Related papers: Explicit Quantum Circuits for Simulating Linear Di…
Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same…
We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Non-Hermitian quantum systems have recently attracted considerable attention due to their exotic properties. Though many experimental realizations of non-Hermitian systems have been reported, the non-Hermiticity usually resorts to the…
Existing quantum discrete adiabatic approaches are hindered by circuit depth that increases linearly with the number of evolution steps, a significant challenge for current quantum hardware with limited coherence times. To address this, we…
Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based…
In dispersive media, dissipation appears in the Schr\"odinger representation of classical Maxwell equations as a sparse diagonal operator occupying an $r$-dimensional subspace. A first order Suzuki-Trotter approximation for the evolution…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal…
We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs), extending previous work to incorporate (a) Robin boundary conditions - which include Neumann and…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
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…
Differential-algebraic equations (DAEs) arise naturally in constrained dynamical systems, but their algebraic constraints and hidden compatibility conditions make them more subtle than standard ordinary differential equations. This paper…
Simulation of physical systems is one of the most promising use cases of future digital quantum computers. In this work we systematically analyze the quantum circuit complexities of block encoding the discretized elliptic operators that…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary (closed--system) dynamics. For open dynamics, however, the reduced evolution is described by quantum…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…