Special-Unitary Parameterization for Trainable Variational Quantum Circuits

• URL: http://arxiv.org/abs/2507.05535v1
• Date: Mon, 07 Jul 2025 23:21:02 GMT
• Title: Special-Unitary Parameterization for Trainable Variational Quantum Circuits
• Authors: Kuan-Cheng Chen, Huan-Hsin Tseng, Samuel Yen-Chi Chen, Chen-Yu Liu, Kin K. Leung,
• Abstract summary: SUN-VQC is a variational-circuit architecture whose elementary layers are single exponentials of a symmetry-restricted Lie subgroup.<n>We show that SUN-VQCs sustain order-of-rotation larger gradient signals, converge 2--3$times$ faster, and reach higher final fidelities than depth-matched Pauli circuits.
• Score: 7.2687813325879045
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose SUN-VQC, a variational-circuit architecture whose elementary layers are single exponentials of a symmetry-restricted Lie subgroup, $\mathrm{SU}(2^{k}) \subset \mathrm{SU}(2^{n})$ with $k \ll n$. Confining the evolution to this compact subspace reduces the dynamical Lie-algebra dimension from $\mathcal{O}(4^{n})$ to $\mathcal{O}(4^{k})$, ensuring only polynomial suppression of gradient variance and circumventing barren plateaus that plague hardware-efficient ans\"atze. Exact, hardware-compatible gradients are obtained using a generalized parameter-shift rule, avoiding ancillary qubits and finite-difference bias. Numerical experiments on quantum auto-encoding and classification show that SUN-VQCs sustain order-of-magnitude larger gradient signals, converge 2--3$\times$ faster, and reach higher final fidelities than depth-matched Pauli-rotation or hardware-efficient circuits. These results demonstrate that Lie-subalgebra engineering provides a principled, scalable route to barren-plateau-resilient VQAs compatible with near-term quantum processors.

Related papers

• Efficient circuit compression by multi-qudit entangling gates in linear optical quantum computation [1.9157770789584179]
  We show the existence of multi-level control ent-Z gates for qudits encoded in multiple modes in LOQC.<n>We present explicit linear optical schemes that realize such operations.<n>Our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.
  arXiv  Detail & Related papers  (2026-02-09T08:52:41Z)
• Analysis of Hessian Scaling for Local and Global Costs in Variational Quantum Algorithm [0.42970700836450487]
  We quantify the entrywise resolvability of the Hessian for Variational Quantum Algorithms.<n>We show two distinct scaling regimes that govern the sample complexity required to resolve Hessian entries against shot noise.
  arXiv  Detail & Related papers  (2026-01-31T15:49:23Z)
• A Quantum Algorithm for the Finite Element Method [0.0]
  finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs)<n>We present $textbfQu-FEM$, a fault-tolerant era quantum algorithm for the finite element method.
  arXiv  Detail & Related papers  (2025-10-20T23:00:12Z)
• Gradient-Based Excitation Filter for Molecular Ground-State Simulation [6.627541720714792]
  We introduce a method to efficiently simplify the Unitary Coupled-Cluster with Single and Double Excitations (UCCSD) ansatz on classical computers.<n>We demonstrate that our approach achieves up to $46%$ parameter decrease, $60%$ circuit depth reduction and $678times runtime.
  arXiv  Detail & Related papers  (2025-06-25T13:12:45Z)
• Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure [0.0]
  Fixed Unitary Coupled-Cluster (UCC) ans"atze are attractive for performing quantum chemistry Variational Quantumsolver (VQE) computations.<n>We introduce $k$-NI-DUCC, a fixed and Non-iterative Disentangled Unitary Coupled-Cluster compact ansatz.
  arXiv  Detail & Related papers  (2024-08-26T14:19:53Z)
• High-Entanglement Capabilities for Variational Quantum Algorithms: The Poisson Equation Case [0.07366405857677226]
  This research attempts to resolve problems by utilizing the IonQ Aria quantum computer capabilities. We propose a decomposition of the discretized equation matrix (DPEM) based on 2- or 3-qubit entanglement gates and is shown to have $O(1)$ terms with respect to system size. We also introduce the Globally-Entangling Ansatz which reduces the parameter space of the quantum ansatz while maintaining enough expressibility to find the solution.
  arXiv  Detail & Related papers  (2024-06-14T16:16:50Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Transformers as Support Vector Machines [54.642793677472724]
  We establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem. We characterize the implicit bias of 1-layer transformers optimized with gradient descent. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.
  arXiv  Detail & Related papers  (2023-08-31T17:57:50Z)
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories [40.772310187078475]
  We propose a novel variational ansatz for the ground-state preparation of the $mathbbZ$ lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve $>!99%$ precision in energy in both the confined and deconfined phase of the $mathbbZ$ LGT.
  arXiv  Detail & Related papers  (2023-08-07T14:23:00Z)
• Quantum simulation of dissipation for Maxwell equations in dispersive media [0.0]
  dissipation appears in the Schr"odinger representation of classical Maxwell equations as a sparse diagonal operator occupying an $r$-dimensional subspace. The unitary operators can be implemented through qubit lattice algorithm (QLA) on $n$ qubits. The non-unitary-dissipative part poses a challenge on how it should be implemented on a quantum computer.
  arXiv  Detail & Related papers  (2023-07-31T18:22:40Z)
• Efficient variational quantum circuit structure for correlated topological phases [0.0]
  We propose an efficient circuit structure of variational quantum circuit textitAnsatz used for the variational quantum eigensolver (VQE) algorithm. We investigate the symmetry-protected topological Haldane phase in a textitnon-exactly solvable alternating spin-$1/2$ Heisenberg chain by VQE calculations.
  arXiv  Detail & Related papers  (2023-03-30T06:49:28Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• 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)

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.