About

Chao-Ming Jian is an Assistant Professor in the Department of Physics at Cornell University. He holds a B.S. in Fundamental Science from Tsinghua University and a Ph.D. in Physics from Stanford University. His research focuses on the theoretical study of strongly-correlated quantum many-body systems, with particular interest in exotic phases in quantum magnets, such as spin liquids that host fractionalized quasi-particle excitations. He investigates the inner workings of these phases and their signatures in experimental systems using non-perturbative approaches, considering the constraints imposed by symmetries. His work also encompasses the study of strongly-interacting quantum critical points and gapless quantum matter, developing and applying non-perturbative methods to understand universal behaviors in these systems. Additionally, Jian explores the dynamics of quantum entanglement, aiming to understand phase transitions between different dynamical phases and the evolution of entanglement in quantum chaotic systems. His contributions advance the theoretical frameworks necessary to characterize complex phenomena in quantum condensed matter physics.

Research topics

• Statistical physics
• Computer Science
• Quantum mechanics
• Physics
• Mathematics
• Nuclear physics
• Law
• Theoretical physics
• Pure mathematics

Selected publications

• Decoding coherent errors in toric codes on honeycomb and square lattices: duality to Majorana monitored dynamics and symmetry classes

  ArXiv.org · 2026-04-09

  articleOpen accessSenior author

  Topological stabilizer codes, such as the toric and surface codes, are leading candidates for fault-tolerant quantum computation. While their decodability under stochastic noise has been extensively studied, the effects of coherent errors, which involve quantum interference, remain less explored. In this work, we study the decodability of toric codes on honeycomb and square lattices subject to $X$- and $Z$-type coherent errors generated by the $X$- and $Z$-rotations on each qubit. We establish a duality between these decoding problems and 1+1D monitored dynamics of non-interacting Majorana fermions. This duality shows that the Altland-Zirnbauer symmetry class of the dual Majorana dynamics governs the universal structure of the decodability phase diagram. We show that the honeycomb-lattice toric code (hTC) with $X$-type error is dual to class-DIII dynamics, while the hTC with $Z$-type error and the square-lattice toric code (sTC) with both error types are dual to class-D dynamics. The key distinction arises from time-reversal symmetry. In class DIII, the generic transition out of the decodable phase is dual to a measurement-induced transition between dynamical phases with area-law and logarithmic entanglement scaling. In contrast, in class D, the generic decodability transition corresponds to a transition between two topologically distinct area-law phases. To explore these transitions in microscopic models, we consider hTC and sTC with $X$-type errors as representatives and introduce a minimal two-parameter coherent error model with spatially varying rotation angles. Using analytical and numerical methods, we map out the decodability phase diagrams and characterize the universal behavior of the transitions. We find that the decodability of sTC is more vulnerable to spatially varying coherent errors than uniform ones.

  PublisherOA PDF

• Decoding coherent errors in toric codes on honeycomb and square lattices: duality to Majorana monitored dynamics and symmetry classes

  arXiv (Cornell University) · 2026-04-09

  preprintOpen accessSenior author

  Topological stabilizer codes, such as the toric and surface codes, are leading candidates for fault-tolerant quantum computation. While their decodability under stochastic noise has been extensively studied, the effects of coherent errors, which involve quantum interference, remain less explored. In this work, we study the decodability of toric codes on honeycomb and square lattices subject to $X$- and $Z$-type coherent errors generated by the $X$- and $Z$-rotations on each qubit. We establish a duality between these decoding problems and 1+1D monitored dynamics of non-interacting Majorana fermions. This duality shows that the Altland-Zirnbauer symmetry class of the dual Majorana dynamics governs the universal structure of the decodability phase diagram. We show that the honeycomb-lattice toric code (hTC) with $X$-type error is dual to class-DIII dynamics, while the hTC with $Z$-type error and the square-lattice toric code (sTC) with both error types are dual to class-D dynamics. The key distinction arises from time-reversal symmetry. In class DIII, the generic transition out of the decodable phase is dual to a measurement-induced transition between dynamical phases with area-law and logarithmic entanglement scaling. In contrast, in class D, the generic decodability transition corresponds to a transition between two topologically distinct area-law phases. To explore these transitions in microscopic models, we consider hTC and sTC with $X$-type errors as representatives and introduce a minimal two-parameter coherent error model with spatially varying rotation angles. Using analytical and numerical methods, we map out the decodability phase diagrams and characterize the universal behavior of the transitions. We find that the decodability of sTC is more vulnerable to spatially varying coherent errors than uniform ones.

