arXiv subjects

Jong Yeon Lee

Publications and source records attributed to Jong Yeon Lee.

At least 19 recordsLinked to original sources

arXiv2026

Evidence for a $\mathbb{Z}_{2}$ Dirac spin liquid in the generalized Shastry-Sutherland model

We present a multimethod investigation of the recently reported quantum spin liquid (QSL) phase in the spin-1/2 Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ansätze on this lattice yields 46 U(1) and 80 $\mathbb{Z}_2$ states. Using density-matrix renormalization group (DMRG) and exact diagonalization, we find that the Shastry-Sutherland model and the square-lattice $J_1$-$J_2$ Heisenberg antiferromagnet share the same QSL phase. We therefore map our Ansätze to those on the square lattice and identify the counterpart of the square-lattice $\mathbb{Z}_2$ Dirac QSL (Z2Azz13) in the Shastry-Sutherland system. Using state-of-the-art variational Monte Carlo with Gutzwiller-projected wavefunctions improved by Lánczos steps, we demonstrate excellent agreement in energies and correlation functions between a gapless (Dirac) $\mathbb{Z}_2$ spin liquid, characterized by only a few variational parameters, and results from neural quantum states and DMRG. Within a unified variational family that continuously connects the spin liquid to the adjacent Néel and plaquette valence-bond-crystal states, we locate both phase boundaries in an unbiased way from order-parameter finite-size scaling and correlation-ratio crossings, and find that both order parameters vanish continuously. Finally, the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group yields a dynamical spin structure factor with features consistent with Dirac cones, providing strong independent evidence for a Dirac QSL ground state. Our identification of a $d$-wave pairing $\mathbb{Z}_2$ Dirac QSL is consistent with recently observed signatures of QSL behavior in Pr$_2$Ga$_2$BeO$_7$ and makes predictions for future experiments.

cond-mat.str-el↗

arXiv2026

Design Principles for Ultra-High-Rate Quantum Codes

Reducing the qubit overhead of quantum error correction is a central challenge for scalable fault-tolerant quantum computing. Recent ultra-high-rate quantum codes offer a promising route toward this goal, with some constructions requiring as few as two physical data qubits per logical qubit. However, systematic principles for navigating the tradeoffs among encoding rate, distance, check weight, and blocklength remain lacking. Here, we develop and analyze principles for exploring this design space, and use them to design compact code constructions with improved performance. We develop code templates based on a pair-partition construction and a halving transformation that further reduces blocklength. Motivated by ensemble analysis of the degree distributions, we identify column weight as a key design parameter: increasing the column weight enables larger distances at compact blocklengths, at the cost of heavier checks. We find that at physical error rates of 0.1%, the benefits of increased distance often outweigh the penalty associated with heavier checks. Applying this framework, we identify numerous compact codes with favorable parameters, including [[90,21,11]], [[140,31,15]], and [[200,43,20]] non-CSS codes with check weight 10. Moreover, we develop symmetry-informed strategies for identifying low-weight logical bases. These results provide systematic strategies for designing ultra-high-rate quantum codes and navigating their Pareto frontier.

quant-ph↗

arXiv2026

Transparent Domain Walls through Information Convex Sets

In $(2+1)$-dimensional topologically ordered many-body states, transparent (topologically deformable) domain walls are invisible to local topological probes, yet can modify the ground state degeneracy (GSD) and transmute anyons transported across them. Here, we develop an entanglement-bootstrap framework using information convex sets (ICSs) on local and noncontractible annuli to extract information about transparent domain walls directly from ground state wavefunctions at fixed points of Abelian topological phases on a torus, without taking categorical defect data as input. We derive fusion rules governing the action of anyons on extreme points of ICSs on noncontractible annuli and determine their quantum dimensions. Extreme points invariant under transport around the complementary cycle correspond one-to-one to minimum entropy states (MESs), and their number equals the GSD. The maximal topological entanglement entropy (TEE), $γ_{\rm LW}^{\max}=\log({D}/d_α)$, probes the net effect of walls crossing the chosen annulus, where ${ D}$ is the total quantum dimension and $d_α$ is the quantum dimension of an extreme point of its ICS. In contrast, the maximal entanglement asymmetry is $ΔS_X^{\max}=\log\mathrm{GSD}$. This value is the same for both annulus orientations and reflects the combined effect of the transparent domain walls. We further show that transparent domain walls can give rise to symmetries supported jointly on the two chosen fundamental cycles that cannot be decomposed into a product of two $1$-form symmetry operators, one supported on each cycle. By relating their action on MESs to anyon tunneling and the fusion rules, we clarify how these symmetries connect distinct ground states. Additionally, we apply the framework to Wen's plaquette model, the anisotropic dipolar toric code, and the rank-2 toric code.

