Abstract
Randomness is an essential tool in many disciplines of modern sciences, such as cryptography, black hole physics, random matrix theory, and Monte Carlo sampling. In quantum systems, random operations can be obtained via random circuits thanks to so-called -designs and play a central role in condensed-matter physics and in the fast scrambling conjecture for black holes. Here, we consider a more physically motivated way of generating random evolutions by exploiting the many-body dynamics of a quantum system driven with stochastic external pulses. We combine techniques from quantum control, open quantum systems, and exactly solvable models (via the Bethe ansatz) to generate Haar-uniform random operations in driven many-body systems. We show that any fully controllable system converges to a unitary -design in the long-time limit. Moreover, we study the convergence time of a driven spin chain by mapping its random evolution into a semigroup with an integrable Liouvillian and finding its gap. Remarkably, we find via Bethe-ansatz techniques that the gap is independent of . We use mean-field techniques to argue that this property may be typical for other controllable systems, although we explicitly construct counterexamples via symmetry-breaking arguments to show that this is not always the case. Our findings open up new physical methods to transform classical randomness into quantum randomness, via a combination of quantum many-body dynamics and random driving.
- Received 4 May 2017
DOI:https://doi.org/10.1103/PhysRevX.7.041015
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Random number generators play a prominent role in many technologies such as cryptography, computer science, and numerical computation algorithms (such as the ubiquitous Monte Carlo methods). Within quantum information science, random quantum operations have found a similar pivotal role in applications such as quantum encryption, noise estimation, and demonstrating quantum supremacy. Unfortunately, creating quantum randomness is much harder than creating its classical analog. Quantum algorithms that can generate truly random or pseudorandom operations require quantum devices as complex as a universal quantum computer, far exceeding the capability of any current technology. On the other hand, nature already provides us with complex quantum systems, namely, many-body systems. Such systems are central to condensed-matter physics and quantum simulation but are incapable of creating randomness on their own. We pose the following key question: If we provide a many-body system with classical randomness through driving, then does it efficiently blend it into quantum randomness via its natural dynamics? We find that this is, indeed, sometimes true.
More precisely, we show that whenever the mean-field approximation is valid, then the system scrambles efficiently. We also provide an example for which the scrambling is inefficient (which implies that mean-field theory is invalid for this model). Finally, we provide an integrable model of experimental interest, for which the efficiency is provably true.
Our results show that some quantum many-body systems can also be used as “quantum blenders.”