相关论文: An Optimal Product-State Approximation for 2-Local…

The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…

Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the…

We provide a method to prepare a warm-started quantum state from measurements with an iterative framework to enhance the quantum approximate optimisation algorithm (QAOA). The numerical simulations show the method can effectively address…

The Lie--Trotter product formula is a foundational approximation for the quantum partition function, yet obtaining rigorous error bounds for the unbounded Hamiltonians common in physics remains a significant challenge. This paper provides a…

We learn optimal instance-specific heuristics for the global minimization of nonconvex quadratically-constrained quadratic programs (QCQPs). Specifically, we consider partitioning-based convex mixed-integer programming relaxations for…

A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…

As a means to solve optimization problems using quantum computers, the problem is typically recast into a Ising spin model whose ground-state is the solution of the optimization problem. An alternative to the Ising formulation is the…

Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space…

Contextuality, one of the strongest forms of quantum correlations, delineates the quantum world and the classical one. It has been shown recently that some quantum models, in the form of infinite one-dimensional translation-invariant…

The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…

Quantum Max Cut (QMC) problem for systems of qubits is an example of a 2-local Hamiltonian problem, and a prominent paradigm in computational complexity theory. This paper investigates the algebraic structure of a higher-dimensional analog…

Planning energy production is a challenging task due to its cost-sensitivity, fast-moving energy markets, uncertainties in demand, and technical constraints of power plants. Thus, more complex models of this so-called \emph{unit commitment…

Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…

The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…

We prove a vector-valued inequality for the Gaussian noise stability (i.e. we prove a vector-valued Borell inequality) for Euclidean functions taking values in the two-dimensional sphere, for all correlation parameters at most $1/10$ in…

A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all local terms simultaneously. In general, even deciding whether a Hamiltonian is frustration-free is a hard task, as it is closely related…

We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…

We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [DPMRF22]; (ii) injective matrix product states; (iii) output states of dense…

Quantum optimization methods use a continuous degree-of-freedom of quantum states to heuristically solve combinatorial problems, such as the MAX-CUT problem, which can be attributed to various NP-hard combinatorial problems. This paper…

One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to…