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arXiv:2308.15066

Extracting vacuum expectation values from approximate vacuum prepared by the adiabatic quantum computation

Kazuto Oshima

Published Aug 29, 2023• 0 citations
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Abstract

We propose a procedure to extract vacuum expectation values from approximate vacuum prepared by the adiabatic quantum computation. We use plural ancilla bits with hierarchical structure, intending to gradually put up approximate precision. We exhibit simulation results for a typical one-qubit system and a two-qubits system based on the (1+1)-dimensional Schwinger model using classically emulated digital quantum simulator.

DOI
10.48550/arxiv.2308.15066

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We propose a procedure to extract vacuum expectation values from approximate vacuum prepared by the adiabatic quantum computation. We use plural ancilla bits with hierarchical structure, intending to gradually put up approximate precision. We exhibit simulation results for a typical one-qubit system and a two-qubits system based on the (1+1)-dimensional Schwinger model using classically emulated digital quantum simulator.
Abstract We propose a procedure to extract a true ground state from an approximate ground state by using quantum entanglement. We use plural ancilla qubits with hierarchical structure, intending to gradually improve the precision of the approximation. We demonstrate the procedure for quantum systems with a few qubits that derive from the (1+1)-dimensional Schwinger model by classically emulated digital quantum simulation. Although we use for simplicity an approximate ground state prepared by adiabatic quantum computation, our procedure is applicable to any approximate ground state that is a superposition of a true ground state and excited states. Our procedure is applicable for an NNN-qubits Hamiltonian with a nondegenerate ground state.
This note discusses a method for computing the energy spectra of quantum field theory utilizing digital quantum simulation. A quantum algorithm, called coherent imaging spectroscopy, quenches the vacuum with a time-oscillating perturbation and then reads off the excited energy levels from the loss in the vacuum-to-vacuum probability following the quench. As a practical demonstration, we apply this algorithm to the (1+1)-dimensional quantum electrodynamics with a topological term known as the Schwinger model, where the conventional Monte Carlo approach is practically inaccessible. In particular, on a classical simulator, we prepare the vacuum of the Schwinger model on a lattice by adiabatic state preparation and then apply various types of quenches to the approximate vacuum through Suzuki-Trotter time evolution. We discuss the dependence of the simulation results on the specific types of quenches and introduce various consistency checks, including the exact diagonalization and the continuum limit extrapolation. The estimation of the computational complexity required to obtain physically reasonable results implies that the method is likely efficient in the coming era of early fault-tolerant quantum computers.
We indicate that there are points to keep in mind in utilizing quantum states prepared by the adiabatic quantum computation. Even if an instantaneous expectation value of a physical quantity for the adiabatically prepared quantum state is close to an expectation value for the true vacuum, this does not assure us that the prepared vacuum is close to the true vacuum. In general time average of the expectation value tend to systematically differ from the true value. Using a simple model we discuss how to diminish this systematic difference.
We discuss a method to efficiently compute energy spectra in quantum field theories by digital quantum simulation. We utilize a quantum algorithm called coherent imaging spectroscopy which quenches the ground state with a perturbation oscillating periodically in time for various frequencies and then reads off excited energy levels from values of frequencies having loss of the vacuum-to-vacuum probability by the quench. We demonstrate this method in the Schwinger model which is the (1+1)-dimensional quantum electrodynamics with a topological term. In particular, the ground state of the Schwinger model on lattice is prepared by adiabatic state preparation and then we apply various types of quenches to the approximate ground state via Suzuki-Trotter time evolution. We benchmark the types of quenches and argue their (dis)advantages especially in the context of studying quantum field theories. We also estimate the computational complexity to obtain physically reasonable results which likely implies efficiency of the method in the early fault-tolerant quantum computer era
We designed a protocol for digital quantum computation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on 1+11+11+1 dimensional quantum electrodynamics with the $\ensuremath{\theta}$ term known as the Schwinger model and test our protocol for this on an IBM simulator. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in the massless case agrees with the known exact result. In the massive case, we find an agreement with mass perturbation theory in the small-mass regime and deviations in the large-mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation appears a promising tool to explore nonperturbative aspects of gauge theories with real time and topological terms.