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Article ; Online: Stable Measurement-Induced Floquet Enriched Topological Order.

Vu, DinhDuy / Lavasani, Ali / Lee, Jong Yeon / Fisher, Matthew P A

2024 Volume 132, Issue 7, Page(s) 70401

Abstract: The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The ... ...

Abstract	The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The code also possesses a time-crystal order-the e-m transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule. This behavior is distinct from the stationary topological order realized in either random circuits or time-independent Hamiltonian. Therefore, the resultant phase belongs to the overlap between the classes of Floquet enriched topological orders and measurement-induced phases. In this Letter, we construct a continuous path interpolating between the Floquet and toric codes, focusing on the transition between the time-crystal and stationary topological phases. We show that this transition is characterized by a divergent length scale. We also add single-qubit perturbations to the model and obtain a richer two-dimensional parametric phase diagram of the Floquet code, showing the stability of the Floquet enriched topological order.
Language	English
Publishing date	2024-03-01
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.132.070401
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Article ; Online: Cross Entropy Benchmark for Measurement-Induced Phase Transitions.

Li, Yaodong / Zou, Yijian / Glorioso, Paolo / Altman, Ehud / Fisher, Matthew P A

Physical review letters

2023 Volume 130, Issue 22, Page(s) 220404

Abstract: We investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with ... ...

Abstract	We investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross entropy χ between the bulk measurement outcome distributions in the two circuits acts as an order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and χ=1. In the area law phase χ<1. For circuits with Clifford gates, we provide numerical evidence that χ can be sampled to accuracy ϵ from O(1/ϵ^{2}) trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the measurement-induced phase transitions is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the "classical" side can be simulated efficiently, while simulating the "quantum" side is still classically hard.
MeSH term(s)	Entropy ; Benchmarking ; Thermodynamics ; Computer Simulation ; Phase Transition
Language	English
Publishing date	2023-06-16
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.130.220404
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Book ; Online: Universality of the cross entropy in $\mathbb{Z}_2$ symmetric monitored quantum circuits

Tikhanovskaya, Maria / Lavasani, Ali / Fisher, Matthew P. A. / Vijay, Sagar

2023

Abstract: The linear cross-entropy (LXE) has been recently proposed as a scalable probe of the measurement-driven phase transition between volume- and area-law-entangled phases of pure-state trajectories in certain monitored quantum circuits. Here, we demonstrate ... ...

Abstract	The linear cross-entropy (LXE) has been recently proposed as a scalable probe of the measurement-driven phase transition between volume- and area-law-entangled phases of pure-state trajectories in certain monitored quantum circuits. Here, we demonstrate that the LXE can distinguish distinct area-law-entangled phases of monitored circuits with symmetries, and extract universal behavior at the critical points separating these phases. We focus on (1+1)-dimensional monitored circuits with an on-site $\mathbb{Z}_{2}$ symmetry. For an appropriate choice of initial states, the LXE distinguishes the area-law-entangled spin glass and paramagnetic phases of the monitored trajectories. At the critical point, described by two-dimensional percolation, the LXE exhibits universal behavior which depends sensitively on boundary conditions, and the choice of initial states. With open boundary conditions, we show that the LXE relates to crossing probabilities in critical percolation, and is thus given by a known universal function of the aspect ratio of the dynamics, which quantitatively agrees with numerical studies of the LXE at criticality. The LXE probes correlations of other operators in percolation with periodic boundary conditions. We show that the LXE is sensitive to the richer phase diagram of the circuit model in the presence of symmmetric unitary gates. Lastly, we consider the effect of noise during the circuit evolution, and propose potential solutions to counter it. Comment: 11+6 pages, 16 figures
Keywords	Quantum Physics ; Condensed Matter - Statistical Mechanics
Subject code	612
Publishing date	2023-05-31
Publishing country	us
Document type	Book ; Online
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Article ; Online: Quantum indistinguishability in chemical reactions.

Fisher, Matthew P A / Radzihovsky, Leo

Proceedings of the National Academy of Sciences of the United States of America

2018 Volume 115, Issue 20, Page(s) E4551–E4558

Abstract: Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly ... ...

Abstract	Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a "quantum dynamical selection" (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include (
Language	English
Publishing date	2018-04-30
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.
ZDB-ID	209104-5
ISSN	1091-6490 ; 0027-8424
ISSN (online)	1091-6490
ISSN	0027-8424
DOI	10.1073/pnas.1718402115
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Book ; Online: Statistical Mechanics of Quantum Error-Correcting Codes

Li, Yaodong / Fisher, Matthew P. A.

2020

Abstract: We study stabilizer quantum error-correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a subregion to ... ...

Abstract	We study stabilizer quantum error-correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a subregion to its entanglement properties, and 2) a previously established mapping between entanglement entropies and domain wall free energies of an underlying spin model, we propose a statistical mechanical description of the QECC in terms of "entanglement domain walls". Free energies of such domain walls generically feature a leading volume law term coming from its "surface energy", and a sub-volume law correction coming from thermodynamic entropies of its transverse fluctuations. These are most easily accounted for by capillary-wave theory of liquid-gas interfaces, which we use as an illustrative tool. We show that the information-theoretic decoupling criterion corresponds to a geometric decoupling of domain walls, which further leads to the identification of the "contiguous code distance" of the QECC as the crossover length scale at which the energy and entropy of the domain wall are comparable. The contiguous code distance thus diverges with the system size as the subleading entropic term of the free energy, protecting a finite code rate against local undetectable errors. We support these correspondences with numerical evidence, where we find capillary-wave theory describes many qualitative features of the QECC; we also discuss when and why it fails to do so. Comment: 22 pages, 8 figures. v2: fixed .bbl file, new footnote 12. v3: updated references and acknowledgements
Keywords	Quantum Physics ; Condensed Matter - Disordered Systems and Neural Networks ; Condensed Matter - Statistical Mechanics
Subject code	612
Publishing date	2020-07-07
Publishing country	us
Document type	Book ; Online
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Book ; Online: Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment

Li, Yaodong / Vijay, Sagar / Fisher, Matthew P. A.

2021

Abstract: Monitored quantum dynamics reveal quantum state trajectories which exhibit a rich phenomenology of entanglement structures, including a transition from a weakly-monitored volume law entangled phase to a strongly-monitored area law phase. For one- ... ...

Abstract	Monitored quantum dynamics reveal quantum state trajectories which exhibit a rich phenomenology of entanglement structures, including a transition from a weakly-monitored volume law entangled phase to a strongly-monitored area law phase. For one-dimensional hybrid circuits with both random unitary dynamics and interspersed measurements, we combine analytic mappings to an effective statistical mechanics model with extensive numerical simulations on hybrid Clifford circuits to demonstrate that the universal entanglement properties of the volume law phase can be quantitatively described by a fluctuating entanglement domain wall that is equivalent to a "directed polymer in a random environment" (DPRE). This relationship improves upon a qualitative "mean-field" statistical mechanics of the volume-law-entangled phase [1, 2]. For the Clifford circuit in various geometries, we obtain agreement between the subleading entanglement entropies and error correcting properties of the volume-law phase (which quantify its stability to projective measurements) with predictions of the DPRE. We further demonstrate that depolarizing noise in the hybrid dynamics near the final circuit time can drive a continuous phase transition to a non-error correcting volume law phase that is not immune to the disentangling action of projective measurements. We observe this transition in hybrid Clifford dynamics, and obtain quantitative agreement with critical exponents for a "pinning" phase transition of the DPRE in the presence of an attractive interface. Comment: 22 pages, 18 figures
Keywords	Condensed Matter - Statistical Mechanics ; Condensed Matter - Disordered Systems and Neural Networks ; Quantum Physics
Subject code	612
Publishing date	2021-05-27
Publishing country	us
Document type	Book ; Online
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Book ; Online: Entanglement phase transitions in random stabilizer tensor networks

Yang, Zhi-Cheng / Li, Yaodong / Fisher, Matthew P. A. / Chen, Xiao

2021

Abstract: We explore a class of random tensor network models with "stabilizer" local tensors which we name Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement ... ...

Abstract	We explore a class of random tensor network models with "stabilizer" local tensors which we name Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement phase transitions between volume-law and area-law entangled phases of the one-dimensional boundary states. These transitions occur when either (a) the bond dimension $D$ of the constituent tensors is varied, or (b) the tensor network is subject to random breaking of bulk bonds, implemented by forced measurements. In the absence of broken bonds, we find that the RSTN supports a volume-law entangled boundary state with bond dimension $D\geq3$ where $D$ is a prime number, and an area-law entangled boundary state for $D=2$. Upon breaking bonds at random in the bulk with probability $p$, there exists a critical measurement rate $p_c$ for each $D\geq 3$ above which the boundary state becomes area-law entangled. To explore the conformal invariance at these entanglement transitions for different prime $D$, we consider tensor networks on a finite rectangular geometry with a variety of boundary conditions, and extract universal operator scaling dimensions via extensive numerical calculations of the entanglement entropy, mutual information and mutual negativity at their respective critical points. Our results at large $D$ approach known universal data of percolation conformal field theory, while showing clear discrepancies at smaller $D$, suggesting a distinct entanglement transition universality class for each prime $D$. We further study universal entanglement properties in the volume-law phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment. Comment: Updated to published version
Keywords	Condensed Matter - Statistical Mechanics ; Condensed Matter - Disordered Systems and Neural Networks ; High Energy Physics - Theory ; Quantum Physics
Subject code	612
Publishing date	2021-07-26
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids.

Veness, Thomas / Essler, Fabian H L / Fisher, Matthew P A

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

2017 Volume 375, Issue 2108

Abstract: We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the ...

Abstract	We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the sense of Grover & Fisher (2014
Language	English
Publishing date	2017-10-30
Publishing country	England
Document type	Journal Article
ZDB-ID	208381-4
ISSN	1471-2962 ; 0080-4614 ; 0264-3820 ; 0264-3952 ; 1364-503X
ISSN (online)	1471-2962
ISSN	0080-4614 ; 0264-3820 ; 0264-3952 ; 1364-503X
DOI	10.1098/rsta.2016.0433
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Article ; Online: Differential effects of lithium isotopes in a ketamine-induced hyperactivity model of mania.

Ettenberg, Aaron / Ayala, Kathy / Krug, Jacob T / Collins, Lisette / Mayes, Matthew S / Fisher, Matthew P A

Pharmacology, biochemistry, and behavior

2020 Volume 190, Page(s) 172875

Abstract: Sub-anesthetic doses of ketamine produce an increase in rodent ambulation that is attenuated by co-administration of naturally-occurring lithium (LiN), the drug most commonly employed in the treatment of bipolar illness. As a consequence, ketamine- ... ...

Abstract	Sub-anesthetic doses of ketamine produce an increase in rodent ambulation that is attenuated by co-administration of naturally-occurring lithium (LiN), the drug most commonly employed in the treatment of bipolar illness. As a consequence, ketamine-induced hyperactivity has been proposed as an animal model of manic behavior. The current study employed a modified version of this model to compare the potency of LiN to that of each of its two stable isotopes - lithium-6 (Li-6) and lithium-7 (Li-7). Since Li-7 constitutes 92.4% of the parent compound it was hypothesized to produce comparable behavioral effects to that of LiN. The current study was devised to determine whether Li-6 might be more, less, or equally effective at tempering hyperactivity relative to Li-7 or to LiN in an animal model of manic behavior. Male rats were maintained on a restricted but high-incentive diet containing a daily dose of 2.0 mEq/kg of lithium (LiN), Li-6 or Li-7 for 30 days. A control group consumed a diet infused with sodium chloride (NaCl) in place of lithium to control for the salty taste of the food. On day 30, baseline testing revealed no differences in the locomotor behavior among the four treatment groups. Animals then continued their Li/NaCl diets for an additional 11 days during which every subject received a single IP injection of either ketamine (25 mg/kg) or 0.9% physiological saline. On the final four days of this regimen, locomotor activity was assessed during 60 min sessions each beginning immediately after ketamine injection. While all three lithium groups produced comparable decreases in ketamine-induced hyperactivity on the first trial, by the fourth trial Li-6 animals exhibited significantly greater and more prolonged reductions in hyperactivity compared to either Li-7 and Li. These results suggest that Li-6 may be more effective at treating mania than its parent compound.
MeSH term(s)	Animals ; Antimanic Agents/therapeutic use ; Behavior, Animal/drug effects ; Disease Models, Animal ; Isotopes/administration & dosage ; Ketamine/pharmacology ; Lithium/administration & dosage ; Lithium Chloride/administration & dosage ; Locomotion/drug effects ; Male ; Mania/chemically induced ; Mania/drug therapy ; Rats ; Rats, Sprague-Dawley ; Treatment Outcome
Chemical Substances	Antimanic Agents ; Isotopes ; Lithium-6 ; Ketamine (690G0D6V8H) ; Lithium (9FN79X2M3F) ; Lithium Chloride (G4962QA067)
Language	English
Publishing date	2020-02-19
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	191042-5
ISSN	1873-5177 ; 0091-3057
ISSN (online)	1873-5177
ISSN	0091-3057
DOI	10.1016/j.pbb.2020.172875
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Article ; Online: Posner molecules: from atomic structure to nuclear spins.

Swift, Michael W / Van de Walle, Chris G / Fisher, Matthew P A

Physical chemistry chemical physics : PCCP

2018 Volume 20, Issue 18, Page(s) 12373–12380

Abstract: We investigate "Posner molecules", calcium phosphate clusters with chemical formula Ca9(PO4)6. Originally identified in hydroxyapatite, Posner molecules have also been observed as free-floating molecules in vitro. The formation and aggregation of Posner ... ...

Abstract	We investigate "Posner molecules", calcium phosphate clusters with chemical formula Ca9(PO4)6. Originally identified in hydroxyapatite, Posner molecules have also been observed as free-floating molecules in vitro. The formation and aggregation of Posner molecules have important implications for bone growth, and may also play a role in other biological processes such as the modulation of calcium and phosphate ion concentrations within the mitochondrial matrix. In this work, we use a first-principles computational methodology to study the structure of Posner molecules, their vibrational spectra, their interactions with other cations, and the process of pairwise bonding. Additionally, we show that the Posner molecule provides an ideal environment for the six constituent 31P nuclear spins to obtain very long spin coherence times. In vitro, the spins could provide a platform for liquid-state nuclear magnetic resonance quantum computation. In vivo, the spins may have medical imaging applications. The spins have also been suggested as "neural qubits" in a proposed mechanism for quantum processing in the brain.
MeSH term(s)	Calcium Phosphates/chemistry ; Magnetic Resonance Spectroscopy ; Models, Chemical ; Quantum Theory
Chemical Substances	Calcium Phosphates
Language	English
Publishing date	2018-05-09
Publishing country	England
Document type	Journal Article
ZDB-ID	1476244-4
ISSN	1463-9084 ; 1463-9076
ISSN (online)	1463-9084
ISSN	1463-9076
DOI	10.1039/c7cp07720c
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