Related papers: Optimal Bounds, Barriers, and Extensions for Non-H…

High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…

Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…

Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study…

Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for…

Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum…

Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…

The interaction between a quantum system and its environment limits our ability to control it and perform quantum operations on it. We present an efficient method to find optimal controls for quantum systems coupled to non-Markovian…

We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…

Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…

Nonlocal Hamiltonian-type operators, like e.g. fractional and quasirelativistic, seem to be instrumental for a conceptual broadening of current quantum paradigms. However physically relevant properties of related quantum systems have not…

Combinatorial optimization with a smooth and convex objective function arises naturally in applications such as discrete mean-variance portfolio optimization, where assets must be traded in integer quantities. Although optimal solutions to…

Recently, we have theoretically proposed and experimentally demonstrated an exact and efficient quantum simulation of photosynthetic light harvesting in nuclear magnetic resonance (NMR), cf. B. X. Wang, \textit{et al.} npj Quantum…

In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…

This paper addresses the challenge of solving Constrained Markov Decision Processes (CMDPs) with $d > 1$ constraints when the transition dynamics are unknown, but samples can be drawn from a generative model. We propose a model-based…

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…

Accurate models of the dynamics of quantum circuits are essential for optimizing and advancing quantum devices. Since first-principles models of environmental noise and dissipation in real quantum systems are often unavailable, deriving…

Non-Hermitian quantum many-body systems exhibit a rich array of physical phenomena, including non-Hermitian skin effects and exceptional points, that remain largely inaccessible to existing numerical techniques. In this work, we investigate…

We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…

Achieving practical quantum advantage on near-term noisy hardware is a central goal of quantum computation. However, without efficient pre-execution diagnostics, circuit design and scheme selection often rely on costly hardware-in-the-loop…