Related papers: Second order cone relaxations for quantum Max Cut
Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide…
We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a…
We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with $\mathcal{O}(\kappa~\text{poly}(\log(\kappa/\epsilon)))$ runtime, where…
The central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits ("qubits") are susceptible to two types of error, corresponding to flips of the…
The quantum circuit Born machine (QCBM) is a quantum physics inspired implicit generative model naturally suitable for learning binary images, with a potential advantage of modeling discrete distributions that are hard to simulate…
We consider the Einstein equation with first order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth order derivatives of the metric, the solutions which are physically relevant satisfy a reduced…
Quantum approximate optimization algorithm (QAOA) is one of the popular quantum algorithms that are used to solve combinatorial optimization problems via approximations. QAOA is able to be evaluated on both physical and virtual quantum…
Probing correlated states of many-body systems is one of the central tasks for quantum simulators and processors. A promising approach to state preparation is to realize desired correlated states as steady states of engineered dissipative…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
The reduced density matrix (RDM) is crucial in quantum many-body systems for understanding physical properties, including all local physical quantity information. This study aims to minimize various error constraints that causes challenges…
Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is studied by means of a modified spin-wave theory. Calculating beyond the first-order mechanism, where a nuclear spin directly interacts with spin waves through the…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
We study the Max-Cut semidefinite programming (SDP) relaxation in the regime where a near-optimal solution admits a low-dimensional realization. While the Goemans--Williamson hyperplane rounding achieves the worst-case optimal approximation…
A theoretical study of an antiferromagnetically coupled spin system, specifically $\rm{Cu}_{3}-\rm{X}$ $(\rm{X=As, Sb})$, characterized by a slightly distorted equilateral triangle configuration is presented. Using the Heisenberg model with…
We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by…
Quantum Monte Carlo (QMC) simulations are performed to study ground-state properties of a mixed spin-1 and spin-1/2 Lieb-lattice Heisenberg antiferromagnet, in order to get further insight beyond the modified spin-wave (MSW) study reported…