Related papers: Universal Early-Time Growth in Quantum Circuit Com…
In this work, we propose a testing procedure to distinguish between the different approaches for computing complexity. Our test does not require a direct comparison between the approaches and thus avoids the issue of choice of gates, basis,…
Motivated by studies of ultimate speed of computers, we examine the question of minimum time of orthogonalization in a simple anharmonic oscillator and find an upper bound on the rate of computations. Furthermore, we investigate the growth…
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…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
Hamiltonian quantum simulation of bosons on digital quantum computers requires truncating the Hilbert space to finite dimensions. The method of truncation and the choice of basis states can significantly impact the complexity of the quantum…
Dual-unitary circuits are a class of locally-interacting quantum many-body systems displaying unitary dynamics also when the roles of space and time are exchanged. These systems have recently emerged as a remarkable framework where certain…
We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared…
Our main goal in this paper is to extend to any system of coupled quadratic Hamiltonians some properties known for systems of quantum harmonic oscillators related with the Brownian Quantum Motion model. In a first part we get a rather…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of…
Quantum simulations of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of improved lattice actions in classical simulations strongly suggests that Hamiltonians with improved…
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new…
We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas…
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
We derive and investigate a general non-Markovian equation for the time-dependence of a Hamiltonian that maximizes the fidelity of a desired quantum gate on any finite-dimensional quantum system in the presence of arbitrary bath and noise…
We study an open quantum system of free fermions on an infinite lattice coupled to a localized particle source. In the long time limit, the total number of fermions in the system increases linearly with growth rate dependent on the lattice…
As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we…