arXiv subjects

Tianci Zhou

Publications and source records attributed to Tianci Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics

Participation entropy (PE) quantifies the spread of a many-body wavefunction across configuration space. While PE relaxes rapidly in generic chaotic systems, we show that $\mathrm{U}(1)$ conservation laws slow it down by imprinting with the slow hydrodynamic modes. Using a cluster expansion around equilibrium, we show that, after local density inhomogeneities decay, the leading PE deficit is dominated by squared connected density correlations. The long time relaxation is therefore controlled by diffusive correlation spreading, giving $ΔS(t)\sim t^{-1/2}$ in the hydrodynamic regime and crossing over to $\sim \exp[-O(t/L^2)]$ when $t\geq L^2$. We confirm this entropy correlation relation using exact computation and infinite system tensor network simulations in various quantum $\mathrm{U}(1)$ conserving circuits. Our results establish PE as a sensitive probe of hydrodynamic memory and suggest that slow relaxation is a generic consequence of conservation laws.

quant-ph↗

arXiv2026

Low Rank Structure of the Reduced Transition Matrix

The influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics. Because influence matrices retain information only about the effective bath seen by local observables, they are expected to be easier to simulate than the full wavefunction. Recent work, however, has shown that they carry strong temporal correlations even in maximally chaotic systems, making them difficult to represent efficiently. Here we show that the reduced transition matrix, a suitable combination of influence matrices that directly determines local expectation values, can nevertheless be efficiently approximated. We first show that the truncation error is controlled by its singular-value spectrum, which naturally motivates a low-rank approximation. We then prove that, for chaotic dual-unitary circuits, the associated entropy grows at most logarithmically in time. Our conclusions follow from exact results for random dual-unitary circuits and are further supported by numerical results for fixed instances of both dual-unitary and random circuits.

quant-ph↗

arXiv2026

Probing the Critical Point (CritPt) of AI Reasoning: a Frontier Physics Research Benchmark

While large language models (LLMs) with reasoning capabilities are progressing rapidly on high-school math competitions and coding, can they reason effectively through complex, open-ended challenges found in frontier physics research? And crucially, what kinds of reasoning tasks do physicists want LLMs to assist with? To address these questions, we present the CritPt (Complex Research using Integrated Thinking - Physics Test, pronounced "critical point"), the first benchmark designed to test LLMs on unpublished, research-level reasoning tasks that broadly covers modern physics research areas, including condensed matter, quantum physics, atomic, molecular & optical physics, astrophysics, high energy physics, mathematical physics, statistical physics, nuclear physics, nonlinear dynamics, fluid dynamics and biophysics. CritPt consists of 71 composite research challenges designed to simulate full-scale research projects at the entry level, which are also decomposed to 190 simpler checkpoint tasks for more fine-grained insights. All problems are newly created by 50+ active physics researchers based on their own research. Every problem is hand-curated to admit a guess-resistant and machine-verifiable answer and is evaluated by an automated grading pipeline heavily customized for advanced physics-specific output formats. We find that while current state-of-the-art LLMs show early promise on isolated checkpoints, they remain far from being able to reliably solve full research-scale challenges: the best average accuracy among base models is only 5.7%, achieved by GPT-5 (high), moderately rising to around 10% when equipped with coding tools. Through the realistic yet standardized evaluation offered by CritPt, we highlight a large disconnect between current model capabilities and realistic physics research demands, offering a foundation to guide the development of scientifically grounded AI tools.

cs.AI↗

arXiv2026

Critical behaviors of magic and participation entropy at measurement induced phase transitions

We study the participation and stabilizer entropy of non-unitary quantum circuit dynamics, focusing on the critical line that separates the low-entanglement spin-glass phase and the paramagnetic phase. Along this critical line, the entanglement has a logarithmic scaling, which enables us to access the critical regime using large-scale matrix product state simulations with modest bond dimension. We find that both the participation entropy and stabilizer entropy exhibit critical slowing down: their saturation time scales linearly with the system size, in stark contrast to purely unitary dynamics, where saturation occurs on logarithmic time scales. In addition, we study bipartite participation and stabilizer mutual information, and find that it shows similar scaling behavior to the entanglement entropy. Finally, by analyzing the participation entropy of several paradigmatic Clifford circuits, we identify similar slow dynamical behavior near their respective critical points.

