TY - JOUR T1 - Complexity-constrained quantum thermodynamics Y1 - 2024 A1 - Anthony Munson A1 - Naga Bhavya Teja Kothakonda A1 - Jonas Haferkamp A1 - Nicole Yunger Halpern A1 - Jens Eisert A1 - Philippe Faist AB -

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process's complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state's complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer's ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy's behavior under random circuits. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy, which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time, as quantified by complexity.

UR - https://arxiv.org/abs/2403.04828 ER - TY - JOUR T1 - Estimation of Hamiltonian parameters from thermal states Y1 - 2024 A1 - Luis Pedro García-Pintos A1 - Kishor Bharti A1 - Jacob Bringewatt A1 - Hossein Dehghani A1 - Adam Ehrenberg A1 - Nicole Yunger Halpern A1 - Alexey V. Gorshkov AB -

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n−−√, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

UR - https://arxiv.org/abs/2401.10343 ER - TY - JOUR T1 - Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits JF - Physical Review B Y1 - 2023 A1 - Shayan Majidy A1 - Utkarsh Agrawal A1 - Sarang Gopalakrishnan A1 - Andrew C. Potter A1 - Romain Vasseur A1 - Nicole Yunger Halpern AB -

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot.

VL - 108 UR - https://arxiv.org/abs/2305.13356 U5 - 10.1103/physrevb.108.054307 ER - TY - JOUR T1 - DiVincenzo-like criteria for autonomous quantum machines Y1 - 2023 A1 - José Antonio Marín Guzmán A1 - Paul Erker A1 - Simone Gasparinetti A1 - Marcus Huber A1 - Nicole Yunger Halpern AB -

Controlled quantum machines have matured significantly. A natural next step is to grant them autonomy, freeing them from timed external control. For example, autonomy could unfetter quantum computers from classical control wires that heat and decohere them; and an autonomous quantum refrigerator recently reset superconducting qubits to near their ground states, as is necessary before a computation. What conditions are necessary for realizing useful autonomous quantum machines? Inspired by recent quantum thermodynamics and chemistry, we posit conditions analogous to DiVincenzo's criteria for quantum computing. Our criteria are intended to foment and guide the development of useful autonomous quantum machines.

UR - https://arxiv.org/abs/2307.08739 ER - TY - JOUR T1 - Experimental Observation of Thermalization with Noncommuting Charges JF - PRX Quantum Y1 - 2023 A1 - Florian Kranzl A1 - Aleksander Lasek A1 - Manoj K. Joshi A1 - Amir Kalev A1 - Rainer Blatt A1 - Christian F. Roos A1 - Nicole Yunger Halpern AB -

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.

VL - 4 UR - https://arxiv.org/abs/2202.04652 U5 - 10.1103/prxquantum.4.020318 ER - TY - JOUR T1 - Non-Abelian eigenstate thermalization hypothesis JF - Phys. Rev. Lett. Y1 - 2023 A1 - Murthy, Chaitanya A1 - Babakhani, Arman A1 - Iniguez, Fernando A1 - Srednicki, Mark A1 - Nicole Yunger Halpern KW - FOS: Physical sciences KW - High Energy Physics - Theory (hep-th) KW - Quantum Gases (cond-mat.quant-gas) KW - Quantum Physics (quant-ph) KW - Statistical Mechanics (cond-mat.stat-mech) KW - Strongly Correlated Electrons (cond-mat.str-el) AB -

The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local observables' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

VL - 130 UR - https://arxiv.org/abs/2206.05310 U5 - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.140402 ER - TY - JOUR T1 - Non-Abelian symmetry can increase entanglement entropy JF - Physical Review B Y1 - 2023 A1 - Shayan Majidy A1 - Aleksander Lasek A1 - David A. Huse A1 - Nicole Yunger Halpern AB -

The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges' noncommutation -- of a symmetry's non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement.

VL - 107 UR - https://arxiv.org/abs/2209.14303 U5 - 10.1103/physrevb.107.045102 ER - TY - JOUR T1 - Noncommuting conserved charges in quantum thermodynamics and beyond JF - Nature Reviews Physics Y1 - 2023 A1 - Shayan Majidy A1 - William F. Braasch A1 - Aleksander Lasek A1 - Twesh Upadhyaya A1 - Amir Kalev A1 - Nicole Yunger Halpern AB -

Thermodynamic systems typically conserve quantities ("charges") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on observables' failure to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Charges' noncommutation has been found to invalidate derivations of the thermal state's form, decrease entropy production, conflict with the eigenstate thermalization hypothesis, and more. This Perspective surveys key results in, opportunities for, and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: Evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.

UR - https://arxiv.org/abs/2306.00054 U5 - 10.1038/s42254-023-00641-9 ER - TY - JOUR T1 - Quantum simulations of time travel can power nonclassical metrology JF - Phys. Rev. Lett. Y1 - 2023 A1 - David R. M. Arvidsson-Shukur A1 - Aidan G. McConnell A1 - Nicole Yunger Halpern AB -

We construct a metrology experiment in which the metrologist can sometimes amend her input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change her input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist's winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.

VL - 131 UR - arXiv:2207.07666 CP - 150202 U5 - https://doi.org/10.48550/arXiv.2207.07666 ER - TY - JOUR T1 - Thermally driven quantum refrigerator autonomously resets superconducting qubit Y1 - 2023 A1 - Mohammed Ali Aamir A1 - Paul Jamet Suria A1 - José Antonio Marín Guzmán A1 - Claudia Castillo-Moreno A1 - Jeffrey M. Epstein A1 - Nicole Yunger Halpern A1 - Simone Gasparinetti AB -

The first thermal machines steered the industrial revolution, but their quantum analogs have yet to prove useful. Here, we demonstrate a useful quantum absorption refrigerator formed from superconducting circuits. We use it to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments. The environments consist of microwave waveguides populated with synthesized thermal photons. The target qubit, if initially fully excited, reaches a steady-state excited-level population of 5×10−4±5×10−4 (an effective temperature of 23.5~mK) in about 1.6~μs. Our results epitomize how quantum thermal machines can be leveraged for quantum information-processing tasks. They also initiate a path toward experimental studies of quantum thermodynamics with superconducting circuits coupled to propagating thermal microwave fields.

UR - https://arxiv.org/abs/2305.16710 ER - TY - JOUR T1 - What happens to entropy production when conserved quantities fail to commute with each other Y1 - 2023 A1 - Twesh Upadhyaya A1 - William F. Braasch, Jr. A1 - Gabriel T. Landi A1 - Nicole Yunger Halpern AB -

We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, of the three formulae. Charges' noncommutation, we find, breaks the formulae's equivalence. Furthermore, different formulae quantify different physical effects of charges' noncommutation on entropy production. For instance, entropy production can signal contextuality - true nonclassicality - by becoming nonreal. This work opens up stochastic thermodynamics to noncommuting - and so particularly quantum - charges.

UR - https://arxiv.org/abs/2305.15480 ER - TY - JOUR T1 - Experimental observation of thermalisation with noncommuting charges Y1 - 2022 A1 - Kranzl, Florian A1 - Lasek, Aleksander A1 - Joshi, Manoj K. A1 - Kalev, Amir A1 - Blatt, Rainer A1 - Roos, Christian F. A1 - Nicole Yunger Halpern KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) KW - Statistical Mechanics (cond-mat.stat-mech) AB -

Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalisation. 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 6-15 spins in an approximate microcanonical subspace, a generalisation 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.

UR - https://arxiv.org/abs/2202.04652 U5 - 10.48550/ARXIV.2202.04652 ER - TY - JOUR T1 - Experimentally Measuring Rolling and Sliding in Three-Dimensional Dense Granular Packings JF - Phys. Rev. Lett. Y1 - 2022 A1 - Zackery A. Benson A1 - Anton Peshkov A1 - Nicole Yunger Halpern A1 - Derek C. Richardson A1 - Wolfgang Losert AB -

We experimentally measure a three-dimensional (3D) granular system’s reversibility under cyclic compression. We image the grains using a refractive-index-matched fluid, then analyze the images using the artificial intelligence of variational autoencoders. These techniques allow us to track all the grains’ translations and 3D rotations with accuracy sufficient to infer sliding and rolling displacements. Our observations reveal unique roles played by 3D rotational motions in granular flows. We find that rotations and contact-point motion dominate the dynamics in the bulk, far from the perturbation’s source. Furthermore, we determine that 3D rotations are irreversible under cyclic compression. Consequently, contact-point sliding, which is dissipative, accumulates throughout the cycle. Using numerical simulations whose accuracy our experiment supports, we discover that much of the dissipation occurs in the bulk, where grains rotate more than they translate. Our observations suggest that the analysis of 3D rotations is needed for understanding granular materials’ unique and powerful ability to absorb and dissipate energy.

VL - 129 U4 - 048001 UR - https://arxiv.org/abs/2108.11975 CP - 4 U5 - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.048001 ER - TY - JOUR T1 - How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics JF - npj Quantum Inf Y1 - 2022 A1 - Nicole Yunger Halpern A1 - Shayan Majidy AB -

Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and a bath 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 an algorithm 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. Special cases of our construction have appeared in quantum chromodynamics (QCD). Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, with trapped ions, and in QCD.

VL - 8 UR - https://arxiv.org/abs/2103.14041v1 CP - 10 U5 - https://doi.org/10.1038/s41534-022-00516-4 ER - TY - JOUR T1 - Linear growth of quantum circuit complexity JF - Nat. Phys. Y1 - 2022 A1 - Jonas Haferkamp A1 - Philippe Faist A1 - Naga B. T. Kothakonda A1 - Jens Eisert A1 - Nicole Yunger Halpern AB -

The complexity of quantum states has become a key quantity of interest across various subfields of physics, from quantum computing to the theory of black holes. The evolution of generic quantum systems can be modelled by considering a collection of qubits subjected to sequences of random unitary gates. Here we investigate how the complexity of these random quantum circuits increases by considering how to construct a unitary operation from Haar-random two-qubit quantum gates. Implementing the unitary operation exactly requires a minimal number of gates—this is the operation’s exact circuit complexity. We prove a conjecture that this complexity grows linearly, before saturating when the number of applied gates reaches a threshold that grows exponentially with the number of qubits. Our proof overcomes difficulties in establishing lower bounds for the exact circuit complexity by combining differential topology and elementary algebraic geometry with an inductive construction of Clifford circuits.

