Related papers: Limits of Short-Time Evolution of Local Hamiltonia…
We establish necessary and sufficient conditions for viability of evolution inclusions with locally monotone operators in the sense of Liu and R\"ockner [J. Funct. Anal., 259 (2010), pp. 2902-2922]. This allows us to prove wellposedness of…
Reliable quantum technology requires knowledge of the dynamics governing the underlying system. This problem of characterizing and benchmarking quantum devices or experiments in continuous time is referred to as the Hamiltonian learning…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light-cone with exponentially decaying tails. We discuss several consequences of this…
We extend the concept of locality to enclose a situation where a tensor-product structure for the Hilbert space is not \textit {a priori} assumed; rather, this locality is related to a given matrix representation of the Hamiltonian…
We study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the…
The evolution speed in projective Hilbert space is considered for Hermitian Hamiltonians and for non-Hermitian (NH) ones. Based on the Hilbert-Schmidt norm and the spectral norm of a Hamiltonian, resource-related upper bounds on the…
We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian $A$ under a small geometrically local perturbation $\alpha B$. In certain regimes, the algorithm achieves the optimal scaling and outperforms the…
Classical hardness-of-sampling results are largely established for random quantum circuits, whereas analog simulators natively realize time evolutions under geometrically local Hamiltonians. Does a typical such Hamiltonian already yield…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest…
The commutator between operators at different space and time has been a diagnostic for locality of unitary evolution. Most existing results are either for specific tractable (random) Hamiltonians(Out-of-Time-Order-Correlators calculations),…
Time-local master equations are more generally applicable than is often recognised, but at first sight it would seem that they can only safely be used in time intervals where the time evolution is invertible. Using the Jaynes-Cummings…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
Recently, the notion of a quantum acceleration limit has been proposed for any unitary time evolution of quantum systems governed by arbitrary nonstationary Hamiltonians. This limit articulates that the rate of change over time of the…
We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…
Locality is a fundamental feature of many physical time evolutions. Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time…