Related papers: On the Computational Complexity of Curing the Sign…
The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for…
Due to the intrinsic complexity of the quantum many-body problem, quantum Monte Carlo algorithms and their corresponding Monte Carlo configurations can be defined in various ways. Configurations corresponding to few Feynman diagrams often…
We introduce $k$-local quasi-quantum states: a superset of the regular quantum states, defined by relaxing the positivity constraint. We show that a $k$-local quasi-quantum state on $n$ qubits can be 1-1 mapped to a distribution of…
We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer. We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian,…
We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
We propose a mechanism for solving the `negative sign problem'---the inability to assign non-negative weights to quantum Monte Carlo configurations---for a toy model consisting of a frustrated triplet of spin-$1/2$ particles interacting…
Quantum computation provides exponential speedup for solving certain mathematical problems against classical computers. Motivated by current rapid experimental progress on quantum computing devices, various models of quantum computation…
Recently, the quantum brachistochrone problem is discussed in the literature by using non-Hermitian Hamilton operators of different type. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the…
Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap…
We derive explicit closed-form matrix representations of Hamiltonians drawn from tensored algebras, such as quantum spin Hamiltonians. These formulas enable us to soft-code generic Hamiltonian systems and to systematize the input data for…
We present an encoding and hardware-independent formulation of optimization problems for quantum computing. Using this generalized approach, we present an extensive library of optimization problems and their various derived spin encodings.…
Quantum simulations are a powerful tool for exploring strongly correlated many-body phenomena. Yet, their reach is limited by the fermion sign problem, which causes configuration weights to become negative, compromising statistical…