arXiv subjects

Guo-Yi Zhu

Publications and source records attributed to Guo-Yi Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Sampling isometric tensor network states with monitored quantum circuits

Projected entangled pair states (PEPS) provide an efficient variational ansatz for two-dimensional quantum phases, but computing observables remains challenging because PEPS contraction is generally costly. Here, we parameterize two-dimensional quantum states using variational PEPS subject to isometric constraints and map the resulting ansatz onto monitored quantum circuits, replacing tensor-network contraction with circuit sampling. For infinite cylinders, the transfer matrix defines a quantum channel on the virtual boundary. We use a fixed-point treatment and a monitored-circuit unraveling of this channel to evaluate observables efficiently. Using a constant number of variational parameters and a number of qubits that scales only with the cylinder width, our method yields a phase diagram for the $J_1$-$J_2$ model in qualitative agreement with DMRG results. Because the monitored circuits are compatible with near-term quantum hardware, this approach provides a hybrid quantum-classical framework for simulating two-dimensional quantum many-body systems.

quant-ph↗

arXiv2026

Learning Potts Models and $Z_3$ Toric Codes: Higher and Ordinary Nishimori Criticality

Motivated by a previous Ising study, we identify a ${\it higher}$ Nishimori line in the learning phase diagram of the $2D$ $q$-state Potts model $(2 < q\leq 4)$ under bond-energy measurements. This ${\it higher}$ Nishimori line meets the critical temperature line of the Potts model, in a ${\it higher}$ Nishimori critical point -- a tricritical point at finite inference strength that separates a paramagnetic, a ferromagnetic and a 'spin-glass' phase. With analytical tools, we discuss the general structure of the rich phase diagram, which contains two unstable and three stable fixed points, and obtain a number of exact results for universal quantities, including the decay exponent of the Edwards-Anderson correlator, using a Gaussian measurement protocol which allows for exact calculations. Using extensive numerical tools, we confirm these statements for a generic, discrete $q$-state measurement protocol and determine precise numerical estimates for the location of higher and ordinary Nishimori critical points as well as RG flows between the various fixed points. We also discuss the Casimir effective central charges of the critical points in the learning phase diagram, and their monotonic ${\it decrease}$ along measurement-induced RG flows, as established non-perturbatively by the c-effective theorem and its extensions, and contrast it to the monotonic increase along the corresponding RG flows in the random-bond Potts model. Finally, we discuss a general argument based on ${\it Elitzur's \; theorem}$ that establishes stability of the ordinary Nishimori critical points in their respective learning phase diagrams. Equivalently, our results describe a monitored deformed $\mathbb{Z}_q$ toric code where the tricritical ${\it higher}$ Nishimori point is an 'information' critical point that separates stable quantum, classical, and no memory phases.

cond-mat.stat-mech↗

arXiv2026

Dynamical self-dual criticality in Fibonacci-monitored quantum Ising chains

For the quantum phase transition in the transverse-field Ising chain, Kramers-Wannier duality not only protects its critical properties but also pinpoints the location of the phase transition. Its role in out-of-equilibrium, monitored dynamics, however, remains largely unexplored beyond time-periodic Floquet protocols where self-duality turns into a statistical average symmetry. Here we explore the emergence of dynamical self-duality in the absence of time-translation symmetry by investigating the monitored dynamics of one-dimensional Ising/Majorana chains where measurements are arranged in a quasiperiodic Fibonacci sequence. We find that the dynamical extension of this non-invertible symmetry to an out-of-equilibrium setting allows one to organize the dynamical phase diagram of entangled phases, both predicting the transition locations and protecting universal critical behavior. Analytically and numerically, we identify two distinct critical lines, both related to the golden ratio, for Born-rule weak measurements and for random Clifford projective measurements. The latter coincides with the transition of a pure imaginary-time evolution, which can be viewed as a post-selected trajectory. The universality classes of the long-time critical steady states at Fibonacci times are determined, while the transient dynamics between Fibonacci times is deformed by measurements, realizing dynamical measurement-altered quantum criticality in real time.

