Related papers: Operator dynamics in k-Markov random circuits
The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can,…
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…
We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a…
Despite rapid advances in quantum computing technologies, the qubit connectivity limitation remains to be a critical challenge. Both near-term NISQ quantum computers and relatively long-term scalable quantum architectures do not offer full…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
Randomness is a fundamental resource in quantum information, with crucial applications in cryptography, algorithms, and error correction. A central challenge is to construct unitary $k$-designs that closely approximate Haar-random unitaries…
We consider quantum gates for trapped ions using state-selective displacement of the ions. We generalize earlier work in order to treat arbitrary separations between the traps. This requires the impact of anharmonicity arising from the…
A semi-Markov process method for obtaining general counting statistics for open quantum systems is extended to the scenario of resetting. The simultaneous presence of random resets and wave function collapses means that the quantum jump…
Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $Cd^+$ ion trapped in a slightly anharmonic potential to simulate the…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
We study statistical process control (SPC) through charting of $p$-values. When in control (IC), any valid sequence $(P_{t})_{t}$ is super-uniform, a requirement that can hold in nonparametric and two-phase designs without parametric…
Non-positive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a…
The asymptotic dynamics of quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space on which the resulting quantum Markov chain is…
In this work, we show that ma-QAOA is equivalent to a restriction of continuous-time quantum walks on dynamic graphs. We then show it is universal for computation by finding the appropriate $B$ and $C$ operators and angles that implement…
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…
In this article we continue our investigations of one particle quantum scattering theory for Schroedinger operators on a set of connected (idealized one-dimensional) wires forming a graph with an arbitrary number of open ends. The…
This article investigates discrete-time matrix-weighted consensus of multi-agent networks over undirected and connected graphs. We first present consensus protocols for the agents in common networks of symmetric matrix weights with possibly…