quant-ph↗

arXiv2026

Anomalous transport in non-integrable classical field theories

Anomalous KPZ spin transport is well established in integrable non-Abelian lattice models but has not been investigated in continuum field theories as discretization in numerics generally break the continuum theory's integrability. We show that finite temperature acts as a regulator that can restore anomalous transport over a broad time window. In a family of spin field theories labeled by integer $n$, the $n = 1$ case is the Landau-Lifshitz model, whose numerical data shows spin superdiffusion with Kardar-Parisi-Zhang (KPZ) scaling and, at lower temperature ballistic energy transport, whereas both observables are diffusive at high temperature. The non-integrable $n = 2$ case shows the same crossover. While Lyapunov analysis confirms the model's non-integrability, the structure of spin-density space-time profiles suggests that long-lived soliton-like trajectories exist at low temperature.

cond-mat.stat-mech↗

arXiv2025

An efficient algorithm to compute entanglement in states with low magic

A bottleneck for analyzing the interplay between magic and entanglement is the computation of these quantities in highly entangled quantum many-body magic states. Efficient extraction of entanglement can also inform our understanding of dynamical quantum processes such as measurement-induced phase transition and approximate unitary designs. We develop an efficient classical algorithm to compute the von Neumann entropy and entanglement spectrum for such states under the condition that they have low stabilizer nullity. The algorithm exploits the property of stabilizer codes to separate entanglement into two pieces: one generated by the common stabilizer group and the other from the logical state. The low-nullity constraint ensures both pieces can be computed efficiently. Our algorithm can be applied to study the entanglement in sparsely $T$-doped circuits with possible Pauli measurements as well as certain classes of states that have both high entanglement and magic. Combining with stabilizer learning subroutines, it also enables the efficient learning of von Neumann entropies for low-nullity states prepared on quantum devices.

quant-ph↗

arXiv2025

Magic transition in monitored free fermion dynamics

We investigate magic and its connection to entanglement in 1+1 dimensional random free fermion circuits, with a focus on hybrid free fermion dynamics that can exhibit an entanglement phase transition. To quantify magic, we use the Stabilizer Rényi Entropy (SRE), which we compute numerically via a perfect sampling algorithm. We show that although the SRE remains extensive as the system transitions from a critical phase to an area-law (disentangled) phase, the structure of magic itself undergoes a delocalization phase transition. This transition is characterized using the bipartite stabilizer mutual information, which exhibits the same scaling behavior as entanglement entropy: logarithmic scaling in the critical phase and a finite constant in the area-law phase. Additionally, we explore the dynamics of SRE. While the total SRE becomes extensive in $O(1)$ time, we find that in the critical phase, the relaxation time to the steady-state value is parameterically longer than that in generic random circuits. The relaxation follows a universal form, with a relaxation time that grows linearly with the system size, providing further evidence for the critical nature of the phase.

quant-ph↗

arXiv2025

Scrambling Dynamics with Imperfections in a Solvable Model

We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order correlator (ROTOC) in the model with $N$ qubits, and we show that the circuit-averaged ROTOC is controlled by an effective probability distribution in operator weight space which obeys a system of $N$ non-linear equations of motion. These equations can be easily solved numerically for large system sizes which are beyond the reach of exact methods. Moreover, for an operator initially concentrated on weight one $w_0=1$, we provide an exact solution to the equations in the thermodynamic limit of many qubits that is valid for all times, all non-vanishing perturbation strengths $p\gtrsim 1/\sqrt{N}$, and all decoherence strengths. We also show that a generic initial condition $w_0 >1$ leads to a metastable state that eventually collapses to the $w_0=1$ case after a lifetime $\sim \log(N/w_0)$. Our results highlight situations where it is still possible to extract the unperturbed chaos exponent even in the presence of imperfections, and we comment on the applications of our results to existing experiments with nuclear spins and to future scrambling experiments.

quant-ph↗

arXiv2025

Operator Spreading, Duality, and the Noisy Long-Range FKPP Equation

Operator spreading provides a new characterization of quantum chaos beyond the semi-classical limit. There are two complementary views of how the characteristic size of an operator, also known as the butterfly light cone, grows under chaotic quantum time evolution: A discrete stochastic population dynamics or a stochastic reaction-diffusion equation in the continuum. When the interaction decays as a power function of distance, the discrete population dynamics model features superlinear butterfly light cones with stretched exponential or power-law scaling. Its continuum counterpart, a noisy long-range Fisher-Kolmogorov-Petrovsky-Piscunov (FKPP) equation, remains less understood. We use a mathematical duality to demonstrate their equivalence through an intermediate model, which replaces the hard local population limit by an equilibrium population. Through an algorithm with no finite size effect, we demonstrate numerically remarkable agreements in their light cone scalings.