quant-ph↗

arXiv2026

Born-rule statistical dynamical quantum phase transitions under measurement

Dynamical quantum phase transitions (DQPTs) occur at times when a quantum state exhibits a nonanalytic change in its return probability. This can be viewed as the probability of collapsing the evolved state to the initial state by quantum measurement. However, the initial wave function usually has exponentially small amplitude in the late time evolved state. Here we perform statistical characterization for all the possible post-measurement states distributed according to the Born's rule, by sampling a one-dimensional quantum Ising chain after a quantum quench dynamics. The statistical ensemble can also be viewed as a mixed state when the time evolved state is subjected to maximally dephasing noise in a certain basis. We map the distribution to a statistical model and characterize its effective "energy" spectrum, and introduce the average dynamical free energy, establishing a framework for the statistical DQPTs. We show the recovering of DQPT under high-moment average and a delocalized level distribution following critical times. Through analytic continuation into the complex time plane, we demonstrate the vanishing of Yang-Lee-Fisher zeros and the emergent level crossing near critical times. Finally, we propose a measurement-based quantum computation protocol to simulate the unitary evolution via single-qubit measurements on a two-dimensional cluster state. Our results provide a way for experimentally investigating statistical DQPTs in quantum devices, shedding light on the structured circuit sampling with insights from DQPT and generalizing the understanding of mixed state due to decoherence beyond equilibrium.

quant-ph↗

arXiv2026

Ergotropy of quantum many-body scars

Quantum many-body scars break ergodicity and evade thermalization, resulting in sub-volume law entanglement entropy even with high energy density. While their quantum correlations and entanglement have been elaborated previously, their capacity in storing extractable energy, quantified by the notion ergotropy, remains an open question. Here we focus on the representative PXP model, and unveil the extensive ergotropy scaling of a family of states interpolating between quantum many-body scars and thermal states, the latter of which are known to be passive with vanishing ergotropy in the thermodynamic limit. A phenomenological relation between ergotropy and entanglement is uncovered, which generalizes the existing free fermion integrable results to an interacting scenario. The ergotropy in a dynamical protocol shows that a reset with a global uniform coherent rotation can inject extractable energy, as a proof of principle way to charge a quantum "battery". Our protocol is tailored for near term Rydberg neutral atoms array, while also being feasible for other quantum processors. Our results establish that quantum many-body scars, despite the tiny fraction of the Hilbert space they occupy, can be efficiently exploited for storing extractable energy, and "scarring" a many-body system as a promising route for engineering quantum many-body battery.

quant-ph↗

arXiv2026

Learning transitions in classical Ising models and deformed toric codes

Conditional probability distributions describe the effect of learning an initially unknown classical state through Bayesian inference. Here we demonstrate the existence of a \textit{learning transition}, having signatures in the long distance behavior of conditional correlation functions, in the two-dimensional classical Ising model. This transition, which arises when learning local energy densities, extends all the way from the infinite-temperature paramagnetic state down to the thermal critical state. The intersection of the line of learning transitions and the thermal Ising transition is a new tricritical point. Our model for learning also exactly describes the effects of weak measurements on ground states of frustration-free quantum Hamiltonians, which interpolate between the toric code and a paramagnet. Notably, the location of the above tricritical point implies that the quantum memory defined by the degenerate ground states in the topological phase is robust to weak measurement, even when the initial state is arbitrarily close to the quantum phase transition separating topological and trivial phases. Our analysis uses a replica field theory combined with the renormalization group, and we chart out the phase diagram using a combination of tensor network and Monte Carlo techniques. Our methods can be extended to study the more general effects of learning on both classical and quantum states. The learning induced critical states can be realized in classical or quantum devices.

cond-mat.stat-mech↗

arXiv2026

Revisiting Nishimori multicriticality through the lens of information measures

The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp indicators of phase transitions over the full $p$-$T$ plane. These generalized measures admit a natural operational interpretation as diagnostics of inference mismatch for decoders operating at an effective temperature. We derive exact inequalities for several generalized measures, demonstrating that each attains its extremum along the Nishimori line. As a direct application, we study these measures in the 2d $\pm J$ random-bond Ising model-corresponding to a surface code under bit-flip noise-and revisit the Nishimori multicritical point. Among all indicators, coherent information exhibits the weakest finite-size effects, enabling a high-precision estimate $p_c=0.1092212(4)$ and the associated critical exponents.

cond-mat.stat-mech↗

arXiv2026

Higher Nishimori Criticality and Exact Results at the Learning Transition of Deformed Toric Codes

