Related papers: Random unitaries from Hamiltonian dynamics
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of…
Characterizing the Hamiltonians of continuous-variable (CV) quantum systems is a fundamental challenge laden with difficulties arising from infinite-dimensional Hilbert spaces and unbounded operators. Existing protocols for achieving the…
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
Random dynamics in isolated quantum systems is of practical use in quantum information and is of theoretical interest in fundamental physics. Despite a large number of theoretical studies, it has not been addressed how random dynamics can…
Understanding how fast physical systems can resemble Haar-random unitaries is a fundamental question in physics. Many experiments of interest in quantum gravity and many-body physics, including the butterfly effect in quantum information…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
We discuss the time evolution of physical finite dimensional systems which are modelled by non-hermitian Hamiltonians. We address both general non-hermitian Hamiltonians and pseudo-hermitian ones. We apply the theory of Krein Spaces to…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
A new class of random quantum--dynamical systems in continuous space is introduced and studied in some detail. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic,…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…
Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space…
Imaginary time evolution is a powerful tool applied in quantum physics, while existing classical algorithms for simulating imaginary time evolution suffer high computational complexity as the quantum systems become larger and more complex.…
The quantum Haar random oracle model is an idealized model where every party has access to a single Haar random unitary and its inverse. We construct strong pseudorandom unitaries in the quantum Haar random oracle model. This strictly…
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in…
We study a non-interacting quantum particle, moving on a one-dimensional lattice, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial…