Symmetry breaking and restoration for many-body problems treated on quantum computers

• URL: http://arxiv.org/abs/2310.17996v2
• Date: Thu, 9 Nov 2023 10:57:22 GMT
• Title: Symmetry breaking and restoration for many-body problems treated on quantum computers
• Authors: Andres Ruiz
• Abstract summary: This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers. It involves intentionally breaking and restoring the symmetries of the wave function ansatz at different stages of the variational search for the ground state. In the final part, hybrid quantum-classical techniques were introduced to extract an approximation of the low-lying spectrum of a Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers to better approximate a Hamiltonian's ground state energy within a variational framework in many-body physics. This involves intentionally breaking and restoring the symmetries of the wave function ansatz at different stages of the variational search for the ground state. The Variational Quantum Eigensolver (VQE) is utilized for the variational component together with an ansatz inspired by the Bardeen-Cooper-Schrieffer (BCS) theory. The applications were demonstrated using the pairing and Hubbard Hamiltonians. Two approaches were identified with the VQE method: varying the symmetry-breaking ansatz parameters before or after symmetry restoration, termed Quantum Projection After Variation and Quantum Variation After Projection, respectively. The main contribution of this thesis was the development of a variety of symmetry restoration techniques based on the principles of the Quantum Phase Estimation algorithm, the notion of a Quantum "Oracle," and the Classical Shadow formalism. In the final part, hybrid quantum-classical techniques were introduced to extract an approximation of the low-lying spectrum of a Hamiltonian. Assuming accurate Hamiltonian moment extraction from their generating function with a quantum computer, two methods were presented for spectral analysis: the t-expansion method and the Krylov method, which provides, in particular, information about the evolution of the survival probability. Furthermore, the Quantum Krylov method was introduced, offering similar insights without the need to estimate Hamiltonian moments, a task that can be difficult on near-term quantum computers.

Related papers

• Quantum Boltzmann machine learning of ground-state energies [3.187381965457262]
  Esting the ground-state energy of Hamiltonians is a fundamental task for which quantum computers can be helpful. We analyze the performance of quantum Boltzmann machines for this task. Our algorithm estimates the gradient of the energy function efficiently by means of a novel quantum circuit construction.
  arXiv  Detail & Related papers  (2024-10-16T18:22:03Z)
• Truncation technique for variational quantum eigensolver for Molecular Hamiltonians [0.0]
  variational quantum eigensolver (VQE) is one of the most promising quantum algorithms for noisy quantum devices. We propose a physically intuitive truncation technique that starts the optimization procedure with a truncated Hamiltonian. This strategy allows us to reduce the required number of evaluations for the expectation value of Hamiltonian on a quantum computer.
  arXiv  Detail & Related papers  (2024-02-02T18:45:12Z)
• Variational Coherent Quantum Annealing [0.0]
  We present a hybrid classical-quantum computing paradigm where the quantum part strictly runs within the coherence time of a quantum annealer. We introduce auxiliary Hamiltonians that vanish at the beginning and end of the evolution to increase the energy gap during the process. We achieve a substantial reduction in the ground-state error with just six variational parameters and a duration within the device coherence times.
  arXiv  Detail & Related papers  (2023-10-03T17:53:03Z)
• Variational quantum algorithms for local Hamiltonian problems [0.0]
  Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. We primarily focus on the algorithm called variational quantum eigensolver (VQE), which takes a qubit Hamiltonian and returns its approximate ground state.
  arXiv  Detail & Related papers  (2022-08-23T22:32:56Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Quantum Variational Learning of the Entanglement Hamiltonian [0.0]
  Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions.
  arXiv  Detail & Related papers  (2021-05-10T12:54:50Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.