Provably Optimal Quantum Circuits with Mixed-Integer Programming

• URL: http://arxiv.org/abs/2510.00649v1
• Date: Wed, 01 Oct 2025 08:25:43 GMT
• Title: Provably Optimal Quantum Circuits with Mixed-Integer Programming
• Authors: Harsha Nagarajan, Zsolt Szabó,
• Abstract summary: We present a depth-aware optimization framework for quantum circuit compilation.<n>For exact synthesis of a target unitary, we formulate a mixed-integer linear program (MILP) that linearly global-phase equivalence.<n>To scale beyond exact MILP, we propose a novel rolling-Circuit optimization (RHO) that rolls primarily in time, caps the active-qubits, and enforces per-qubit closure.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a depth-aware optimization framework for quantum circuit compilation that unifies provable optimality with scalable heuristics. For exact synthesis of a target unitary, we formulate a mixed-integer linear program (MILP) that linearly handles global-phase equivalence and uses explicit parallel scheduling variables to certify depth-optimal solutions for small-to-medium circuits. Domain-specific valid constraints, including identity ordering, commuting-gate pruning, short-sequence redundancy cuts, and Hermitian-conjugate linkages, significantly accelerate branch-and-bound, yielding speedups up to 43x on standard benchmarks. The framework supports hardware-aware objectives, enabling fault-tolerant (e.g. T-count) and NISQ-era (e.g. entangling gates) devices. For approximate synthesis, we propose 3 objectives: (i) exact, but non-convex, phase-invariant fidelity maximization; (ii) a linear surrogate that maximizes the real trace overlap, yielding a tight lower bound to fidelity; and (iii) a convex quadratic function that minimizes the circuit's Frobenius error. To scale beyond exact MILP, we propose a novel rolling-horizon optimization (RHO) that rolls primarily in time, caps the active-qubits, and enforces per-qubit closure while globally optimizing windowed segments. This preserves local context, reduces the Hilbert-space dimension, and enables iterative improvements without ancillas. On a 142-gate seed circuit, RHO yields 116 gates, an 18.3% reduction from the seed, while avoiding the trade-off between myopic passes and long run times. Empirically, our exact compilation framework achieves certified depth-optimal circuits on standard targets, high-fidelity Fibonacci-anyon weaves, and a 36% gate-count reduction on multi-body parity circuits. All methods are in the open-source QuantumCircuitOpt, providing a single framework that bridges exact certification and scalable synthesis.

Related papers

• Scalable Preparation of Matrix Product States with Sequential and Brick Wall Quantum Circuits [0.0]
  Matrix Product States (MPS) admit more efficient constructions when accuracy is traded for circuit complexity.<n>This work introduces an end-to-end MPS preparation framework that combines the strengths of both strategies within a single pipeline.
  arXiv  Detail & Related papers  (2026-02-12T15:07:11Z)
• BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models [56.504879072674015]
  We propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients.<n>BPDQ enables serving Qwen2.5-72B on a single GTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit)
  arXiv  Detail & Related papers  (2026-02-04T02:54:37Z)
• Optimization and Synthesis of Quantum Circuits with Global Gates [44.99833362998488]
  We use global interactions, such as the Global Molmer-Sorensen gate present in ion trap hardware, to optimize and synthesize quantum circuits.<n>The algorithm is based on the ZX-calculus and uses a specialized circuit extraction routine that groups entangling gates into Global MolmerSorensen gates.<n>We benchmark the algorithm in a variety of circuits, and show how it improves their performance under state-of-the-art hardware considerations.
  arXiv  Detail & Related papers  (2025-07-28T10:25:31Z)
• Optimizing Quantum Circuits via ZX Diagrams using Reinforcement Learning and Graph Neural Networks [38.499527873574436]
  We introduce a framework based on ZX calculus, graph-neural networks and reinforcement learning for quantum circuit optimization.<n>By combining reinforcement learning and tree search, our method addresses the challenge of selecting optimal sequences of ZX calculus rewrite rules.<n>We demonstrate our method's competetiveness with state-of-the-art circuit generalizations and capabilities on large sets of diverse random circuits.
  arXiv  Detail & Related papers  (2025-04-04T13:19:08Z)
• Coqa: Blazing Fast Compiler Optimizations for QAOA [3.165516590671437]
  We propose Coqa to optimize QAOA circuit compilation tailored to different types of quantum hardware. We are able to achieve an average of 30% reduction in gate count and a 39x acceleration in compilation time across our benchmarks.
  arXiv  Detail & Related papers  (2024-08-15T18:12:04Z)
• Sparsity-Constraint Optimization via Splicing Iteration [1.3622424109977902]
  We develop an algorithm named Sparsity-Constraint Optimization via sPlicing itEration (SCOPE) SCOPE converges effectively without tuning parameters. We apply SCOPE to solve quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. Our open-source Python package skscope based on C++ implementation is publicly available on GitHub.
  arXiv  Detail & Related papers  (2024-06-17T18:34:51Z)
• Decomposed Global Optimization for Robust Point Matching with Low-Dimensional Branching [41.05165517541873]
  We introduce a novel global optimization method for align partially overlapping point sets.<n>Our method exhibits superior robustness to non-rigid deformations, positional noise and outliers.<n> Experiments on 2D and 3D synthetic and real-world data demonstrate that our method, compared to state-of-the-art approaches, exhibits superior robustness to outliers.
  arXiv  Detail & Related papers  (2024-05-14T13:28:57Z)
• Efficient Implementation of Multi-Controlled Quantum Gates [0.0]
  We present an implementation of multi-controlled quantum gates which provides significant reductions of cost compared to state-of-the-art methods.<n>We generalize our methods for any number of target qubits, and provide further cost reductions if additional ancilla qubits are available.
  arXiv  Detail & Related papers  (2024-04-02T20:13:18Z)
• Direct pulse-level compilation of arbitrary quantum logic gates on superconducting qutrits [36.30869856057226]
  We demonstrate any arbitrary qubit and qutrit gate can be realized with high-fidelity, which can significantly reduce the length of a gate sequence. We show that optimal control gates are robust to drift for at least three hours and that the same calibration parameters can be used for all implemented gates.
  arXiv  Detail & Related papers  (2023-03-07T22:15:43Z)
• Wide Quantum Circuit Optimization with Topology Aware Synthesis [0.8469686352132708]
  Unitary synthesis is an optimization technique that can achieve optimal multi-qubit gate counts while mapping quantum circuits to restrictive qubit topologies. We present TopAS, a topology aware synthesis tool built with the emphBQSKit framework that preconditions quantum circuits before mapping.
  arXiv  Detail & Related papers  (2022-06-27T21:59:30Z)
• Optimization-based Block Coordinate Gradient Coding for Mitigating Partial Stragglers in Distributed Learning [58.91954425047425]
  This paper aims to design a new gradient coding scheme for mitigating partial stragglers in distributed learning. We propose a gradient coordinate coding scheme with L coding parameters representing L possibly different diversities for the L coordinates, which generates most gradient coding schemes.
  arXiv  Detail & Related papers  (2022-06-06T09:25:40Z)
• A Structured Method for Compilation of QAOA Circuits in Quantum Computing [5.560410979877026]
  The flexibility in reordering the two-qubit gates allows compiler optimizations to generate circuits with better depths, gate count, and fidelity. We propose a structured method that ensures linear depth for any compiled QAOA circuit on multi-dimensional quantum architectures. Overall, we can compile a circuit with up to 1024 qubits in 10 seconds with a 3.8X speedup in depth, 17% reduction in gate count, and 18X improvement for circuit ESP.
  arXiv  Detail & Related papers  (2021-12-12T04:00:45Z)
• 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)
• Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets [47.00474212574662]
  Variational quantum algorithms are believed to be promising for solving computationally hard problems. In this paper, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
  arXiv  Detail & Related papers  (2020-05-11T17:20:51Z)

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.