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This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A small gain approach is used to evaluate the performance of the given quantum system. In order to get improved…
We study possible advantages of randomized and quantum computing over deterministic computing for scalar initial-value problems for ordinary differential equations of order k. For systems of equations of the first order this question has…
In fault-tolerant quantum computing, the cost of calculating Hamiltonian eigenvalues using the quantum phase estimation algorithm is proportional to the constant scaling the Hamiltonian matrix block-encoded in a unitary circuit. We present…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
We establish a comprehensive theoretical framework for coherent quantum speed limits (QSLs), deriving fundamental bounds on the rate of quantum evolution that explicitly isolate the contribution of quantum coherence. By applying H\"older's…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
Computational fluid dynamics (CFD) is a specialised branch of fluid mechanics that utilises numerical methods and algorithms to solve and analyze fluid-flow problems. One promising avenue to enhance CFD is the use of quantum computing,…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
We show how to efficiently simulate continuous-time quantum query algorithms that run in time T in a manner that preserves the query complexity (within a polylogarithmic factor) while also incurring a small overhead cost in the total number…
Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault…
Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity;…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…