About

Matthew Fisher is a Professor at UC Santa Barbara in the Department of Physics. His present research interests lie at the border between many-body theory and quantum information theory, with a particular focus on the non-equilibrium quantum dynamics of open and monitored quantum systems. This research area involves understanding complex quantum systems that are not isolated but interact with their environment, which is crucial for advancing quantum information science and condensed matter theory.

Research topics

• Computer Science
• Quantum mechanics
• Physics
• Algorithm
• Statistical physics
• Mathematics

Selected publications

• Strong-to-Weak Symmetry Breaking in Open Quantum Systems: From Discrete Particles to Continuum Hydrodynamics

  arXiv (Cornell University) · 2026-02-17

  articleOpen accessSenior author

  We explore the onset of spontaneous strong-to-weak symmetry breaking (SW-SSB) under U(1)-symmetric (i.e., charge-conserving) open-system dynamics. We define this phenomenon for quantum states and classical probability distributions, and explore it in three complementary models, one of which exhibits nontrivial quantum coherence at short times. Our main conclusions are as follows. In one dimension, the strong symmetry is not spontaneously broken at any finite time; however, correlators probing strong-to-weak symmetry breaking develop order on length scales that grow linearly in time, parametrically faster than charge diffusion. We provide numerical evidence for this scaling in multiple distinct probes of SW-SSB, and derive it from a field-theory analysis. Moreover, we relate this scaling to the problem of inferring the charge inside a subregion by measuring its surroundings, and construct explicit decoding protocols that illustrate its origin. In two dimensions, field theory and numerical simulations support a finite-time Berezinskii-Kosterlitz-Thouless-like SW-SSB transition. Within continuum hydrodynamics, by contrast, SW-SSB happens at infinitesimal time in two or more dimensions. The SW-SSB transition time can thus be interpreted as marking the emergence of a continuum hydrodynamic description, or (more precisely) the timescale beyond which non-hydrodynamic information such as discrete particle worldlines can no longer be inferred. We support this picture by analyzing a model in which we exploit SW-SSB to derive a classical stochastic hydrodynamic description from the underlying quantum dynamics.

  PublisherOA PDF

• Strong-to-Weak Symmetry Breaking in Open Quantum Systems: From Discrete Particles to Continuum Hydrodynamics

  Open MIND · 2026-02-17

  preprintSenior author

  We explore the onset of spontaneous strong-to-weak symmetry breaking (SW-SSB) under U(1)-symmetric (i.e., charge-conserving) open-system dynamics. We define this phenomenon for quantum states and classical probability distributions, and explore it in three complementary models, one of which exhibits nontrivial quantum coherence at short times. Our main conclusions are as follows. In one dimension, the strong symmetry is not spontaneously broken at any finite time; however, correlators probing strong-to-weak symmetry breaking develop order on length scales that grow linearly in time, parametrically faster than charge diffusion. We provide numerical evidence for this scaling in multiple distinct probes of SW-SSB, and derive it from a field-theory analysis. Moreover, we relate this scaling to the problem of inferring the charge inside a subregion by measuring its surroundings, and construct explicit decoding protocols that illustrate its origin. In two dimensions, field theory and numerical simulations support a finite-time Berezinskii-Kosterlitz-Thouless-like SW-SSB transition. Within continuum hydrodynamics, by contrast, SW-SSB happens at infinitesimal time in two or more dimensions. The SW-SSB transition time can thus be interpreted as marking the emergence of a continuum hydrodynamic description, or (more precisely) the timescale beyond which non-hydrodynamic information such as discrete particle worldlines can no longer be inferred. We support this picture by analyzing a model in which we exploit SW-SSB to derive a classical stochastic hydrodynamic description from the underlying quantum dynamics.

  DOI

• Observation of Strong-to-Weak Spontaneous Symmetry Breaking in a Dephased Fermi Gas

  arXiv (Cornell University) · 2026-04-17

  preprintOpen access

  Symmetry-based classification of quantum phases of matter is one of the most foundational organizing principles in physics; however, an analogous framework for mixed, decohered quantum states has only begun to emerge. A central new concept is strong-to-weak spontaneous symmetry breaking (SW-SSB), a sharp transition in mixed quantum states that is invisible to any observable linear in the density matrix and that has since been predicted across a broad class of open and monitored quantum systems. It also provides a unifying language for phenomena as disparate as the decodability of topological quantum memories and the emergence of classical hydrodynamics from decohered quantum dynamics. Here we report the first experimental observation of SW-SSB, in dephased single-component fermionic matter imaged by a quantum gas microscope. A quantum-classical estimator built on a machine-learned Gaussian reference state gives direct access to the nonlinear Rényi-1 and Rényi-2 correlators that diagnose SW-SSB, and reveals long-range Rényi order in the dephased Fermi liquid. Adding a commensurate superlattice drives the underlying fermions through a metal-to-insulator transition that, after full dephasing, manifests as a sharp SW-SSB phase transition. Our results uncover the symmetry principle behind information-theoretic transitions in open quantum systems, and extend Landau's symmetry paradigm into the regime of real, decohering quantum devices.

