Related papers: Quantum Hamiltonian Algorithms for Maximum Indepen…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz [Phys. Rev. A 67, 033407 (2003)], we define mechanism via pathways of…
By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…
We present a quantum algorithm for adiabatic state preparation on a gate-based quantum computer, with complexity polylogarithmic in the inverse error. Our algorithm digitally simulates the adiabatic evolution between two self-adjoint…
Variational quantum algorithms are of special importance in the research on quantum computing applications because of their applicability to current Noisy Intermediate-Scale Quantum (NISQ) devices. The main building blocks of these…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Quantum annealers can be used to solve many (possibly NP-hard) combinatorial optimization problems, by formulating them as quadratic unconstrained binary optimization (QUBO) problems or, equivalently, using the Ising formulation. In this…
Recently, there has been growing interest in simulating time-dependent Hamiltonians using quantum algorithms, driven by diverse applications, such as quantum adiabatic computing. While techniques for simulating time-independent Hamiltonian…
We study the algorithmic tractability of finding large independent sets in dense random hypergraphs. In the sparse regime, much of the natural algorithms can be formulated within either the local or the low-degree polynomial (LDP)…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in…
We point out that, when an optimization problem has more than one solution, the quantum adiabatic algorithms (QAA) encounter topological obstructions leading to adiabatic spectral flows where spectral branches unavoidably traverse the…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to…
Neutral atom arrays have emerged as a versatile platform towards scalable quantum computation and optimization. In this paper we present demonstrations of solving maximum weighted independent set problems on a Rydberg atom array using…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
This paper studies the Hamiltonian Cycle Problem (HCP) and the Traveling Salesman Problem (TSP) on D-Wave's quantum systems. Initially, motivated by the fact that most libraries present their benchmark instances in terms of adjacency…
Utilizing quantum computer to investigate quantum chemistry is an important research field nowadays. In addition to the ground-state problems that have been widely studied, the determination of excited-states plays a crucial role in the…