cond-mat.stat-mech↗

arXiv2024

Scrambling Transition in Free Fermion Systems Induced by a Single Impurity

In quantum many-body systems, interactions play a crucial role in the emergence of information scrambling. When particles interact throughout the system, the entanglement between them can lead to a rapid and chaotic spreading of quantum information, typically probed by the growth in operator size in the Heisenberg picture. In this study, we explore whether the operator undergoes scrambling when particles interact solely through a single impurity in generic spatial dimensions, focusing on fermion systems with spatial and temporal random hoppings. By connecting the dynamics of the operator to the symmetric exclusion process with a source term, we demonstrate the presence of an escape-to-scrambling transition when tuning the interaction strength for fermions in three dimensions. As a comparison, systems in lower dimensions are proven to scramble at arbitrarily weak interactions unless the hopping becomes sufficiently long-ranged. Our predictions are validated using both a Brownian circuit with a single Majorana fermion per site and a solvable Brownian SYK model with a large local Hilbert space dimension. This suggests the universality of the theoretical picture for free fermion systems with spatial and temporal randomness.

quant-ph↗

arXiv2024

Two-stage relaxation of operators through domain wall and magnon dynamics

The out-of-time ordered correlator (OTOC) has become a popular probe for quantum information spreading and thermalization. In systems with local interactions, the OTOC defines a characteristic butterfly lightcone that separates a regime not yet disturbed by chaos from one where time-evolved operators and the OTOC approach their equilibrium value. This relaxation has been shown to proceed in two stages, with the first stage exhibiting an extensive timescale and a decay rate slower than the gap of the transfer matrix -- known as the ``phantom eigenvalue". In this work, we investigate the two-stage relaxation of the OTOC towards its equilibrium value in various local quantum circuits. We apply a systematic framework based on an emergent statistical model, where the dynamics of two single-particle modes -- a domain wall and a magnon -- govern the decay rates. Specifically, a configuration with coexisting domain wall and magnon modes generates the phantom rate in the first stage, and competition between these modes determines the second stage. We also examine this relaxation within the operator cluster picture. The magnon modes translates into a bound state of clusters and domain wall into a random operator, giving consistent rates. Finally, we extend our findings from random in time circuits to a broad class of Floquet models.

quant-ph↗

arXiv2024

Universality classes for purification in nonunitary quantum processes

We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random matrices. Each kind of process is associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product. We argue that, for a broad class of models, each process is described by universal scaling forms for purification, and that (i) and (ii) represent distinct ``universality classes'' with distinct scaling functions. Using the replica trick, these universality classes correspond to one-dimensional effective statistical mechanics models for a gas of ``kinks'', representing domain walls between elements of the permutation group. (This is an instructive low-dimensional limit of the effective statistical mechanics models for random circuits and tensor networks.) These results apply to long-time purification in spatially local monitored circuit models on the entangled side of the measurement phase transition.

cond-mat.stat-mech↗

arXiv2023

A Physical Theory of Two-stage Thermalization

One indication of thermalization time is subsystem entanglement reaching thermal values. Recent studies on local quantum circuits reveal two exponential stages with decay rates $r_1$ and $r_2$ of the purity before and after thermalization. We provide an entanglement membrane theory interpretation, with $r_1$ corresponding to the domain wall free energy. Circuit geometry can lead to $r_1 < r_2$, producing a ``phantom eigenvalue". Competition between the domain wall and magnon leads to $r_2 < r_1$ when the magnon prevails. However, when the domain wall wins, this mechanism provides a practical approach for measuring entanglement growth through local correlation functions.