  PublisherDOI

• Field theory of monitored interacting fermion dynamics with charge conservation

  Physical review. B./Physical review. B · 2025-08-12 · 12 citations

  article

  Measurement-induced phase transitions (MIPTs) in monitored quantum dynamics are nonequilibrium phase transitions between quantum-chaotic (volume-law entangled) and entanglement-suppressed, area-law phases. Here we reveal how monitored dynamics are situated within the framework of general far-from-equilibrium, quantum condensed-matter physics. Measurement-induced heating effects scramble the distribution function in generic (interacting) monitored fermion systems, and this enables a simplified symmetry-based description of the dynamics. We demonstrate the equivalence of the Keldysh technique with the conventional Statistical-Mechanics Model for circuits, resulting from a doubled Hilbert-space (Choi-Jamio\l{}kowski) mapping. We illustrate this using the monitored dynamics of interacting fermions with a conserved charge, deriving a unified effective-field theory that captures all phases and phase transitions. The noninteracting counterpart in one-dimensional space only has an area-law phase, with no MIPT. This was explained via an effective nonlinear sigma model replica field theory possessing a very large symmetry. We show that other phases and phase transitions emerge when the replica symmetry is reduced by interactions. The reduced symmetry combines a replica permutation symmetry and charge-conservation within each replica. The former and its spontaneous breaking govern the MIPT, which can be recognized via a separatrix in the renormalization-group flow. The replica-resolved charge conservation dictates the ``charge-sharpening'' transition between two kinds of dynamics, where the global charge information is either hidden or reconstructible from the measurements. The field theory explains why the charge-sharpening transition should occur only in the volume-law phase. Our framework provides a template for other classes of MIPTs and situates these within the arena of nonequilibrium condensed-matter physics.

  PublisherDOI

• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States

  ArXiv.org · 2025-07-17

  preprintOpen accessSenior author

  We develop a general framework for classifying fermionic dynamical systems with measurements using symmetry and topology. We discuss two complementary classification schemes based on the Altland-Zirnbauer tenfold way: (1) the many-body evolution operator (mEO) symmetry class, which classifies fermionic dynamics at the many-body level and generalizes to interacting dynamics, and (2) the single-particle transfer matrix (sTM) symmetry class, which classifies free-fermion dynamics at the single-particle level and connects to Anderson localization physics. In the free-fermion limit, these two frameworks are in one-to-one correspondence and yield equivalent topological classifications of area-law entangled dynamical phases. This leads to a novel dynamical bulk-boundary correspondence: the topology of the dynamical system's spacetime \textit{bulk} determines the topology of the area-law entangled steady-state ensemble living on its temporal \textit{boundary}. Building on this correspondence, we provide a general realization of topological dynamical phases using Gaussian adaptive circuits. They are designed to prepare and stabilize free-fermion topological states as their steady states in \textit{any} spatial dimension. While circuits with exponentially local operations can stabilize a single topological steady state, those with finite-range operations can reach a topological steady-state ensemble. As a demonstration, we explicitly construct and simulate 2+1d adaptive circuits that realize mEO-class-A topological dynamics. We show that the finite-range versions converge to an ensemble of Chern insulators in ${\cal O}(1)$ circuit depth. We numerically study the topological phase transitions and dynamical domain-wall modes between different topological dynamical phases in this symmetry class. We also analyze the robustness of our adaptive circuit protocol to coherent noise.

