Quantum Physics: States, Observables and Their Time Evolution

Yakir Aharonov, David Z. Albert

Circumstances are described wherein no state at a given time (nor any definite evolution from one time to another) can be ascribed to a given physical system, but wherein the system can nonetheless be associated with definite dispersion-free values of a new sort of observable, which we call a "multiple-time" observable. The description of physical systems in terms of these new observables is discussed. It emerges as a by-product of our work that no experiment whatever (albeit that its result is certain) can be carried out on a system without disturbing the values of other measurable quantities.

Roman Schmied

Kazutaka G. Nakamura

Edward Parker

Abstract 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 principles whether this claim is true: if we assume only that the time-evolution operator is linear, then does the stronger requirement that it be unitary follow from the other axioms of quantum mechanics? The answer is subtle. We discuss two mathematically distinct but physically equivalent formulations of the axioms of quantum mechanics, and consider generalizing each to postulate only that time evolution is linear. Within one formulation, the unitarity of time evolution follows logically from the other axioms – but within the other formulation, it does not. Allowing the time-evolution operator to be (a priori) arbitrarily linear does not change the physical observables in one formulation of quantum mechanics, but changes the other formulation to a distinct (internally consistent) physical theory that allows new phenomenology like (e.g.) faster-than-light communication. Therefore, the unitarity of time evolution is arguably better thought of as a logically independent and experimentally falsifiable axiom of quantum mechanics, not as a tautological consequence of the other axioms.

Julien Gacon, Jannes Nys, Riccardo Rossi +2 more

Real- and imaginary-time quantum state evolutions are crucial in physics and chemistry for exploring quantum dynamics, preparing ground states, and computing thermodynamic observables. On near-term devices, variational quantum time evolution is a promising candidate for these tasks, as the required circuit model can be tailored to the available devices' capabilities. Due to the evaluation of the quantum geometric tensor (QGT), however, this approach quickly becomes infeasible for relevant system sizes. Here, we propose a dual formulation for variational time evolution, which replaces the calculation of the QGT by solving a fidelity-based optimization to compute updates to the dynamics in each time step. We demonstrate our algorithm for the time evolution of the Heisenberg Hamiltonian and show that it accurately reproduces the system dynamics at a fraction of the cost of standard variational quantum time evolution algorithms. Published by the American Physical Society 2024

H. David Sheets, Michael Dupin