Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification

• URL: http://arxiv.org/abs/2608.11579v1
• Date: Wed, 12 Aug 2026 02:38:42 GMT
• Title: Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification
• Abstract summary: Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution.<n>We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings.
• Score: 24.878868093642307
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods. We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, adaptively reducing active Pauli rows and emitting eligible two-qubit blocks other than single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It strictly Pareto-dominates prior state-of-the-art compilers, requiring 1.14--1.58$\times$ fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67$\times$ on average.

Related papers

• AlphaClifford: Efficient Clifford Synthesis and Transpilation with Model-based RL [2.018550249418405]
  We introduce AlphaClifford, a model-based Reinforcement Learning framework powered by Monte Carlo Tree Search.<n>By modeling the state space through the algebraic properties of the symplectic group, AlphaClifford effectively explores this space to minimize overall circuit cost.<n>We demonstrate the broad applicability of our framework on two additional tasks: hardware-constrained Clifford transpilation, and as a post-synthesis optimization component within a full Clifford+T logical pipeline.
  arXiv  Detail & Related papers  (2026-08-19T14:13:26Z)
• A Scalable Distributed Quantum Optimization Framework via Factor Graph Paradigm [46.08923284345648]
  We introduce a structure-aware framework for distributed quantum optimization.<n>We find that for a search space of size $N$, our framework achieves $O(sqrtN)$ query complexity up to processors and separator dependent factors.<n>We show that structure-aware decomposition delivers a practical path to scalable distributed quantum optimization on quantum networks.
  arXiv  Detail & Related papers  (2026-03-08T15:15:52Z)
• On the Convergence of Single-Loop Stochastic Bilevel Optimization with Approximate Implicit Differentiation [44.084531611147305]
  We provide a refined convergence analysis of the Single-loop Approximate Implicit Differentiation (SSAID) algorithm.<n>Our result is noteworthy in two aspects: (i) it matches the optimal $mathcalO(-2)$ rate of state-of-the-art multi-loop methods; and (ii) it provides the first explicit, fine-grained characterization of the $$-dependence.
  arXiv  Detail & Related papers  (2026-02-27T03:12:08Z)
• Para-B&B: Load-Balanced Deterministic Parallelization of Solving MIP [50.917107318582715]
  Mixed-integer programming (MIP) extends linear programming by incorporating both continuous and integer decision variables.<n>This paper presents the first fully open-source implementation of deterministic parallel branch-and-bound for HiGHS, a high-performance MIP solver.<n>Our approach introduces a novel data-parallel architecture ensuring strict determinism by replicating complete solver state across worker threads.
  arXiv  Detail & Related papers  (2026-02-10T14:17:53Z)
• Efficient and Noise-Resilient Molecular Quantum Simulation with the Generalized Superfast Encoding [0.5833117322405447]
  Simulating molecular systems on quantum computers requires efficient mappings from Fermionic operators to qubit operators.<n>Traditional mappings such as Jordan-Wigner or Bravyi-Kitaev often produce high-weight Pauli terms.<n>We propose a suite of techniques to construct compact and noise-resilient Fermion GSE-to-qubit mappings.
  arXiv  Detail & Related papers  (2025-11-12T13:30:51Z)
• CNOT Oriented Synthesis for Small-Scale Boolean Functions Using Spatial Structures of Parallelotopes [2.5255874956844933]
  In the Noisy Intermediate-Scale Quantum (NISQ) era, quantum circuit scalability remains limited by gate fidelity and qubit counts.<n>We propose the Spatial Structure-based Hypercube Reduction(SSHR), a novel synthesis method tailored for small-scale Boolean functions.<n>Our approach outperforms existing techniques in small-scale circuit synthesis, achieving 56% and 81% reductions in CNOT gate counts.
  arXiv  Detail & Related papers  (2025-09-02T03:17:22Z)
• PHOENIX: Pauli-Based High-Level Optimization Engine for Instruction Execution on NISQ Devices [19.624706655544422]
  This study introduces PHOENIX, a compilation framework that primarily operates at the high-level Pauli-based intermediate representation (IR) for generic Hamiltonian simulation programs.<n> Experimental results demonstrate that PHOENIX outperforms SOTA VQA compilers across diverse program categories, backend ISAs, and hardware topologies.
  arXiv  Detail & Related papers  (2025-04-04T15:29:18Z)
• On the Constant Depth Implementation of Pauli Exponentials [49.48516314472825]
  We decompose $Zotimes n$ exponentials of arbitrary length into circuits of constant depth using $mathcalO(n)$ ancillae and two-body XX and ZZ interactions.<n>We prove the correctness of our approach, after introducing novel rewrite rules for circuits which benefit from qubit recycling.
  arXiv  Detail & Related papers  (2024-08-15T17:09:08Z)
• Optimization at the Interface of Unitary and Non-unitary Quantum Operations in PCOAST [0.3496513815948205]
  Pauli-based Circuit Optimization, Analysis and Synthesis Toolchain (PCOAST) introduced as framework for optimizing quantum circuits. In this paper, we focus on the set of subroutines which look to optimize the PCOAST graph in cases involving unitary and non-unitary operations. We evaluate the PCOAST optimization subroutines using the Intel Quantum SDK on examples of the Variational Quantum Eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2023-05-16T22:58:14Z)
• Paulihedral: A Generalized Block-Wise Compiler Optimization Framework For Quantum Simulation Kernels [17.038656780131692]
  Paulihedral is a block-wise compiler framework that can deeply optimize the quantum simulation kernel. We show that Paulihedral can outperform state-of-the-art compiler infrastructures in a wide-range of applications on both near-term superconducting quantum processors and future fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2021-09-07T23:52:58Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.