U5 - https://doi.org/10.1038/s41567-022-01539-6 ER - TY - JOUR T1 - Negative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment JF - Phys. Rev. Lett. Y1 - 2022 A1 - Lupu-Gladstein, Noah A1 - Yilmaz, Y. Batuhan A1 - Arvidsson-Shukur, David R. M. A1 - Brodutch, Aharon A1 - Pang, Arthur O. T. A1 - Steinberg, Aephraim M. A1 - Nicole Yunger Halpern AB -

Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities—quantum extensions of probabilities—engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a wave plate’s birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter’s amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA’s metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.

VL - 128 U4 - 220504 UR - https://link.aps.org/doi/10.1103/PhysRevLett.128.220504 U5 - 10.1103/PhysRevLett.128.220504 ER - TY - JOUR T1 - Resource theory of quantum uncomplexity JF - Physical Review A Y1 - 2022 A1 - Nicole Yunger Halpern A1 - Naga B. T. Kothakonda A1 - Jonas Haferkamp A1 - Anthony Munson A1 - Jens Eisert A1 - Philippe Faist AB -

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or "uncomplexity," the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

VL - 106 UR - https://arxiv.org/abs/2110.11371 U5 - 10.1103/physreva.106.062417 ER - TY - JOUR T1 - Entangled quantum cellular automata, physical complexity, and Goldilocks rules JF - Quantum Science and Technology Y1 - 2021 A1 - Hillberry, Logan E A1 - Jones, Matthew T A1 - Vargas, David L A1 - Rall, Patrick A1 - Nicole Yunger Halpern A1 - Bao, Ning A1 - Notarnicola, Simone A1 - Montangero, Simone A1 - Carr, Lincoln D AB -

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.

VL - 6 U4 - 045017 UR - http://dx.doi.org/10.1088/2058-9565/ac1c41 U5 - 10.1088/2058-9565/ac1c41 ER - TY - JOUR T1 - Machine learning outperforms thermodynamics in measuring how well a many-body system learns a drive JF - Scientific Reports Y1 - 2021 A1 - Zhong, Weishun A1 - Gold, Jacob M. A1 - Marzen, Sarah A1 - England, Jeremy L. A1 - Nicole Yunger Halpern AB -

Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems' learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning. 

VL - 11 UR - https://arxiv.org/abs/2004.03604 U5 - https://doi.org/10.1038/s41598-021-88311-7 ER - TY - JOUR T1 - Resource theory of quantum uncomplexity Y1 - 2021 A1 - Nicole Yunger Halpern A1 - Naga B. T. Kothakonda A1 - Jonas Haferkamp A1 - Anthony Munson A1 - Jens Eisert A1 - Philippe Faist AB -

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or ``uncomplexity,'' the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

UR - https://arxiv.org/abs/2110.11371 ER - TY - JOUR T1 - Noncommuting conserved charges in quantum many-body thermalization JF - Phys. Rev. E Y1 - 2020 A1 - Nicole Yunger Halpern A1 - Michael E. Beverland A1 - Amir Kalev AB -

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 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 forms 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 near 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.

VL - 101 UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.042117 CP - 042117 U5 - https://doi.org/10.1103/PhysRevE.101.042117 ER - TY - JOUR T1 - Equilibration to the non-Abelian thermal state in quantum many-body physics Y1 - 2019 A1 - Nicole Yunger Halpern A1 - Michael E. Beverland A1 - Amir Kalev AB -

In statistical mechanics, a small system exchanges conserved charges---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 charges. The charges are usually represented by operators 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 charges manifest as spin components. Heisenberg interactions push the charges 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 charges from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter. 

UR - https://arxiv.org/abs/1906.09227 ER - TY - JOUR T1 - The quasiprobability behind the out-of-time-ordered correlator JF - Phys. Rev. Y1 - 2018 A1 - Nicole Yunger Halpern A1 - Brian Swingle A1 - Justin Dressel AB -

Two topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC has been shown to equal a moment of a summed quasiprobability. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze the weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

VL - A UR - https://arxiv.org/abs/1704.01971 CP - 97 U5 - https://doi.org/10.1103/PhysRevA.97.042105 ER - TY - JOUR T1 - Resilience of scrambling measurements JF - Phys. Rev. Y1 - 2018 A1 - Brian Swingle A1 - Nicole Yunger Halpern AB -

Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backwards time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum-chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

VL - A UR - https://arxiv.org/abs/1802.01587 CP - 97 U5 - https://doi.org/10.1103/PhysRevA.97.062113 ER -