quant-ph↗

arXiv2026

Hierarchy of Rényi Coherent Information in Stabilizer Codes

Rényi coherent information, a computable proxy for the von Neumann coherent information, is widely used to study mixed-state phases of matter and decodability transitions in noisy quantum error-correcting codes. However, being a difference of two Rényi entropies, it need not be monotonic in the Rényi index, and lacks the operational meaning of its von Neumann counterpart. Here we address both issues for stabilizer codes. First, for Pauli noise generated by independent Bernoulli events, we prove that the Rényi-$n$ coherent information is nondecreasing in $n \in \mathbb{Z}^+$. This follows from a general theorem: if independent random bits are mapped linearly to a fine label $T$ and a coarse label $C$, then the Rényi entropy difference $H_n(C)-H_n(T)$ is nondecreasing in $n$. For stabilizer codes, $T$ is the joint syndrome--logical class and $C$ is the syndrome, and the difference is the Rényi-$n$ coherent information up to a constant. The same theorem covers classical linear codes and independent detector error models. Second, for arbitrary stochastic Pauli noise, we give the Rényi-$n$ coherent information an operational meaning via postselection on matching syndromes between one data block and $n-1$ auxiliary blocks. We determine when this defines a quantum channel and show that saturation of the Rényi-$n$ coherent information is equivalent to asymptotically perfect recovery of the postselected channel. Moreover, the Rényi-$n$ coherent information also upper-bounds the ordinary coherent information achievable after any syndrome-conditioned recovery.

quant-ph↗

arXiv2026

Information Critical Phases under Decoherence

Quantum critical phases are extended regions of phase space characterized by a diverging correlation length. By analogy, we define an \emph{information critical phase} as an extended region of a mixed state phase diagram where the Markov length, the characteristic length scale governing the decay of the conditional mutual information (CMI), diverges. We demonstrate that such a phase arises in decohered $\mathbb{Z}_{N}$ toric codes by assessing both the CMI and the coherent information, the latter quantifying the robustness of the encoded logical qudits. For $N>4$, we find that the system hosts an information critical phase intervening between the decodable and non-decodable phases where the coherent information saturates to a fractional value in the thermodynamic limit, indicating that a finite fraction of logical information is still preserved. We show that the density matrix in this phase can be decomposed into a convex sum of Coulombic pure states, where gapped anyons reorganize into gapless photons. We further consider the ungauged $\mathbb{Z}_{N}$ toric code and interpret its mixed state phase diagram in the language of strong-to-weak spontaneous symmetry breaking. We argue that in the dual model, the information critical phase arises because the spontaneously broken off-diagonal $\mathbb{Z}_{N}$ symmetry gets enhanced to a $U(1)$ symmetry, resulting in a novel superfluid phase whose gapless modes involve coherent excitations of both the system and the environment. Finally, we propose an optimal decoding protocol for the corrupted $\mathbb{Z}_{N}$ toric code and show that its logical error rate saturates to a fractional value in the information critical phase. Our findings identify a gapless analog for mixed-state phases that still acts as a fractional topological quantum memory, thereby extending the conventional paradigm of quantum memory phases.

quant-ph↗

arXiv2026

Approximate Quantum Error Correction at Chiral Topological Edges

Topologically ordered phases naturally realize quantum error correction through nonlocal encoding of quantum information. More recently, conformal field theories have been shown to realize approximate quantum error-correcting codes, but such constructions generally require fine tuning to criticality. Here we introduce a family of approximate quantum error-correcting codes realized by the chiral edges of two-dimensional topologically ordered phases. The proposed encoding combines the robustness of a gapped topological bulk with the flexibility of gapless edge conformal field theories. To characterize its robustness, we study coherent-information loss under local erasure. We derive an exact expression relating coherent-information loss to relative entropy, reducing the recoverability problem to universal properties of the edge theory. This leads to power-law scaling of coherent-information loss with the size of the erased region. We further show that, for geometrically local erasures near one edge, the two-dimensional chiral edge code is at least as robust as the dimensionally reduced CFT code, and is strictly more robust in several representative examples. For Abelian code subspaces, we further construct a power-law-range recovery map supported on the erased region together with a power-law-range buffer; this recovery map depends only on the code subspace, not on the unknown encoded state. We provide numerical calculations for lattice realizations of compact free boson and Ising CFT examples that support the theoretical predictions of the power-law exponents.

