Spectral Fingerprints of Gauge Theories on a Quantum Computer

• URL: http://arxiv.org/abs/2608.27457v1
• Date: Thu, 27 Aug 2026 17:59:51 GMT
• Title: Spectral Fingerprints of Gauge Theories on a Quantum Computer
• Abstract summary: Maximally mixed state spectral sampling is an unbiased quantum algorithm that allows for extraction of a finite-resolution spectral distribution from a Hamiltonian over potentially the entire allowed range of energies.<n>We show how it may be focused on any desired area of the spectrum in order to learn about the full textitfingerprint of the model of interest.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Maximally mixed state spectral sampling is an unbiased quantum algorithm that allows for extraction of a finite-resolution spectral distribution from a Hamiltonian over potentially the entire allowed range of energies. We show how it may be focused on any desired area of the spectrum in order to learn about the full \textit{fingerprint} of the model of interest: from its ground state phenomena such as quantum criticality, obtained from the lowest lying energies, to its thermalization behavior, obtained from the mid-spectrum. We demonstrate this technique specifically on a $(1+1)d$ non-Abelian $SO(3)$ gauge theory, providing a comprehensive analysis of the steps necessary for performing this algorithm, as well as what is possible in the near-term with superconducting quantum hardware, performing simulations with circuits that are $78$ two-qubit gates deep. We show how this algorithm is able to take advantage of emerging dynamical circuit capabilities in near-term hardware to roughly halve the number required qubits, as well as how quantum readout error mitigation is trivial for this method. Along the way, we propose a novel strategy for compiling the controlled-time evolutions needed for spectral sampling by means of Pauli-frame optimizations. We illustrate two physical applications of quantum spectral sampling -- disordered many-body transitions, and mid-spectrum densities of states -- and what postprocessing steps they require beyond the Fourier outputs of the algorithm.

Related papers

• Qudit Implementation of the Rodeo Algorithm for Quantum Spectral Filtering [0.0]
  We present a formulation of the Rodeo algorithm employing a general $d$-level ancilla qudit.<n>Second, we introduce the concept of the emphRodeo kernel, which acts as a spectral filter in the energy domain.<n>Third, we propose a microcanonical protocol for the Rodeo algorithm.
  arXiv  Detail & Related papers  (2026-03-17T01:24:44Z)
• Low-Resource Quantum Energy Gap Estimation via Randomization [0.0]
  Estimating the energy spectra of quantum many-body systems is a fundamental task in quantum physics.<n>We propose a hybrid quantum-classical protocol that integrates Time Evolution via Probabilistic Angle Interpolation (TE-PAI) into the shadow spectroscopy framework.
  arXiv  Detail & Related papers  (2026-01-20T11:53:29Z)
• Near-Optimal Simultaneous Estimation of Quantum State Moments [7.1834855718325805]
  We introduce a framework for resource-efficient simultaneous estimation of quantum state moments via qubit reuse.<n>By leveraging qubit reset operations, our core circuit for simultaneous moment estimation requires only $2m+1$ physical qubits and $mathcalO(k)$ CSWAP gates.<n>We demonstrate this protocol's utility by showing that the estimated moments yield tight bounds on a state's maximum eigenvalue and present applications in quantum virtual cooling to access low-energy states of the Heisenberg model.
  arXiv  Detail & Related papers  (2025-09-29T14:23:26Z)
• Implementation and readout of maximally entangled two-qubit gates quantum circuits in a superconducting quantum processor [32.40607221598716]
  In a transmon-based 5-qubit superconducting quantum processor, we compared the performance of quantum circuits involving an increasing level of complexity.<n>Here we report the results obtained from the analysis of the outputs of quantum circuits using two readout paradigms.<n>The first method is suitable for single-qubit circuits, while the second is essential for accurately interpreting the outputs of circuits involving two-qubit gates.
  arXiv  Detail & Related papers  (2025-03-31T16:20:56Z)
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions [36.94429692322632]
  We propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for extraction of low-lying energy states.<n>As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.
  arXiv  Detail & Related papers  (2024-11-25T20:33:47Z)
• Genuine Multipartite Entanglement in Quantum Optimization [0.3495246564946556]
  We show that multipartite entanglement provides an upper bound to the overlap of the instantaneous state with an exact solution.<n>Our results help to shed light on how complex quantum correlations come to bear as a resource in quantum optimization.
  arXiv  Detail & Related papers  (2024-11-12T19:00:16Z)
• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• A Novel Quantum-Classical Hybrid Algorithm for Determining Eigenstate Energies in Quantum Systems [1.9714447272714082]
  This paper presents a novel quantum algorithm, XZ24, for efficiently computing the eigen-energy spectra of arbitrary quantum systems. XZ24 has three key advantages: It removes the need for eigenstate preparation, requiring only a reference state with non-negligible overlap. It enables simultaneous computation of multiple eigen-energies, depending on the reference state.
  arXiv  Detail & Related papers  (2024-06-01T04:31:43Z)
• Quantivine: A Visualization Approach for Large-scale Quantum Circuit Representation and Analysis [31.203764035373677]
  We develop Quantivine, an interactive system for exploring and understanding quantum circuits. A series of novel circuit visualizations are designed to uncover contextual details such as qubit provenance, parallelism, and entanglement. The effectiveness of Quantivine is demonstrated through two usage scenarios of quantum circuits with up to 100 qubits.
  arXiv  Detail & Related papers  (2023-07-18T04:51:28Z)
• Algorithmic Shadow Spectroscopy [0.0]
  We present a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) We demonstrate that our method is intuitively easy to use in practice, robust against gate noise, to a new type of algorithmic error mitigation technique, and uses orders of magnitude fewer number of shots than typical near-term quantum algorithms -- as low as 10 shots per timestep is sufficient.
  arXiv  Detail & Related papers  (2022-12-21T14:23:48Z)
• 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)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)

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.