  PublisherOA PDFDOI

• Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

  Nature Communications · 2025-07-05 · 6 citations

  preprintOpen access

  The remarkable complexity of a topologically ordered many-body quantum system is encoded in the characteristics of its anyons. Quintessential predictions emanating from this complexity employ the Fibonacci string net condensate (Fib SNC) and its anyons: sampling Fib-SNC would estimate chromatic polynomials while exchanging its anyons would implement universal quantum computation. However, physical realizations remained elusive. We introduce a scalable dynamical string net preparation (DSNP) that constructs Fib SNC and its anyons on reconfigurable graphs suitable for near-term superconducting processors. Coupling the DSNP approach with composite error-mitigation on deep circuits, we create, measure, and braids Fibonacci anyons; charge measurements show 94% accuracy, and exchanging the anyons yields the expected golden ratio ϕ with 98% average accuracy. We then sample the Fib SNC to estimate chromatic polynomial at ϕ + 2 for several graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and aim at a classically hard problem.

  PublisherOA PDFDOI

• Topological modes in monitored quantum dynamics

  Physical review. B./Physical review. B · 2025-10-01 · 4 citations

  articleSenior author

  Dynamical quantum systems both driven by unitary evolutions and monitored through measurements have proved to be fertile ground for exploring new dynamical quantum matters. While the entanglement structure and symmetry properties of monitored systems have been intensively studied, the role of topology in monitored dynamics is much less explored. In this work, we investigate novel topological phenomena in the monitored dynamics through the lens of free-fermion systems. Free-fermion monitored dynamics were previously shown to be unified with the Anderson localization problem under the Altland-Zirnbauer symmetry classification. Guided by this unification, we identify the topological area-law-entangled phases in the former setting through the topological classification of disordered insulators and superconductors in the latter. As examples, we focus on $1+1\mathrm{D}$ free-fermion monitored dynamics in two symmetry classes: DIII and A. We construct quantum circuit models to study different topological area-law phases and their domain walls in the respective symmetry classes. We find that the domain wall between topologically distinct area-law phases hosts dynamical topological modes whose entanglement is protected from being quenched by the measurements in the monitored dynamics. We demonstrate how to manipulate these topological modes by programming the domain-wall dynamics. In particular, for topological modes in class DIII, which behave as unmeasured Majorana modes, we devise a protocol to braid them and study the entanglement generated in the braiding process.

  PublisherDOI

• Minimal Fractional Topological Insulator in Half-Filled Conjugate Moiré Chern Bands

  Physical Review X · 2025-05-21 · 8 citations

  articleOpen access1st authorCorresponding

  We propose a “minimal” fractional topological insulator (mFTI), motivated by the recent experimental report on the fractional quantum spin-Hall effect in a transition metal dichalcogenide moiré system. The observed effect suggests the possibility of a topological state living in a pair of half-filled conjugate Chern bands with Chern numbers <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mo>=</a:mo><a:mo>±</a:mo><a:mn>1</a:mn></a:math>. We propose the mFTI as a novel candidate topological state in the half-filled conjugate Chern bands. The mFTI is characterized by the following features. (1) It is a fully gapped topological order (TO) with 16 Abelian anyons if the electron is considered trivial (32 including electrons), (2) the minimally charged anyon carries electric charge <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>e</c:mi><c:mo>*</c:mo></c:msup><c:mo>=</c:mo><c:mi>e</c:mi><c:mo>/</c:mo><c:mn>2</c:mn></c:math>, together with the fractional quantum spin-Hall conductance, implying the robustness of the mFTI’s gapless edge state whenever time-reversal symmetry and charge conservation are present, and (3) the mFTI is minimal in the sense that it has the smallest total quantum dimension (a metric for the TO’s complexity) within all the TOs that can potentially be realized at the same electron filling and with the same Hall transports; the mFTI is also the minimal TO that respects time-reversal symmetry. (4) The mFTI is the common descendant of multiple valley-decoupled “product TOs” with larger quantum dimensions. It can also be viewed as the result of gauging multiple symmetry-protected topological states. Similar mFTIs are classified and constructed for a pair of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>1</e:mn><e:mo>/</e:mo><e:mi>q</e:mi></e:math>-filled conjugate Chern bands. We further classify the mFTIs via the stability of the gapless interfaces between them.

