Nicole Yunger Halpern

Autonomous quantum machines (AQMs) execute tasks without requiring time-dependent external control. Motivations for AQMs include the restrictions imposed by classical control on quantum machines' coherence times and geometries. Most AQM work is theoretical and abstract; yet an experiment recently demonstrated AQMs' usefulness in qubit reset, crucial to quantum computing. To further reduce quantum computing's classical control, we propose realizations of (fully and partially) quantum-autonomous gates on three platforms: Rydberg atoms, trapped ions, and superconducting qubits. First, we show that a Rydberg-blockade interaction or an ultrafast transition can quantum-autonomously effect entangling gates on Rydberg atoms. One can perform $Z$ or entangling gates on trapped ions mostly quantum-autonomously, by sculpting a linear Paul trap or leveraging a ring trap. Passive lasers control these gates, as well as the Rydberg-atom gates, quantum-autonomously. Finally, circuit quantum electrodynamics can enable quantum-autonomous $Z$ and $XY$ gates on superconducting qubits. The gates can serve as building blocks for (fully or partially) quantum-autonomous circuits, which may reduce classical-control burdens.

Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalization. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number - in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6-21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested.

Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities -- energy, particles, electric charge, etc. -- that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries -- about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from abstract theory to experimental reality. This paper provides a methodology for building this bridge systematically: We present a prescription for constructing Hamiltonians that conserve noncommuting quantities globally while transporting the quantities locally. The Hamiltonians can couple arbitrarily many subsystems together and can be integrable or nonintegrable. Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, and with trapped ions.

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under "Goldilocks rules" that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms -- Rydberg arrays, trapped ions, and superconducting qubits -- can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.

The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We consider agents who have little control, implementing only general operations suited to macroscopic experimentalists: preparing small-scale entanglement and measuring macroscopic properties while suffering from noise. That experimentalists so restricted can violate a Bell inequality appears unlikely, in light of earlier literature. Yet we prove a Bell inequality that such an agent can violate, even if experimental errors have variances that scale as the system size. A violation implies nonclassicality, given limitations on particles' interactions. A product of singlets violates the inequality; experimental tests are feasible for photons, solid-state systems, atoms, and trapped ions. Consistently with known results, violations of our Bell inequality cannot disprove local hidden-variables theories. By rejecting the disproof goal, we show, one can certify nonclassical correlations under reasonable experimental assumptions.

In statistical mechanics, a small system exchanges conserved quantities---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the conserved quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed ``the non-Abelian thermal state (NATS).'' We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to decoherence and are immune to false positives caused by decoherence. To reach this conclusion, we numerically simulate spin-chain dynamics and three measurement protocols (the interferometric, quantum-clock, and weak-measurement schemes) for measuring OTOCs. We target experiments based on quantum-computing hardware such as superconducting qubits and trapped ions.