Refining Quantum Phase Estimation Precision Conditions on Unitaries for Many-Electron Systems

• URL: http://arxiv.org/abs/2604.04298v1
• Date: Sun, 05 Apr 2026 22:37:03 GMT
• Title: Refining Quantum Phase Estimation Precision Conditions on Unitaries for Many-Electron Systems
• Abstract summary: We derivation first-order and unified conditions on unitaries that allow us to control the energy estimation precision.<n>We then introduce a novel condition that allows us to also control the state projection precision.<n>The main results in this article are formal, with a first numerical illustration on the H2 molecule that allows us to derive useful insights.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Beyond ground state energy estimation, quantum phase estimation (QPE) applied to many-electron systems has the potential to output a projection on the ground state, that would enable the evaluation of observables other than the energy. In this article, after recalling the role of QPE free parameters, we detail the derivation of first-order and unified conditions on unitaries that allow us to control the energy estimation precision and lead to tighter bounds than in previous works. We then introduce a novel condition that allows us to also control the state projection precision. We apply these conditions to a Trotterization case, leading to tighter bounds than the previous ones. The main results in this article are formal, with a first numerical illustration on the H2 molecule that allows us to derive useful insights.

Related papers

• Programming optical-lattice Fermi-Hubbard quantum simulators [39.58317527488534]
  We develop ground-state preparation algorithms for different fermionic models.<n>In particular, we first design variational, pre-compiled quantum circuits to prepare the ground state of the native Fermi-Hubbard model.<n>We discuss how to approximate the imaginary-time evolution using variational fermionic circuits.
  arXiv  Detail & Related papers  (2025-02-07T16:40:58Z)
• Robust phase estimation of the ground-state energy without controlled time evolution on a quantum device [0.0]
  Estimating the ground-state energy of Hamiltonians in quantum systems is an important task.<n>We demonstrate that the ground-state energy can be accurately estimated without controlled time evolution.<n>Our method is robust against non-adiabatic transitions, making it suitable for use with early fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2024-12-27T11:20:45Z)
• Aspects of Quantum Energy Teleportation [0.0]
  We explore quantum energy teleportation (QET) protocols, focusing on their behavior at finite temperatures.<n>We analyze the role of entanglement as a resource for QET, particularly in thermal states.<n>We then introduce a method to extract ground-state energy through a protocol that employs only quantum measurements.
  arXiv  Detail & Related papers  (2024-11-12T14:40:41Z)
• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Observation of a finite-energy phase transition in a one-dimensional quantum simulator [39.899531336700136]
  We show the first experimental demonstration of a finite-energy phase transition in 1D. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system.
  arXiv  Detail & Related papers  (2023-10-30T18:00:01Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Improving the accuracy of the energy estimation by combining quantum annealing with classical computation [0.0]
  It is essential to estimate a ground state energy of the Hamiltonian with chemical accuracy. We propose a way to improve the accuracy of the estimate of the ground state energy by combining quantum annealing with classical computation. We show that, if an expectation value and variance of the energy of the state after the QA are smaller than certain threshold values, the QA provides us with a better estimate of the ground state energy than that of the pre-estimation.
  arXiv  Detail & Related papers  (2021-02-10T08:52:39Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• Towards simulating 2D effects in lattice gauge theories on a quantum computer [1.327151508840301]
  We propose an experimental quantum simulation scheme to study ground state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology. The proposal builds on a formulation of lattice gauge theories as effective spin models in arXiv:2006.14160. We present two Variational Quantum Eigensolver (VQE) based protocols for the study of magnetic field effects, and for taking an important first step towards computing the running coupling of QED.
  arXiv  Detail & Related papers  (2020-08-21T01:20:55Z)
• In and out of equilibrium quantum metrology with mean-field quantum criticality [68.8204255655161]
  We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
  arXiv  Detail & Related papers  (2020-01-09T19:20:42Z)

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.