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Cellular automata are interacting classical bits that display diverse behaviors, from fractals to random-number generators to Turing-complete computation. We introduce entangled quantum cellular automata subject to Goldilocks rules, tradeoffs of the kind underpinning biological, social, and economic complexity. Tweaking digital and analog quantum-computing protocols generates persistent entropy fluctuations; robust dynamical features, including an entangled breather; and network structure and dynamics consistent with complexity. Present-day quantum platforms---Rydberg arrays, trapped ions, and superconducting qubits---can implement Goldilocks protocols, which generate quantum many-body states with rich entanglement and structure. Moreover, the complexity studies reported here underscore an emerging idea in many-body quantum physics: some systems fall outside the integrable/chaotic dichotomy.
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Hydrodynamic nonlinear response of interacting integrable systems
We develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb–Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.
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- Award ID(s):
- 1653271
- PAR ID:
- 10326249
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 37
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2106945118