  PublisherDOI

• Observation of Strong-to-Weak Spontaneous Symmetry Breaking in a Dephased Fermi Gas

  arXiv (Cornell University) · 2026-04-17

  articleOpen access

  Symmetry-based classification of quantum phases of matter is one of the most foundational organizing principles in physics; however, an analogous framework for mixed, decohered quantum states has only begun to emerge. A central new concept is strong-to-weak spontaneous symmetry breaking (SW-SSB), a sharp transition in mixed quantum states that is invisible to any observable linear in the density matrix and that has since been predicted across a broad class of open and monitored quantum systems. It also provides a unifying language for phenomena as disparate as the decodability of topological quantum memories and the emergence of classical hydrodynamics from decohered quantum dynamics. Here we report the first experimental observation of SW-SSB, in dephased single-component fermionic matter imaged by a quantum gas microscope. A quantum-classical estimator built on a machine-learned Gaussian reference state gives direct access to the nonlinear Rényi-1 and Rényi-2 correlators that diagnose SW-SSB, and reveals long-range Rényi order in the dephased Fermi liquid. Adding a commensurate superlattice drives the underlying fermions through a metal-to-insulator transition that, after full dephasing, manifests as a sharp SW-SSB phase transition. Our results uncover the symmetry principle behind information-theoretic transitions in open quantum systems, and extend Landau's symmetry paradigm into the regime of real, decohering quantum devices.

  PublisherOA PDF

• Spin Liquid and Superconductivity Emerging from Steady States and Measurements

  Physical Review Letters · 2025-08-01 · 4 citations

  article

  We demonstrate that, starting with a simple fermion wave function, the steady mixed state of the evolution of a class of Lindbladians, and the ensemble created by strong local measurement of fermion density without postselection can be mapped to the "Gutzwiller projected" wave functions in the doubled Hilbert space-the representation of the density matrix through the Choi-Jamiołkowski isomorphism. A Gutzwiller projection is a broadly used approach of constructing spin liquid states. For example, if one starts with a gapless free Dirac fermion pure quantum state, the constructed mixed state corresponds to an algebraic spin liquid in the doubled Hilbert space. We also predict that for some initial fermion wave function, the mixed state created following the procedure described above is expected to have a spontaneous "strong-to-weak" U(1) symmetry breaking, which corresponds to the emergence of superconductivity in the doubled Hilbert space. We also design the experimental protocol to construct the desired physics of mixed states.

  PublisherDOI

• Experimental Demonstration of Scalable Cross-Entropy Benchmarking to Detect Measurement-Induced Phase Transitions on a Superconducting Quantum Processor

  Physical Review Letters · 2025-03-25 · 16 citations

  articleOpen access

  Quantum systems subject to random unitary evolution and measurements at random points in spacetime exhibit entanglement phase transitions which depend on the frequency of these measurements. Past work has experimentally observed entanglement phase transitions on near-term quantum computers, but the characterization approach using entanglement entropy is not scalable due to exponential overhead of quantum state tomography and postselection. Recently, an alternative protocol to detect entanglement phase transitions using linear cross entropy was proposed, attempting to eliminate both bottlenecks. Here, we report demonstrations of this protocol in systems with one-dimensional and all-to-all connectivities on IBM's quantum hardware on up to 22 qubits, a regime which is presently inaccessible if postselection is required. We demonstrate data collapses onto scaling functions with critical exponents in semiquantitative agreement with theory. Our demonstration of the cross entropy benchmark (XEB) protocol paves the way for studies of measurement-induced entanglement phase transitions and associated critical phenomena on larger near-term quantum systems.

  PublisherOA PDFDOI

• Evidence for a possible quantum effect on the formation of lithium-doped amorphous calcium phosphate from solution

  Proceedings of the National Academy of Sciences · 2025-03-06 · 2 citations

  articleOpen accessCorresponding

  Differential isotope effects are an emerging tool for discovering possible nontrivial quantum mechanical effects within biological systems. However, it is often nearly impossible to elucidate the exact mechanisms by which a biological isotope effect manifests due to the complexity of these systems. As such, one proposed in vitro system of study for a quantum isotope effect is calcium phosphate aggregation, where symmetric calcium phosphate molecular species, known as Posner molecules, have been theorized to have phosphorus nuclear spin–dependent self-binding rates, which could be differently modulated by doping with stable lithium isotopes. Here, we present in vitro evidence for such a differential lithium isotope effect on the formation and aggregation of amorphous calcium phosphate from solution under certain conditions. Experiments confirm that lithium incorporates into amorphous calcium phosphate, with 7 Li found to promote a greater abundance of observable calcium phosphate particles than 6 Li under identical solution preparations. These in vitro results offer a potential explanation for in vivo biological studies that have shown differential lithium isotope effects. Given the importance of calcium phosphate in biological systems—ranging from mitochondrial signaling pathways to key biomineralization processes, as well as the proposed role of Posner molecules as a “neural qutrit”—these results present an important step in understanding calcium phosphate nucleation as well as the potential role of calcium phosphate for quantum biology and processing.

