Related papers: Quantum Imaginary Time Evolution Algorithm for Qua…
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap \Delta E between the ground state and the first excited…
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold…
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…
Lattice simulations are the only viable way to obtain ab-initio Quantum Chromodynamics (QCD) predictions for low energy nuclear physics. These calculations are done, however, in a finite box and therefore extrapolation is needed to get the…
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
Models of quantum systems scale exponentially with the addition of single-particle states, which can present computationally intractable problems. Alternatively, quantum computers can store a many-body basis of $2^n$ dimensions on $n$…
Variational quantum algorithms provide feasible approaches for simulating quantum systems and are applied widely. For lattice gauge theory, however, variational quantum simulation faces a challenge as local gauge invariance enforces a…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
The Schwinger model, which describes lattice quantum electrodynamics in $1+1$ space-time dimensions, provides a valuable framework to investigate fundamental aspects of quantum field theory, and a stepping stone towards non-Abelian gauge…
This study delves into the concept of quantum phases in open quantum systems, examining the shortcomings of existing approaches that focus on steady states of Lindbladians and highlighting their limitations in capturing key phase…
Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about…
Simulating the full dynamics of a quantum field theory over a wide range of energies requires exceptionally large quantum computing resources. Yet for many observables in particle physics, perturbative techniques are sufficient to…
Lattice gauge theory should be able to address significant new scientific questions when implemented on quantum computers. In practice, error-mitigation techniques have already allowed encouraging progress on small lattices. In this work we…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
We identify a new element in quantum simulations of lattice gauge theories, arising from spacetime-dependent quantum corrections in the relation between the link variables defined on the lattice and their continuum counterparts. While in…
We identify quantum imaginary time evolution as a Riemannian gradient flow on the unitary group. We develop an upper bound for the error between the two evolutions that can be controlled through the step size of the Riemannian gradient…