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The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for…
Hamiltonian simulation is one of the most important problems in the field of quantum computing. There have been extended efforts on designing algorithms for faster simulation, and the evolution time $T$ for the simulation turns out to…
Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction…
Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…
We consider the natural generalization of the Schr\"{o}dinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an $n$-qubit system for time $t$…
We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the…
Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the…
Quantum computers can efficiently simulate Lindbladian dynamics, enabling powerful applications in open system simulation, thermal and ground-state preparation, autonomous quantum error correction, dissipative engineering, and more. Despite…
If an open quantum system is initially uncorrelated from its environment, then its dynamics can be written in terms of a Lindblad-form master equation. The master equation is divided into a unitary piece, represented by an effective…
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
The unraveling of open quantum system dynamics in terms of stochastic quantum trajectories offers a picture of open system dynamics that consistently considers memory effects stemming from the finite correlation time of environment…
We present a numerical method to approximate the long-time asymptotic solution $\rho_\infty(t)$ to the Lindblad master equation for an open quantum system under the influence of an external drive. The proposed scheme uses perturbation…
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional…
Quantum simulation on emerging quantum hardware is a topic of intense interest. While many studies focus on computing ground state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target…
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…