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.
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