Related papers: Random unitaries from Hamiltonian dynamics
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…
It has been recently proposed that the naive semiclassical prediction of non-unitary black hole evaporation can be understood in the fundamental description of the black hole as a consequence of ignorance of high-complexity information.…
We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation. We analyse a Floquet model with disorder, characterised by a…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…
Evolutions of local Hamiltonians in short times are expected to remain local and thus limited. In this paper, we validate this intuition by proving some limitations on short-time evolutions of local time-dependent Hamiltonians. We show that…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
We show that the consequences of an introduction of a manifest time-dependence in a pseudo-Hermitian Hamiltonian H=H(t) are by far less drastic than suggested by A. Mostafazadeh in Phys. Lett. B 650 (2007) 208 (arXiv:0706.1872v2…
We calculate the frame potential for Brownian clusters of $N$ spins or fermions with time-dependent all-to-all interactions. In both cases the problem can be mapped to an effective statistical mechanics problem which we study using a path…
Here we present an strategy for the derivation of a time-dependent Dyson map which ensures simultaneously the unitarity of the time evolution and the observability of a quasi-Hermitian Hamiltonian. The time-dependent Dyson map is derived…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
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…
Learning about a Hamiltonian $H$ from its time evolution $e^{-iHt}$ is a fundamental task in quantum science. A flurry of recent work has developed powerful new algorithms with provable guarantees for this task, for a variety of natural…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian…