AGP-based unitary coupled cluster theory for quantum computers

• URL: http://arxiv.org/abs/2205.13420v2
• Date: Fri, 23 Sep 2022 02:04:54 GMT
• Title: AGP-based unitary coupled cluster theory for quantum computers
• Authors: Armin Khamoshi, Guo P. Chen, Francesco A. Evangelista, Gustavo E. Scuseria
• Abstract summary: We develop a unitary coupled cluster method on the antisymmetrized geminal power (AGP) We demonstrate our method for the single-band Fermi--Hubbard Hamiltonian in one and two dimensions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for Ans\"atze on a quantum computer. We develop a unitary coupled cluster method on the antisymmetrized geminal power (AGP) -- a state formally equivalent to the number-projected Bardeen--Cooper--Schrieffer wavefunction. We demonstrate our method for the single-band Fermi--Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than $\mathcal{O}(\sqrt{M})$ in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.

Related papers

• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements [11.213906010203264]
  Recent developments have highlighted a novel symmetry-breaking pattern. Strong-to-weak symmetry breaking is typically detected using multi-replica correlation functions, such as the R'enyi-2 correlator. We propose a practical protocol for detecting strong-to-weak symmetry breaking in experiments using the randomized measurement toolbox.
  arXiv  Detail & Related papers  (2024-12-24T12:41:38Z)
• Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware [42.52549987351643]
  Quantum homogenization is a reservoir-based quantum state approximation protocol. We extend the standard quantum homogenization protocol to the dynamically-equivalent ($mathttSWAP$)$alpha$ formulation. We show that our proposed protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable.
  arXiv  Detail & Related papers  (2024-12-19T05:50:54Z)
• Theory of free fermions dynamics under partial post-selected monitoring [49.1574468325115]
  We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement. We show that the passage to the monitored universality occurs abruptly at finite partial post-selection. Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
  arXiv  Detail & Related papers  (2023-12-21T16:53:42Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• State preparation of AGP on a quantum computer without number projection [0.0]
  We show that the antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Schrieffer wavefunction. We also show that our circuit is equivalent to a disentangled unitary cluster coupled operator and a layer of unitary Jastrow operator acting on a single Slater.
  arXiv  Detail & Related papers  (2023-01-23T17:39:08Z)
• Random quantum circuits anti-concentrate in log depth [118.18170052022323]
  We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated. Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform. In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
  arXiv  Detail & Related papers  (2020-11-24T18:44:57Z)
• Correlating AGP on a quantum computer [0.0]
  We show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-13T23:56:05Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)
• Proposal to measure out-of-time-ordered correlations using Bell states [0.0]
  We present a protocol to experimentally measure the infinite-temperature out-of-time-ordered correlation (OTOC) OTOC is a probe of quantum information scrambling in a system. We show that the OTOC can be obtained by preparing two entangled systems.
  arXiv  Detail & Related papers  (2020-06-26T16:51:32Z)
• Emergent $\mathcal{PT}$ symmetry in a double-quantum-dot circuit QED set-up [0.0]
  We show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot-circuit-QED set-up. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system.
  arXiv  Detail & Related papers  (2020-04-16T09:08:31Z)
• Hartree-Fock on a superconducting qubit quantum computer [30.152226344347064]
  Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates. We model the binding energy of $rm H_6$, $rm H_8$, $rm H_10$ and $rm H_12$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments.
  arXiv  Detail & Related papers  (2020-04-08T18:00:06Z)

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.