  PublisherOA PDFDOI

• Average-exact mixed anomalies and compatible phases

  Physical review. B./Physical review. B · 2025-03-11 · 9 citations

  articleSenior author

  Quantum anomalies strongly constrain possible low-energy physics of condensed matter systems. In particular, it prohibits the existence of a trivially gapped phase. Here, the authors extend the notion of quantum anomalies to disordered systems, where symmetries can be preserved on average by disorder. Through physical arguments and solvable lattice models, the authors discover a series of phases intrinsic to disordered systems that are compatible with quantum anomalies involving average symmetries. These results serve as compelling evidence of the nontriviality of quantum anomalies, even with loosened requirements on symmetry and quantum coherence.

  PublisherDOI

• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation

  Physical Review Letters · 2024-04-12 · 22 citations

  article

  The "symmetric mass generation" (SMG) quantum phase transition discovered in recent years has attracted great interest from both condensed matter and high energy theory communities. Here, interacting Dirac fermions acquire a gap without condensing any fermion bilinear mass term or any concomitant spontaneous symmetry breaking. It is hence beyond the conventional Gross-Neveu-Yukawa-Higgs paradigm. One important question we address in this Letter is whether the SMG transition corresponds to a true unitary conformal field theory. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true (2+1)d unitary conformal field theory.

  PublisherDOI

• Field theory of monitored, interacting fermion dynamics with charge conservation

  arXiv (Cornell University) · 2024-10-09

  preprintOpen access

  Measurement-induced phase transitions (MIPTs) in monitored quantum dynamics are non-equilibrium phase transitions between quantum-chaotic (volume-law entangled) and entanglement-suppressed, area-law phases. We reveal how monitored dynamics are situated within the framework of general far-from-equilibrium, quantum condensed-matter physics. Measurement-induced heating effects scramble the distribution function in generic (interacting) monitored fermion systems, which enables a simplified symmetry-based description of the dynamics. We demonstrate the equivalence of the Keldysh technique with the conventional Statistical-Mechanics Model for circuits, resulting from a doubled Hilbert-space (Choi-Jamiołkowski) mapping. We illustrate this using the monitored dynamics of interacting fermions with a conserved charge, deriving a unified effective field theory that captures all phases and phase transitions. The non-interacting counterpart in 1D space only has an area-law phase, with no MIPT. This was explained via an effective non-linear sigma model replica field theory possessing a very large symmetry. We show that other phases and phase transitions emerge when the replica symmetry is reduced by interactions. The reduced symmetry combines a replica permutation symmetry and charge-conservation within each replica. The former and its spontaneous breaking govern the MIPT, which can be recognized via a separatrix in the renormalization group flow. The replica-resolved charge conservation dictates the ``charge-sharpening" transition between two kinds of dynamics, where the global charge information is either hidden or reconstructible from the measurements. The field theory explains why the charge-sharpening transition should occur only in the volume-law phase. Our framework provides a template for other classes of MIPTs and situates these within the arena of non-equilibrium condensed matter physics.

  PublisherOA PDFDOI

Frequent coauthors

• Cenke Xu

  University of California, Santa Barbara

  62 shared

• Xiao-Chuan Wu

  22 shared

• Yi‐Zhuang You

  University of California, San Diego

  14 shared

• Xiao-Liang Qi

  Stanford University

  13 shared

• Zhen Bi

  13 shared

• Yichen Xu

  Beihang University

  10 shared

• Po-Shen Hsin

  8 shared

• Xue-Yang Song

  7 shared

Labs

• Jian GroupPI

  Not provided

Education

• Ph.D., Department of Physics

  Stanford University

  2016

• B.S., Department of Physics

  Tsinghua University

  2011

Awards & honors

• Graduate Fellow, Kavli Institute for Theoretical Physics, Un…
• Moore Foundation Fellow, Kavli Institute for Theoretical Phy…
• Postdoctoral researcher, Microsoft Station Q (2017-2018 and…
• Four early-career faculty win 2024 Sloan Research awards