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We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for…
The implementation of time-evolution operators $U(t)$, called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
The advent of near-term digital quantum computers could offer us an exciting opportunity to investigate quantum many-body phenomena beyond that of classical computing. To make the best use of the hardware available, it is paramount that we…
Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here,…
An important aspect in understanding the dynamics in the context of deparametrized models of LQG is to obtain a sufficient control on the quantum evolution generated by a given Hamiltonian operator. More specifically, we need to be able to…
We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
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…
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating…
We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via…
We present two sampled quasi-Newton methods (sampled LBFGS and sampled LSR1) for solving empirical risk minimization problems that arise in machine learning. Contrary to the classical variants of these methods that sequentially build…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
The dynamical evolution of neutrino flavor in supernovae can be modeled by an all-to-all spin Hamiltonian with random couplings. Simulating such two-local Hamiltonian dynamics remains a major challenge, as methods with controllable accuracy…
Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…