Resource-Efficient Synthesis of Sparse Quantum States

• URL: http://arxiv.org/abs/2508.05386v1
• Date: Thu, 07 Aug 2025 13:35:55 GMT
• Title: Resource-Efficient Synthesis of Sparse Quantum States
• Authors: Renaud Vilmart, Sunheang Ty, Chetra Mang,
• Abstract summary: We provide an algorithm for sparse quantum states with a special care for quantum resources.<n>The circuit depth, ancilla count, and crucially non-Clifford count of the circuit produced by the algorithm are all linear in the sparsity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Preparing a quantum circuit that implements a given sparse state is an important building block that is necessary for many different quantum algorithms. In the context of fault-tolerant quantum computing, the so-called non-Clifford gates are much more expensive to perform than the Clifford ones. We hence provide an algorithm for synthesizing sparse quantum states with a special care for quantum resources. The circuit depth, ancilla count, and crucially non-Clifford count of the circuit produced by the algorithm are all linear in the sparsity. We conjecture that the non-Clifford count complexity is tight, and show a weakened version of this claim. The first key component of the algorithm is the synthesis of a generalized W-state. We provide a tree-based circuit construction approach, and the relationship between the tree's structure and the circuit's complexity. The second key component is a classical reversible circuit implementing a permutation that maps the basis states of the W-state to those of the sparse quantum state. We reduce this problem to the diagonalization of a binary matrix, using a specific set of elementary matrix operations corresponding to the classical reversible gates. We then solve this problem using a new version of Gauss-Jordan elimination, that minimizes the circuit complexities including circuit depth using parallel elimination steps.

Related papers

• 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)
• Quantum State Preparation Circuit Optimization Exploiting Don't Cares [6.158168913938158]
  Quantum state preparation initializes the quantum registers and is essential for running quantum algorithms. Existing methods synthesize an initial circuit and leverage compilers to reduce the circuit's gate count. We introduce a peephole optimization algorithm that identifies such unitaries for replacement in the original circuit.
  arXiv  Detail & Related papers  (2024-09-02T18:40:42Z)
• Linear Circuit Synthesis using Weighted Steiner Trees [45.11082946405984]
  CNOT circuits are a common building block of general quantum circuits. This article presents state-of-the-art algorithms for optimizing the number of CNOT gates. A simulated evaluation shows that the suggested is almost always beneficial and reduces the number of CNOT gates by up to 10%.
  arXiv  Detail & Related papers  (2024-08-07T19:51:22Z)
• Optimized synthesis of circuits for diagonal unitary matrices with reflection symmetry [0.0]
  It is important to optimize the quantum circuits in circuit depth and gate count, especially entanglement gates, including the CNOT gate. We show that the quantum circuit by our proposed algorithm achieves nearly half the reduction in both the gate count and circuit depth.
  arXiv  Detail & Related papers  (2023-10-10T14:52:17Z)
• Scalable noisy quantum circuits for biased-noise qubits [37.69303106863453]
  We consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $106$ gates.
  arXiv  Detail & Related papers  (2023-05-03T11:27:50Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Automatic Depth-Optimized Quantum Circuit Synthesis for Diagonal Unitary Matrices with Asymptotically Optimal Gate Count [9.194399933498323]
  It is of great importance to optimize the depth/gate-count when designing quantum circuits for specific tasks. In this paper, we propose a depth-optimized synthesis algorithm that automatically produces a quantum circuit for any given diagonal unitary matrix.
  arXiv  Detail & Related papers  (2022-12-02T06:58:26Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• Symbolic Synthesis of Clifford Circuits and Beyond [0.0]
  We show that the unitarity problem is co-NP-hard in general, but that it is in P when restricted to Clifford path sums. We then provide an algorithm to synthesize a Clifford circuit from a unitary Clifford path sum. We also provide a generalization of our extraction algorithm to arbitrary path sums.
  arXiv  Detail & Related papers  (2022-04-29T16:33:42Z)
• Reducing the Depth of Linear Reversible Quantum Circuits [0.0]
  In quantum computing the decoherence time of the qubits determines the computation time available. We propose a practical formulation of a divide and conquer algorithm that produces quantum circuits that are twice as shallow as those produced by existing algorithms. Overall, we manage to consistently reduce the total depth of a class of reversible functions, with up to 92% savings in an ancilla-free case and up to 99% when ancillary qubits are available.
  arXiv  Detail & Related papers  (2022-01-17T12:36:32Z)
• Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
  Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task. Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate. The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
  arXiv  Detail & Related papers  (2021-06-06T13:15:25Z)
• Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications [1.6329956884407544]
  We introduce two ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. AQCEL is deployed on an iterative and efficient quantum algorithm designed to model final state radiation in high energy physics. Our technique is generic and can be useful for a wide variety of quantum algorithms.
  arXiv  Detail & Related papers  (2021-02-19T16:20:31Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.