  PublisherOA PDFDOI

• Postselection in lattice bosons undergoing continuous measurements

  Physical review. B./Physical review. B · 2025-05-13 · 1 citations

  articleOpen accessSenior author

  We study in detail the postselection problem in a specific model: bosons hopping on a lattice subjected to continuous local measurements of quadrature observables. We solve the model analytically and show that the postselection overhead can be reduced by postprocessing the entire measurement record into one or two numbers for each trajectory and then binning trajectories based only on these numbers. Based on this simplification, we formulate a step-by-step protocol designed to recover connected two-point functions of the quantum trajectories, which display an exponentially decaying profile that is not observable in the unconditional, trajectory averaged, state. We also test this protocol numerically in a way that utilizes only experimentally accessible information, showing that various quantum trajectory observables can be recovered with a few repetitions of the numerical experiment, even after including inevitable coarse-graining procedures expected under realistic experimental conditions. We finalize by providing experimental implementations of these models in cavity-QED and circuit-QED platforms.

  PublisherOA PDFDOI

• Information dynamics and symmetry breaking in generic monitored $\mathbb{Z}_2$-symmetric open quantum systems

  ArXiv.org · 2025-12-02

  preprintOpen accessSenior author

  We investigate the steady-state phases of generic $\mathbb{Z}_2$-symmetric monitored, open quantum dynamics. We describe the phases systematically in terms of both information-theoretic diagnostics and spontaneous breaking of strong and weak symmetries of the dynamics. We find a completely broken phase where information is retained by the quantum system, a strong-to-weak broken phase where information is leaked to the environment, and an unbroken phase where information is learned by the observer. We find that weak measurement and dephasing alone constitute a minimal model for generic open systems with $\mathbb{Z}_2$ symmetry, but we also explore perturbations by unitary gates. For a 1d set of qubits, we examine information-theoretic and symmetry-breaking observables in the path integral of the doubled state. This path integral reduces to the standard classical 2d random-bond Ising model in certain limits but generically involves negative weights, enabling a special self-dual random-bond Ising model at the critical point when only measurements are present. We obtain numerical evidence for the steady-state phases using efficient tensor network simulations of the doubled state.

  PublisherOA PDFDOI

• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits

  Physical review. B./Physical review. B · 2024-05-13 · 30 citations

  article

  The authors explore critical properties of entanglement phase transitions in random tensor networks and monitored quantum circuits with Clifford tensors/gates for on-site Hilbert space dimensions which are powers of a prime number $p$. Exact mappings to replica spin models and characterizations of their symmetry groups predict that all universal properties will depend only on $p$. These predictions are confirmed with extensive numerical simulations. The authors also establish multifractal scaling of the purity, reflected in a continuous spectrum of critical exponents, while the typical exponent is the prefactor of the logarithm in the entanglement entropy.

  PublisherDOI

Recent grants

• Exotic Quantum Phases and Criticality

  NSF · $456k · 2005–2012

• Quantum entanglement in Many-Body Systems

  NSF · $435k · 2014–2018

• Strongly Correlated Quantum Phases

  NSF · $390k · 2011–2014

Frequent coauthors

• Leon Balents

  Canadian Institute for Advanced Research

  53 shared

• T. Senthil

  Massachusetts Institute of Technology

  39 shared

• Olexei I. Motrunich

  California Institute of Technology

  37 shared

• S. M. Girvin

  Yale University

  36 shared

• Chetan Nayak

  34 shared

• Yaodong Li

  28 shared

• F. Drouhin

  Université de Strasbourg

  27 shared

• C. L. Kane

  University of Pennsylvania

  26 shared

Labs

• Matthew Fisher's LabPI

  Not provided

Education

• Ph.D.

  University of Illinois at Urbana-Champaign

  1986

Awards & honors

• Alan T. Waterman Award (1995)
• National Academy of Sciences Award for Initiatives in Resear…
• Oliver E. Buckley Prize in Condensed Matter Physics (2015)
• Member of the American Academy of Arts and Sciences (2003)
• Member of the National Academy of Sciences (2012)