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Optimizing Quantum Circuits, Fast and Slow

Amanda Xu, Abtin Molavi, Swamit Tannu, Aws Albarghouthi

TL;DR

This paper presents a clean, unifying framework for thinking of rewriting and resynthesis as abstract circuit transformations, and presents a radically simple algorithm, guoq, for optimizing quantum circuits that exploits the synergies of rewriting and resynthesis.

Abstract

Optimizing quantum circuits is critical: the number of quantum operations needs to be minimized for a successful evaluation of a circuit on a quantum processor. In this paper we unify two disparate ideas for optimizing quantum circuits, rewrite rules, which are fast standard optimizer passes, and unitary synthesis, which is slow, requiring a search through the space of circuits. We present a clean, unifying framework for thinking of rewriting and resynthesis as abstract circuit transformations. We then present a radically simple algorithm, GUOQ, for optimizing quantum circuits that exploits the synergies of rewriting and resynthesis. Our extensive evaluation demonstrates the ability of GUOQ to strongly outperform existing optimizers on a wide range of benchmarks.

Optimizing Quantum Circuits, Fast and Slow

TL;DR

This paper presents a clean, unifying framework for thinking of rewriting and resynthesis as abstract circuit transformations, and presents a radically simple algorithm, guoq, for optimizing quantum circuits that exploits the synergies of rewriting and resynthesis.

Abstract

Optimizing quantum circuits is critical: the number of quantum operations needs to be minimized for a successful evaluation of a circuit on a quantum processor. In this paper we unify two disparate ideas for optimizing quantum circuits, rewrite rules, which are fast standard optimizer passes, and unitary synthesis, which is slow, requiring a search through the space of circuits. We present a clean, unifying framework for thinking of rewriting and resynthesis as abstract circuit transformations. We then present a radically simple algorithm, GUOQ, for optimizing quantum circuits that exploits the synergies of rewriting and resynthesis. Our extensive evaluation demonstrates the ability of GUOQ to strongly outperform existing optimizers on a wide range of benchmarks.

Paper Structure

This paper contains 54 sections, 2 theorems, 4 equations, 15 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our approach
  3. Contributions
  4. Background and Overview
  5. Quantum Circuits Background
  6. Quantum circuits
  7. Rewrite rules
  8. Resynthesis
  9. Comparing Rewriting and Resynthesis
  10. Our Approach
  11. Unifying rewrite rules and resynthesis
  12. Optimization objectives
  13. The guoq algorithm
  14. A concrete example
  15. Quantum Circuits and Approximations
  16. ...and 39 more sections

Key Result

theorem 1

Suppose we are given a set of transformations $\tau_{\epsilon_{}}^1, \ldots, \tau_{\epsilon_{}}^n$. Let $C_0,\ldots,C_n$ be a sequence of circuits such that $C_i$ is the result of applying transformation $\tau_{\epsilon_{}}^i$ to a subcircuit of $C_{i-1}$ for all $1 \leq i \leq n$. Then, $C_0 \equiv

Figures (15)

  • Figure 1: Summary of guoq compared to state-of-the-art on 2-qubit-gate reduction for the ibmq20 gate set. guoq and BQSKit are allowed to approximate the circuit up to $\epsilon = 10^{-8}$. *Quarl requires an NVIDIA A100 (40GB) GPU to run.
  • Figure 2: Overview of our approach
  • Figure 3: Examples of rewrite rules. Observe how the rules with $R_z^{\theta_{}}\xspace$ use symbolic$\theta$ angles.
  • Figure 4: Example of applying the rule from \ref{['fig:rz-commute-cx']} followed by the rule from \ref{['fig:rz-merge']}.
  • Figure 5: Example of resynthesizing the initial \ref{['fig:rewrite-rule-ex']} circuit.
  • ...and 10 more figures

Theorems & Definitions (6)

  • definition 1: Hilbert--Schmidt distance
  • definition 2: Approximate circuit equivalence
  • definition 3: Transformation
  • theorem 1
  • definition 4: Quantum-Circuit Optimization Problem
  • theorem 2: Correctness of guoq