.
• To provide a practical, approximate synthesis framework that balances depth, speed, and hardware-awareness for real-world quantum algorithms.

Proposed method

• QFAST uses a three-stage hierarchical synthesis approach: first, it builds circuits from generic m-qubit gates (m < n) that encode both unitary function and qubit location.
• Each generic gate is specialized via a single numerical optimization step to minimize unitary distance to the target, using a topology-aware formulation.
• The algorithm proceeds bottom-up, combining smaller optimized gates into larger ones until reaching the full n-qubit circuit.
• The final circuit is reassembled using native gate decompositions from third-party tools, enabling composability with existing synthesis pipelines.
• The method decouples the objective function in the generic gate space from the native gate space, allowing fine-grained approximation control.
• QFAST supports arbitrary gate sets and qubit connectivity, making it adaptable to different quantum hardware targets.

Experimental results

Research questions

• RQ1 Can a quantum circuit synthesis algorithm achieve near-optimal circuit depth while scaling efficiently beyond four qubits?
• RQ2 Can replacing combinatorial search with numerical optimization in a topology-aware manner significantly reduce compilation time without sacrificing circuit quality?
• RQ3 How does the performance of QFAST compare to optimal search-based methods (e.g., QSearch) and rule-based compilers (e.g., Qiskit) in terms of circuit depth and execution time?
• RQ4 To what extent can QFAST be composed with existing native gate synthesis tools to improve scalability and approximation quality?
• RQ5 Can the framework be tuned to trade-off between circuit depth and compilation time based on application-specific needs?

Key findings

• QFAST produces circuits that are on average 1.19× longer than optimal depth circuits generated by QSearch, but compiles 3.55× faster.
• QFAST scales to seven qubits, a significant improvement over state-of-the-art search-based methods that typically cap at four qubits.
• Compared to IBM Qiskit’s rule-based decomposition, QFAST generates circuits that are on average 156× shorter, with a 15× runtime penalty.
• When directly compared to Qiskit’s compilation pipeline, QFAST circuits are on average 10× shorter, demonstrating superior optimization capability.
• The algorithm enables composability with multiple native synthesis tools, including KAK, QSearch, and Qiskit’s native decomposers, enhancing flexibility and portability.
• The use of generic gates that encode both function and location allows QFAST to replace expensive search over circuit structures with a single numerical optimization step per gate.