TIME AND QUANTUM PROCESS

Wolfram Schommers

Neil Dowling, Pedro Figueroa–Romero, Felix A. Pollock +2 more

Quantum stochastic processes are shown, within finite time intervals and for finite dimensional time-independent Hamiltonians, to be close to a corresponding stationary equilibrium process. This occurs for multitime observables that are coarse grained in both space and time, and for systems which have many significantly interacting energy eigenstates. This dictates conditions on time scales at when the multitime statistics of any arbitrary non-equilibrium quantum process look equilibrium on average. We show that this leads to the equilibration of general geometric measures of quantum processes, such as the degree of non-Markovianity or classicality. The implications of this result for the emergence of classical stochastic processes from underlying quantum mechanics are also discussed.

Marek Kanter

In this paper time is indexed by a “time group” G that may be either the real line or the integers. A quantum process is a homomorphic representation of G via unitary operators on a Hilbert space L, with the usual continuity restrictions if time is indexed by the reals. Consider a quantum process subject to nonselective observation at all points in time via an observation operator with purely discrete eigenvalues and corresponding simple eigenvectors. Suppose that the process evolves in such a way that the results of observation at a given time are the same, whether or not there have been previous observations. Suppose further that L is spanned by the set of vectors invariant modulo phase under the quantum evolution. If the time group is the integers, then the process is observed to evolve in a classical manner. If the time group is the real line, then the process is never observed to undergo a change of state. The results of this paper are essentially a corollary of von Neumann’s mean ergodic theorem.

Bob Coecke, Aleks Kissinger

Henry Pierce Stapp

Christina Giarmatzi, Tyler Jones, Alexei Gilchrist +3 more

Current quantum technologies are at the cusp of becoming useful, but still face formidable obstacles such as noise. Noise severely limits the ability to scale quantum devices to the point that they would offer an advantage over classical devices. To understand the sources of noise it is necessary to fully characterise the quantum processes occurring across many time steps; only this would reveal any time-correlated noise called non-Markovian. Previous efforts have attempted such a characterisation but obtained only a limited reconstruction of such multi-time processes. In this work, we fully characterise a multi-time quantum process on superconducting hardware using in-house and cloud-based quantum processors. We achieve this by employing sequential measure-and-prepare operations combined with post-processing. Employing a recently developed formalism for multi-time processes, we detect general multi-time correlated noise. We also detect quantum correlated noise which demonstrates that part of the noise originates from quantum sources, such as physically nearby qubits on the chip.