quant-ph↗

arXiv2023

Temporal Entanglement in Chaotic Quantum Circuits

The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume limit is then described by the fixed points of the latter transfer matrix, also known as influence matrices. To establish the potential of this method as a bona fide computational scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. Here we begin this quest by presenting a systematic characterisation of their entanglement -- dubbed temporal entanglement -- in chaotic quantum systems. We consider the most general form of space-evolution, i.e., evolution in a generic space-like direction, and present two fundamental results. First, we show that temporal entanglement always follows a volume law in time. Second, we identify two marginal cases -- (i) pure space evolution in generic chaotic systems (ii) any space-like evolution in dual-unitary circuits -- where Rényi entropies with index larger than one are sub-linear in time while the von Neumann entanglement entropy grows linearly. We attribute this behaviour to the existence of a product state with large overlap with the influence matrices. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.

quant-ph↗

arXiv2022

Hydrodynamic theory of scrambling in chaotic long-range interacting systems

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density; in the systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here we study this problem using a model of coupled quantum dots with interactions decaying as $\frac{1}{r^α}$, where each dot hosts $N$ degrees of freedom. The large $N$ limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by $\frac{1}{N}$ corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings that we previously found for $N=1$ and generic finite $N$. In order to reproduce these scalings, the fractional index $μ$ in the FKPP equation needs to be shifted from the naïve value of $μ= 2α- 1$ to a renormalized value $μ= 2α- 2$. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

cond-mat.stat-mech↗

arXiv2022

Real-time correlators in chaotic quantum many-body systems

We study real-time local correlators $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle$ in chaotic quantum many-body systems. These correlators show universal structure at late times, determined by the dominant operator-space Feynman trajectories for the evolving operator $\mathcal{O}(\mathbf{x},t)$. The relevant trajectories involve the operator contracting to a point at both the initial and final time and so are structurally different from those dominating the out-of-time-order correlator. In the absence of conservation laws, correlations decay exponentially: $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle\sim\exp(-s_\mathrm{eq} r(\mathbf{v}) t)$, where $\mathbf{v}= \mathbf{x}/ t$ defines a spacetime ray, and $r(\mathbf{v})$ is an associated decay rate. We express $r(\mathbf{v})$ in terms of cost functions for various spacetime structures. In 1+1D, operator histories can show a phase transition at a critical ray velocity $v_c$, where $r(\mathbf{v})$ is nonanalytic. At low $v$, the dominant Feynman histories are "fat": the operator grows to a size of order $t^α\gg 1$ before contracting to a point again. At high $v$ the trajectories are "thin": the operator always remains of order-one size. In a Haar-random unitary circuit, this transition maps to a simple binding transition for a pair of random walks (the two spatial boundaries of the operator). In higher dimensions, thin trajectories always dominate. We discuss ways to extract the butterfly velocity $v_B$ from the time-ordered correlator, rather than the OTOC. Correlators in the random circuit may alternatively be computed with an effective Ising-like model: a special feature of the Ising weights for the Haar brickwork circuit gives $v_c=v_B$. This work addresses lattice models, but also suggests the possibility of morphological phase transitions for real-time Feynman diagrams in quantum field theories.

cond-mat.stat-mech↗

arXiv2022

Maximal entanglement velocity implies dual unitarity

A global quantum quench can be modeled by a quantum circuit with local unitary gates. In general, entanglement grows linearly at a rate given by entanglement velocity, which is upper bounded by the growth of the light cone. We show that the unitary interactions achieving the maximal rate must remain unitary if we exchange the space and time directions -- a property known as dual unitarity. Our results are robust: approximate maximal entanglement velocity also implies approximate dual unitarity. We further show that maximal entanglement velocity is always accompanied by a specific dynamical pattern of entanglement, which yields simpler analyses of several known exactly solvable models.

quant-ph↗

arXiv2022

Measurement induced entanglement transition in two dimensional shallow circuit

We prepare two dimensional states generated by shallow circuits composed of (1) one layer of two-qubit CZ gate or (2) a few layers of two-qubit random Clifford gate. After measuring all of the bulk qubits, we study the entanglement structure of the remaining qubits on the one dimensional boundary. In the first model, we observe that the competition between the bulk X and Z measurements can lead to an entanglement phase transition between an entangled volume law phase and a disentangled area law phase. We numerically evaluate the critical exponents and generalize this idea to other qudit systems with local Hilbert space dimension larger than 2. In the second model, we observe the entanglement transition by varying the density of the two-qubit gate in each layer. We give an interpretation of this transition in terms of random bond Ising model in a similar shallow circuit composed of random Haar gates.

quant-ph↗