quant-ph↗

arXiv2026

Lifting Lifted Product Codes

Lifted product (LP) codes form an important class of quantum error correcting codes with favorable code parameters. We introduce a systematic construction of LP code families based on group extensions and graph lifts. The construction increases the code size while preserving the local structure of the Tanner graph, and relates code parameters, logical operators, and fault-tolerant logical-operation gadgets within the families through chain and cochain maps. As a first application, we obtain LP codes with better code parameters than previously reported ones. We then demonstrate that code-surgery gadgets can be transferred across the selected finite lifts through chain maps and, in several cases, implemented with lower space overhead. We also develop parallel product surgery for lifted clustered cyclic codes. Finally, we propose lifting as a systematic first step toward defining thermodynamic families for algebraically defined qLDPC codes without an underlying Euclidean lattice. For several base codes and selected lifts, coherent information exhibits finite-size crossings, while our results also indicate that additional conditions are needed to determine a unique family.

quant-ph↗

arXiv2026

Monte Carlo Studies of Twisted Bilayer Graphene: Strain and Thermal Fluctuations

We study the phase diagram of twisted bilayer graphene at charge neutrality as a function of twist angle $θ$, uniaxial heterostrain $\varepsilon$, and temperature $T$ using sign-problem-free quantum Monte Carlo simulations. At $T=0$ and zero strain, we find a continuous transition from a Dirac semimetal to a gapped Kramers inter-valley coherent (KIVC) phase as $θ$ decreases toward the magic angle. With finite strain, the KIVC phase undergoes a further continuous transition at smaller $θ$ into an anisotropic semimetal with gapless excitations near the center of the moiré Brillouin zone. In the KIVC regime, the entropy rises sharply with temperature and plateaus at $15\,\text{K} \lesssim T \lesssim 40\,\text{K}$ near the value expected from a Mott-like regime of localized electrons with nearly uncorrelated spin, valley, and orbital degrees of freedom, despite the topological obstruction preventing a localized tight-binding description of the active bands. The spectral function evolves continuously with $θ$: at low $T$, a gap opens at the $K$ points and the minimal gap shifts to $Γ$ as $θ$ decreases; at intermediate $T$, the spectral function smoothly interpolates between a Dirac semimetal spectrum with coherent $K$-point quasiparticles and a spectrum with gapless $Γ$-centered quasiparticles near the magic angle. The later can be a anisotropic or a Mott semimetal and we discuss how to distiguish them in experiment.

cond-mat.str-el↗

arXiv2026

Logical Spectroscopy: Lifted-Product Codes with Addressable Bases

Quantum LDPC memories can encode many logical qubits, but that alone does not make them usable: applications need to know where the logical operators are supported, how they are labeled, and how conjugate $X/Z$ partners pair. For hypergraph-product codes this information follows from row reduction over $\mathbb{F}_2$. For Abelian lifted-product codes, which include prominent high-rate constructions, it does not: the entries of the defining seed matrices live in a group algebra rather than a field, so pivots need not be invertible and row reduction can fail. To address this problem, we introduce \emph{logical spectroscopy}. For an odd-order Abelian lift group, the Chinese remainder theorem splits the group algebra into finite fields, one for each Frobenius orbit of characters; we call these orbits packets. Packet by packet, we solve ordinary finite-field linear algebra, lift the answers back to the physical code with the associated packet projectors, and pair $X$ and $Z$ logicals between reciprocal packets by trace duality. The result is a complete conjugate logical basis for a finite Abelian lifted product code that is addressable: every logical coordinate carries canonical packet and Künneth-summand labels, deterministic within-block indices, a conjugate partner, and an explicit binary representative. The code's own translation symmetry then acts on these coordinates in closed form. We apply the construction to examples with up to 5000 physical qubits, including high-rate examples whose distance-witness is reported explicitly. We further extend the decomposition to even-order lifts. Logical spectroscopy thus equips Abelian lifted products with an explicit logical coordinate system and an algebraic toolkit for high-rate code search.

quant-ph↗

arXiv2026

Holographically Emergent Gauge Theory in Symmetric Quantum Circuits

We develop a novel holographic framework to study dynamical phases in random quantum circuits with a global symmetry $G$. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent gauge wavefunction in one higher dimension, and a non-symmetric layer, composed of random multiplicity tensors. For $G\,{=}\,\mathbb{Z}_N$ symmetric circuits consisting of local unitary gates interspersed with local symmetric noise channels, averaging over the non-symmetric layer yields a dynamically generated noisy $\mathbb{Z}_{N}$ surface code. This allows us to interpret $\mathbb{Z}_{N}$ symmetric circuits in the volume-law phase as quantum error-correcting codes with a distinguished set of logical spin states that inherit the topological protection of the bulk code. By establishing equality of bulk and boundary coherent information, we show that quantum information encoded in these logical states is maximally protected against symmetric noise up to a finite threshold. We further study weakly monitored $\mathbb{Z}_{N}$ symmetric circuits which exhibit a charge-sharpening transition. We show that the point at which the observer gains classical information about the global charge coincides with the point at which measurements destroy the underlying quantum information encoded in the bulk surface code. This also allows for a natural interpretation of the sharpening transition as a confinement transition in the gauge theory. For $N\,{\leq}\,4$, weak measurements drive a single transition from a charge-fuzzy phase with exponential sharpening time $t_{\#}\sim e^{L}$ to a charge-sharp phase with $t_{\#}\sim \mathcal{O}(1)$. On the other hand, for $N>4$, the circuit can enter an intermediate phase with a linear sharpening time $t_{\#}\sim \mathcal{O}(L)$. In this regime, the bulk gauge theory realizes a Coulomb phase with emergent gapless photons.

quant-ph↗

arXiv2026

Charge Scrambling in Strong-to-Weak Spontaneous Symmetry Breaking

Strong-to-weak spontaneous symmetry breaking (SWSSB) is diagnosed by nonlinear correlators, but its direct static implication for conserved charge fluctuations is not automatic. We show that, for continuous symmetries, long-range Rényi-1 correlator, together with a sufficiently rapid approach to its nonzero asymptotic value, forces subsystem charge indefiniteness: the block-charge variance has an extensive lower bound; equivalently, the truncated symmetry expectation has extensive curvature. This gives a precise static fluctuation footprint of charge scrambling. We construct examples to show that the implication is conditional and non-reversible: dephased superfluids retain Rényi-1 SWSSB with subextensive charge variance when the Rényi-1 tail is too slow, while sparse fixed-charge projectors have extensive charge variance but no local charge-transfer Rényi-1 order or long-range conditional mutual information. Finally, we introduce a \emph{twist overlap} correlator, which serves as an analogue of charge variance applicable to both discrete and continuous symmetries. This naturally decomposes local block-charge fluctuations into strong- and weak-symmetry channels. We found that the weak-symmetry channel isolates coherent charge fluctuations and is directly related to the Wigner--Yanase skew information. Taken together, these results give a unified understanding for distinguishing nonlinear SWSSB order, local charge indefiniteness, and coherent charge fluctuations.

cond-mat.stat-mech↗

arXiv2026

Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold

The toric code is a canonical example of a topological error-correcting code. Two logical qubits stored within the toric code are robust against local decoherence, ensuring that these qubits can be faithfully retrieved as long as the error rate remains below a certain threshold. Recent studies have explored such a threshold behavior as an intrinsic information-theoretic transition, independent of the decoding protocol. These studies have shown that information-theoretic metrics, calculated using the Renyi (replica) approximation, demonstrate sharp transitions at a specific error rate. However, an exact analytic expression that avoids using the replica trick has not been shown, and the connection between the transition in information-theoretic capacity and the random bond Ising model (RBIM) has only been indirectly established. In this work, we present the first analytic expression for the coherent information of a decohered toric code, thereby establishing a rigorous connection between the fundamental error threshold and the criticality of the RBIM.

cond-mat.stat-mech↗

arXiv2026

Liouvillian Gap in Dissipative Haar-Doped Clifford Circuits

Quantum chaos is commonly assessed through probe-dependent signatures that need not coincide. Recently, a dissipative signature was proposed for chaotic Floquet systems, where infinitesimal bulk dissipation induces a non-zero constant intrinsic relaxation rate quantified by the Liouvillian gap. This raises a question: what minimal departure from Clifford dynamics is required to generate such intrinsic relaxation? To address this, we study a Floquet two-qubit Clifford circuit doped with Haar-random single-qubit gates and subject to local dissipation of strength $γ$. We find a structure-dependent crossover. The undoped iSWAP-class circuit exhibits a weak-dissipation singularity, with a gap that grows with $N$ for any $γ>0$. Haar doping preserves this undoped-like growth for any subextensive doping pattern. At finite doping density, there exist patterns that yield an $\mathcal{O}(1)$ gap for any fixed $γ$ as $N\to\infty$, yet remain singular as $γ\to0^+$. Because our bounds depend only on the spatial doping pattern, they remain valid even when the Haar rotations are independently redrawn each Floquet period. Overall, our findings provide a circuit-level perspective on intrinsic relaxation, and thus irreversibility, in open many-body systems.

quant-ph↗

arXiv2026

Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits

We introduce an extended framework for the simultaneous gauging of modulated symmetries in $(d+1)$ dimensions, employing {\it multiple} gauge symmetry operators whose corresponding gauging procedures must be carried out simultaneously. Simultaneous gauging can capture a broader class of dualities than sequential gauging, the latter corresponding to the conventional gauging applied in successive steps. In general, performing simultaneous gauging and conventional gauging in sequence constitutes the most general framework for gauging modulated symmetries. We further show that the associated duality transformations can be implemented via adaptive state preparation protocols. As a concrete example, we consider a dipole symmetry in $(2+1)$D and illustrate both the simultaneous gauging procedure and the adaptive preparation protocol. Interestingly, we find that the intermediate state of the simultaneous gauging/adaptive circuit corresponds to a symmetry-protected topological phase protected by the dipole bundle symmetry. Finally, we utilize the duality to analyze the phase diagram of the rank-2 toric code under transverse fields.

cond-mat.str-el↗

arXiv2025

Topological Mixed States: Phases of Matter from Axiomatic Approaches

For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive, often relying on operational definitions without fundamental principles. Here, we fill this gap by proposing an approach based on three axioms: ($i$) local recoverability, ($ii$) absence of long-range correlations, and ($iii$) spatial uniformity. States that satisfy these axioms are fixed points; requiring the axioms only after coarse-graining promotes each fixed point to an equivalence class, i.e., a phase, presenting the first step towards the axiomatic classification of mixed-state phases of matter: mixed-state bootstrap program. From these axioms, a rich set of topological data naturally emerges; importantly, these data are robust under relaxation of axioms. For example, each topological mixed state supports locally indistinguishable classical and/or quantum logical memories with distinct responses to topological operations. These data label distinct mixed-state phases, allowing one to distinguish them. We further uncover a hierarchy of secret-sharing constraints: in non-Abelian phases, reliable recovery-even of information that looks purely classical-demands a specific coordination among spatial subregions, a requirement different across non-Abelian classes. This originates from non-Abelian fusion rules that can stay robust under decoherence. Finally, we performed large-scale numerical simulations to corroborate stability: weakly decohered fixed points respect the axioms once coarse-grained. These results lay the foundation for a systematic classification of topological states in open quantum systems.

cond-mat.str-el↗

arXiv2025

Coherent information for CSS codes under decoherence

Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons. Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state. Here we perform a simple analytic calculation of the coherent information for general CSS codes under local incoherent Pauli errors via diagonalization of the density matrices and mapping to classical statistical mechanical (SM) models. Our result establishes a rigorous connection between the decoding transition of the quantum code and the phase transition in the random classical SM model. It is also directly confirmed for CSS codes that exact error correction is possible if and only if the maximum-likelihood (ML) decoder always succeeds in the thermodynamic limit. Thus, the fundamental threshold is saturated by the optimal decoder.

quant-ph↗

arXiv2025

The Future of the Correlated Electron Problem

A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies.

cond-mat.str-el↗

arXiv2024

Symmetry protected topological phases under decoherence

We study ensembles described by density matrices with potentially nontrivial topological features. In particular, we study a class of symmetry protected topological (SPT) phases under various types of decoherence, which can drive a pure SPT state into a mixed state. We demonstrate that the system can still retain the nontrivial topological information from the SPT ground state even under decoherence. In the "doubled Hilbert space", we provide a general definition for symmetry protected topological ensemble (SPT ensemble), and the main quantity that we investigate is various types of (boundary) anomalies in the doubled Hilbert space. We show that the notion of the strange correlator, previously proposed to as a diagnosis for the SPT ground states, can be generalized to capture these anomalies in mixed-state density matrices. Using both exact calculations of the stabilizer Hamiltonians and field theory evaluations, we demonstrate that under decoherence the nontrivial features of the SPT state can persist in the two types of strange correlators: type-I and type-II. We show that the nontrivial type-I strange correlator corresponds to the presence of the SPT information that can be efficiently identified and utilized from experiments, such as for the purpose of preparing for long-range entangled states. The nontrivial type-II strange correlator encodes the full topological response of the decohered mixed state density matrix, i.e., the information about the presence of the SPT state before decoherence. Therefore, our work provides a unified framework to understand decohered SPT phases from the information-theoretic viewpoint.

cond-mat.str-el↗