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Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
Quantum simulation is a promising application of future quantum computers. Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. For an accurate product formula approximation,…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
Quantum simulation is a cornerstone application for quantum computing, yet standard methods face a trade-off between circuit depth and accuracy: Trotterization depth scales with the number of Hamiltonian terms $L$, while sampling-based…
This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose…
Compiling time-evolution operators of the form $U(t)=e^{-iHt}$ into hardware-native gate sequences is a central bottleneck for digital quantum simulation on noisy intermediate-scale quantum (NISQ) devices. Generic transpilation treats…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…
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…
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…