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Value function based reinforcement learning (RL) algorithms, for example, $Q$-learning, learn optimal policies from datasets of actions, rewards, and state transitions. However, when the underlying state transition dynamics are stochastic…
Hutchinson's method estimates the trace of a matrix function $f(D)$ stochastically using samples $\tau^Hf(D)\tau$, where the components of the random vectors $\tau$ obey an isotropic probability distribution. Estimating the trace of the…
Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
We introduce maximum likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
We propose a quantum multi-level estimation framework for a functional $\sum_{i=1}^n f(p_i)$ of a discrete distribution $(p_i)_{i=1}^n$. We partition the values $p_i$ into logarithmically many intervals whose length decays exponentially.…
Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC…
We provide an explicit recursive divide and conquer approach for simulating quantum dynamics and derive a discrete first quantized non-relativistic QED Hamiltonian based on the many-particle Pauli Fierz Hamiltonian. We apply this recursive…
Simulating the dynamics of large quantum systems is a formidable yet vital pursuit for obtaining a deeper understanding of quantum mechanical phenomena. While quantum computers hold great promise for speeding up such simulations, their…
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…
We conduct a systematic study of quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives, since they are widely-used components in quantum algorithms and also have attracted much experimental interest in recent…
With the advances in customized hardware for quantum annealing and digital/CMOS Annealing, Quadratic Unconstrained Binary Optimization (QUBO) models have received growing attention in the optimization literature. Motivated by an existing…
Conventional approaches to fault-tolerant quantum computing realize logical circuits gate-by-gate, synthesizing each gate independently on one or more code blocks. This incurs excess overhead and doesn't leverage common structures in…
Multiple linear regression assumes an imperative role in supervised machine learning. In 2009, Harrow et al. [Phys. Rev. Lett. 103, 150502 (2009)] showed that their HHL algorithm can be used to sample the solution of a linear system…
When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum…