arXiv:1903.10568 · Quantum

Translating Uncontrolled Systems in Time

David Trillo, Benjamin Dive, Miguel Navascués

Published Dec 15, 2020• 16 citations

Abstract

We show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This ``time translation'' effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes which are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. We fully characterize the possible time translations which we can effect on multiple target systems through a scattering protocol of fixed duration. The core results are: a) when the target is a single system, we can translate it backwards in time for an amount proportional to the experimental runtime; b) when n targets are present in the scattering region, we can make a single system evolve n times faster (backwards or forwards), at the cost of keeping the remaining n−1 systems stationary in time. For high n our protocols therefore allow one to map, in short experimental time, a system to the state it would have reached with a very long unperturbed evolution in either positive or negative time.

DOI: 10.22331/q-2020-12-15-374

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arXiv:1903.10568 · Quantum

Translating Uncontrolled Systems in Time

David Trillo, Benjamin Dive, Miguel Navascués

Published Dec 15, 2020• 16 citations

arXiv HTML PDF

Abstract

DOI: 10.22331/q-2020-12-15-374

Related papers

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M'

M ′ of the interacting time evolution has to be unitarily equivalent to the invariant mass

M= \sqrt{P^2}

M = P 2 where P, acting on many-particle states, is the sum of the one-particle four-momenta. For an observer at rest

P^0

P 0 generates the free time evolution. Poincaré symmetry requires the interacting Hamiltonian

H'

H ′ to Lorentz transform as 0-component of a four-vector and to commute with the four-velocity

U= P / M

U = P / M but not with P, else there is no scattering. Even though

H'

H ′ does not commute with P, the scattering matrix does. The four-velocity U generates translations of states as they are seen by shifted observers. Superpositions of nearly mass degenerate particles such as a

K_{\text {long}}

K long are seen by an inversely shifted observer as a shifted

K_{\text {long}}

K long with an unchanged relative phase. In contrast, the four-momentum P generates oscillated superpositions e.g. a shifted

K_{\text {short}}

K short with a changed relative phase. The probability of scattering of massive particles is shown to be approximately proportional to the spacetime overlap of their position wave functions. This is basic to macroscopic locality and justifies to represent the machinery of actual scattering experiments by the vacuum. In suitable variables the relativistic Hamiltonian of many-particle states is not the sum of a Hamiltonian for the motion of the center and a commuting Hamiltonian for the relative motion but factorizes as their product. They act on different variables of the wave functions.

H

with

||H||\leqΛ

in total evolution time of

Θ(\fracΛ{ε^2}\log(\fracΛε))

. The evolution time cost of our algorithm is optimal for any control-free protocols as we further prove a lower bound of

Ω(\fracΛ{ε^2}\log(\fracΛε))

. Technically, our method introduces a randomized-sampling framework that combines band-limited kernel-based time sampling with a displacement sieve for Hamiltonian structure learning. The characteristic probe time resolution depends only on

Λ

instead of

\varepsilon

, which makes our protocol especially appealing in the high-precision regime for sensing and calibration applications. We also show that the algorithm maintains the same asymptotic total evolution time in the presence of state-preparation-and-measurement (SPAM) noise when the Hamiltonian is local after calibration. Our results demonstrate the fundamental cost of experimentally friendly Hamiltonian learning and provide a practical route to rigorous in situ characterization of near-term quantum platforms.

{{\mathcal{W}}}_{4}

W 4 protocol, with five superconducting qubits, testing it with different types of free evolutions and target–probe interactions. After projection, we obtained a reset state fidelity as high as 0.951, and the process fidelity was found to be 0.792. We also implemented 100 randomly chosen interactions and demonstrated an average success probability of 0.323 for

\left|1\right\rangle

1 and 0.292 for

\left|-\right\rangle

− , and experimentally confirmed the nonzero probability of success for unknown interactions; the numerical simulated values are about 0.3. Our experiment shows that the simplest quantum resetting protocol can be implemented with current technologies, making such protocols a valuable tool in the eternal fight against unwanted evolution in quantum systems.