Related papers: Improving time dynamics simulation by sampling the…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations…
Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
The success probability of a quantum algorithm constructed from noisy quantum gates cannot be accurately predicted from single parameter metrics that compare noisy and ideal gates. We illustrate this concept by examining a system with…
We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
This is a technical report that extends and clarifies the results presented in [1]. The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise…
Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
The implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…
The quantum stochastic drift protocol, also known as qDRIFT, has become a popular algorithm for implementing time-evolution of quantum systems using randomised compiling. In this work we develop qFLO, a higher order randomised algorithm for…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…
Identifying and extracting the past information relevant to the future behaviour of stochastic processes is a central task in the quantitative sciences. Quantum models offer a promising approach to this, allowing for accurate simulation of…
We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each…
Simulating the time-evolution of a Hamiltonian is one of the most promising applications of quantum computers. Multi-Product Formulas (MPFs) are well suited to replace standard product formulas since they scale better with respect to time…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…