We revisit a learning-induced tricritical point, at which three phases with strong, weak, and broken $Z_2$ symmetry meet, in the phase diagram of a deformed toric code wavefunction subjected to weak measurements. This setting is exactly dual to a classical Bayesian inference phase diagram of the $2D$ classical Ising model. Here we demonstrate that this tricritical point lies on a distinct $\textit{higher Nishimori line}$, which has an emergent gauge-invariant formulation, just like the ordinary Nishimori line but with a higher replica symmetry as a replica stat-mech model in the replica number $R\rightarrow2$ limit, where disorder is averaged according to the Born rule. As such, the learning tricritical point is in fact a $\textit{higher Nishimori critical point}$. Using this identification, we obtain a number of $\textit{exact results}$ at this $\textit{higher}$ Nishimori critical point; e.g., we show that the power-law exponent of the Edwards-Anderson correlation function is exactly equal to that of the spin correlation function at the unmeasured Ising critical point and verify this in numerical simulations. Using the tools of the proof of a $c$-effective theorem [arXiv:2507.07959], we show that the Casimir effective central charge $c_{\text{eff}}$ $\textit{decreases}$ under renormalization group (RG) flow from the $\textit{higher}$ Nishimori critical point to the unmeasured $2D$ Ising critical point, and is thus greater than $1/2$. This is corroborated by extensive numerical simulations finding $c_{\text{eff}} = 0.522(1)$. The analytical result also explains, with a physically motivated assumption, the numerically observed increase of the Casimir effective central charge under the RG flow from the ordinary Nishimori critical point to the clean Ising critical point in the random-bond Ising model. We also discuss $\textit{higher}$ Nishimori criticality in general dimensions $D>1$.

cond-mat.stat-mech↗

arXiv2026

Teleportation transition of surface codes on a superconducting quantum processor

The topological surface code is a leading candidate for harnessing long-range entanglement to protect logical quantum information against errors, and teleportation of logical states is desirable for robust quantum information processing. Nevertheless, scaling up the surface code in quantum teleportation poses a formidable challenge to experiment. Here on a superconducting quantum processor with 125 qubits, we demonstrate the robust teleportation of topological rotated surface code prepared by a linear-depth unitary circuit, with code distances up to 7. We obtain the teleportation phase diagram by tuning the local entangling gates uniformly across a finite threshold. Furthermore, we show that the entangling threshold can be boosted by coherent qubit rotations that inject magic resources beyond the Clifford regime, restoring the duality symmetry of the topological phase, which serves as a guiding principle to minimize the entanglement resource. Our results shed light on simulating and leveraging topological quantum matter on quantum devices, and pave the way to the ultimate goal of distributed fault tolerant quantum computation.

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arXiv2025

Decoherence-induced self-dual criticality in topological states of matter

Quantum measurements performed on a subsystem of a quantum many-body state can generate entanglement for its remaining constituents. The whole system including the measurement record is described by a hybrid mixed state, which can exhibit exotic phase transitions and critical phenomena. We demonstrate that generic measurement-induced phase transitions (MIPTs) can be cast as decoherence-induced critical mixed states in one higher dimension, by constructing a projected entangled pair state (PEPS) prior to decoherence or measurement. In this context, a deeper conceptual understanding of such mixed-state criticality is called for, particularly with regard to algebraic symmetry as an advanced organizing principle for such entangled states of matter. Integrating these connections we investigate the role of self-dual symmetry -- a fundamental notion in theoretical physics -- in mixed states, showing that the decoherence of electric (e) and magnetic (m) vortices from the 2D bulk of the toric code, or equivalently, a 2D cluster state with symmetry-protected topological order, can leave a (1+1)D quantum critical mixed state protected by a weak Kramers-Wannier self-dual symmetry. The corresponding self-dual critical bulk is described by the N->1 limit of the 2D Non-linear Sigma Model in symmetry class D with target space SO(2N)/U(N) at $Θ$-angle $π$, and represents a "measurement-version" of the Cho-Fisher network model subjected to Born-rule randomness...

quant-ph↗

arXiv2025

Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss

In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a (2+0)-dimensional non-unitary conformal field theory which, for the two types of imperfections of certain circuits, is described by either percolation or Nishimori criticality, respectively. Here we study the threshold behavior when the two types of errors simultaneously occur and show that, when moving away from the Clifford-regime of projective stabilizer measurements, the percolation critical point becomes unstable and the critical theory flows to Nishimori universality. We track this critical renormalization group (RG) crossover flow by mapping out the entanglement phase diagrams, parametrized by the probability and strength of random weak measurements, of two dual protocols preparing surface code or GHZ-class cat states from a parent cluster state via constant-depth circuits. Extensive numerical simulations, using hybrid Gaussian fermion and tensor network / Monte Carlo sampling techniques on systems with more than a million qubits, demonstrate that an infinitesimal deviation from the Clifford regime leads to a sudden, strongly non-monotonic entanglement growth at the incipient non-unitary RG flow. We argue that spectra of scaling dimensions of both the percolation and Nishimori fixed points exhibit multifractality. For percolation, we provide the exact (non-quadratic) multifractal spectrum of exponents, while for the Nishimori fixed point we show high-precision numerical results for five leading exponents characterizing multifractality.

quant-ph↗

arXiv2025

Learning transitions of topological surface codes

For the surface code, topological quantum order allows one to encode logical quantum information in a robust, long-range entangled many-body quantum state. However, if an observer probes this quantum state by performing measurements on the underlying qubits, thereby collecting an ensemble of highly correlated classical snapshots, two closely related questions arise: (i) do measurements decohere the topological order of the quantum state; and (ii) how much of the logical information can one learn from the snapshots? Here we address these questions for measurements in a uniform basis on all qubits. We find that for generic measurement angles, sufficiently far away from the Clifford X, Y, and Z directions (such as the X+Y+Z basis) the logical information is never lost in one of the following two ways: (i) for weak measurement, the topological order is absolutely robust; (ii) for projective measurement, the quantum state inevitably collapses, but the logical quantum information is faithfully transferred from the quantum system to the observer in the form of a tomographically complete classical shadow. At these generic measurement angles and in the projective-measurement limit, the measurement ensemble enforced by Born probabilities can be represented by a 2D tensor network that can be fermionized into a disordered, free-fermion network model in symmetry class DIII, which gives rise to a Majorana "metal" phase. When the measurement angle is biased towards the X or Z limits, a critical angle indicates the threshold of a learning transition beyond which the classical shadow no longer reveals full tomographic information (but reduces to a measurement of the logical X or Z state). This learning transition can be described in the language of the network model as a "metal to insulator" transition...

quant-ph↗

arXiv2024

Robust teleportation of a surface code and cascade of topological quantum phase transitions

Teleportation is a facet where quantum measurements can act as a powerful resource in quantum physics, as local measurements allow to steer quantum information in a non-local way. While this has long been established for a single Bell pair, the teleportation of a many-qubit entangled state using non-maximally entangled resources presents a fundamentally different challenge. Here we investigate a tangible protocol for teleporting a long-range entangled surface code state using elementary Bell measurements and its stability in the presence of coherent errors that weaken the Bell entanglement. We relate the underlying threshold problem to the physics of anyon condensation under weak measurements and map it to a variant of the Ashkin-Teller model of statistical mechanics with Nishimori type disorder, which gives rise to a cascade of phase transitions. Tuning the angle of the local Bell measurements, we find a continuously varying threshold. Notably, the threshold moves to infinity for the $X+Z$ angle along the self-dual line -- indicating that infinitesimally weak entanglement is sufficient in teleporting a self-dual topological surface code. Our teleportation protocol, which can be readily implemented in dynamically configurable Rydberg atom arrays, thereby gives guidance for a practical demonstration of the power of quantum measurements.

quant-ph↗

arXiv2024

Fractional Chern insulator candidate in twisted bilayer checkboard lattice

We investigate a fractional Chern insulator (FCI) candidate arising from Moiré bands with higher Chern number C=2 on a magic angle twisted bilayer checkboard lattice (MATBCB). There are two nearly flat low lying bands in the single particle energy spectrum under the first magic angle $ϕ\approx 1.608^{\circ}$ and chiral limit. We find MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moiré Brillourin Zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a ten-fold ground state quasi-degeneracy in many body energy spectrum with filling fraction $ν=1/5$. The ten-fold quasi-degenrate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasi-hole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a fractional Chern insulator is realized in this system.

cond-mat.str-el↗

arXiv2024

Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling

Quantum circuits offer a versatile platform for simulating digital quantum dynamics and uncovering novel states of non-equilibrium quantum matter. One principal example are measurement-induced phase transitions arising from non-unitary dynamics in monitored circuits, which employ mid-circuit measurements as an essential building block next to standard unitary gates. Although a comprehensive understanding of dynamics in generic circuits is still evolving, we contend that monitored quantum circuits yield robust phases of dynamic matter, which -- akin to Hamiltonian ground state phases -- can be categorized based on symmetries and spatial dimensionality. To illustrate this concept, we focus on quantum circuits within symmetry classes BDI and D, which are measurement-only adaptations of the paradigmatic Kitaev and Yao-Kivelson models, embodying particle-hole-symmetric Majorana fermions with or without time-reversal. We establish a general framework -- Majorana loop models -- for both symmetry classes to provide access to the phenomenology of the entanglement dynamics in these circuits, displaying both an area-law phase of localized Majorana loops and a delocalized, highly entangled Majorana liquid phase. The two phases are separated by a continuous transition displaying quantum Lifshitz scaling, albeit with critical exponents of two distinct universality classes. The loop model framework provides not only analytical understanding of these universality classes in terms of non-linear sigma models, but also allows for highly efficient numerical techniques capable of simulating excessively large circuits with up to $10^8$ qubits. We utilize this framework to accurately determine universal probes that distinguish both the entangled phases and the critical points of the two symmetry classes. Our work thereby further solidifies the concept of emergent circuit phases and their phase transitions.

quant-ph↗

arXiv2023

Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits

Preparing quantum states across many qubits is necessary to unlock the full potential of quantum computers. However, a key challenge is to realize efficient preparation protocols which are stable to noise and gate imperfections. Here, using a measurement-based protocol on a 127 superconducting qubit device, we study the generation of the simplest long-range order -- Ising order, familiar from Greenberger-Horne-Zeilinger (GHZ) states and the repetition code -- on 54 system qubits. Our efficient implementation of the constant-depth protocol and classical decoder shows higher fidelities for GHZ states compared to size-dependent, unitary protocols. By experimentally tuning coherent and incoherent error rates, we demonstrate stability of this decoded long-range order in two spatial dimensions, up to a critical point which corresponds to a transition belonging to the unusual Nishimori universality class. Although in classical systems Nishimori physics requires fine-tuning multiple parameters, here it arises as a direct result of the Born rule for measurement probabilities -- locking the effective temperature and disorder driving this transition. Our study exemplifies how measurement-based state preparation can be meaningfully explored on quantum processors beyond a hundred qubits.

quant-ph↗

arXiv2023

Dynamical localization transition of string breaking in quantum spin chains

The fission of a string connecting two charges is an astounding phenomenon in confining gauge theories. The dynamics of this process have been studied intensively in recent years, with plenty of numerical results yielding a dichotomy: the confining string can decay relatively fast or persist up to extremely long times. Here, we put forward a dynamical localization transition as the mechanism underlying this dichotomy. To this end, we derive an effective string breaking description in the light-meson sector of a confined spin chain and show that the problem can be regarded as a dynamical localization transition in Fock space. Fast and suppressed string breaking dynamics are identified with delocalized and localized behavior, respectively. We then provide a further reduction of the dynamical string breaking problem onto a quantum impurity model, where the string is represented as an "impurity" immersed in a meson bath. It is shown that this model features a localization-delocalization transition, giving a general and simple physical basis to understand the qualitatively distinct string breaking regimes. These findings are directly relevant for a wider class of confining lattice models in any dimension and could be realized on present-day Rydberg quantum simulators.

cond-mat.str-el↗

arXiv2023

Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements

In the field of monitored quantum circuits, it has remained an open question whether finite-time protocols for preparing long-range entangled states lead to phases of matter which are stable to gate imperfections, which can convert projective into weak measurements. Here we show that in certain cases, long-range entanglement persists in the presence of weak measurements, and gives rise to novel forms of quantum criticality. We demonstrate this explicitly for preparing the two-dimensional Greenberger-Horne-Zeilinger cat state and the three-dimensional toric code as minimal instances. In contrast to the monitored random unitary circuits, In contrast to random monitored circuits, our circuit of gates and measurements is deterministic; the only randomness is in the measurement outcomes. We show how the randomness in these weak measurements allows us to track the solvable Nishimori line of the random-bond Ising model, rigorously establishing the stability of the glassy long-range entangled states in two and three spatial dimensions. Away from this exactly solvable construction, we use hybrid tensor network and Monte Carlo simulations to obtain a nonzero Edwards-Anderson order parameter as an indicator of long-range entanglement in the two-dimensional scenario. We argue that our protocol admits a natural implementation in existing quantum computing architectures, requiring only a depth-3 circuit on IBM's heavy-hexagon transmon chips.

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