arXiv subjects

Andrew C. Yuan

Publications and source records attributed to Andrew C. Yuan.

14 recordsLinked to original sources

arXiv2026

Non-CSS Quantum Code Embedding

We generalize the unified framework in [Phys. Rev. A 113, 022438 (2026)] to accommodate arbitrary stabilizer codes (referred as non-CSS for emphasis). The generalization has immediate consequences in areas including logical measurement, quantum weight reduction and Euclidean embedding. For example, currently CSS (pure $X,Z$-type) logical measurements are well-understood based on the (height-1) cone, while non-CSS (e.g., $Y$-type) logical measurements are ad hoc (e.g., rely on local Clifford transform). Similarly, quantum weight reduction and optimal Euclidean embeddings only exist for CSS input codes. Here, we show that our generalized framework addresses this issue, and thus many constructions, including qLDPC surgery, Layer Codes and quantum weight reduction generalize to non-CSS codes in a relatively straightforward fashion. The previously mentioned examples are derived in detail for clarity.

quant-ph↗

arXiv2026

4D and 5D Layer Codes through Color Routing

We introduce and explicit Calderbank-Shor-Steane (CSS) code construction that generalizes the Layer codes to $D=4,5$ dimensions. Much like its predecessor, the present construction is based on embedding quantum low-density parity check (qLDPC) codes; from an $[[n,k,d]]$ code with energy barrier $Δ$, we obtain a $D=4,5$ dimensional Layer code with parameters $[[Θ(n^{D/(D-2)}), k, Θ(dn^{1/(D-2)})]]$ and energy barrier $Ω(Δ)$. Using good qLDPC codes as input, our construction saturates the $D=4,5$ dimensional BPT bounds exactly. The higher dimensional Layer Codes are modular, and thus well suited to architectures composed of modular network patches, despite our physical limitation to three dimensions. We overcome the hurdles encountered by previous generalization attempts through the use of \textit{color routing}, allowing us to resolve the structure of the check layers and line defects.

quant-ph↗

arXiv2026

Quantum Weight Reduction with Layer Codes

Quantum weight reduction procedures ease the implementation of quantum codes by sparsifying them, resulting in low-weight checks and low-degree qubits. However, to date, only few quantum weight reduction methods have been explored. In this work we introduce a simple and general procedure for quantum weight reduction that achieves check weight 6 and total qubit degree 6, lower than existing procedures at the cost of a potentially larger qubit overhead. Our quantum weight reduction procedure replaces each qubit and check in an arbitrary Calderbank-Shor-Steane code with an ample patch of surface code, these patches are then joined together to form a geometrically nonlocal Layer Code. This is a quantum analog of the simple classical weight reduction procedure where each bit and check is replaced by a repetition code. Due to the simplicity of our weight reduction procedure, bounds on the weight and degree of the resulting code follow directly from the Layer Code construction and hence are easily verified by inspection. Our procedure is well suited for implementation in modular architectures that consist of surface code patches networked via long-range interconnects.

quant-ph↗

arXiv2026

Parsimonious Quantum Low-Density Parity-Check Code Surgery

Quantum code surgery offers a flexible, low-overhead framework for executing logical measurements within quantum error-correcting codes. It encompasses several fault-tolerant logical computation schemes, including parallel surgery, universal adapters and fast surgery, and serves as the key primitive in extractor architectures. The efficiency of these schemes crucially depends on constructing low-overhead ancilla systems for measuring arbitrary logical operators in general quantum Low-Density Parity-Check (qLDPC) codes. In this work, we introduce a method to construct an ancilla system of qubit size $O(W \log W)$ to measure an arbitrary logical Pauli operator of weight $W$ in any qLDPC stabilizer code. This new construction immediately reduces the asymptotic overhead across various quantum code surgery schemes.

quant-ph↗

arXiv2026

Unified Framework for Quantum Code Embedding

Given a Calderbank-Shor-Steane (CSS) code, it is sometimes necessary to modify the code by adding an arbitrary number of physical qubits and parity checks. Motivations may include concatenating codes, embedding low-density parity check (LDPC) codes into finite-dimensional Euclidean space, or reducing the weights of parity checks. During this embedding, it is essential that the modified code possesses an isomorphic set of logical qubits as the original code. However, despite numerous explicit constructions, the conditions of when such a property holds true is not known in general. Therefore, using the language of homological algebra, we provide a unified framework that guarantees a natural isomorphism between the output and input codes. In particular, we explicitly show how previous works fit into our framework.

quant-ph↗

arXiv2025

Infinite Stability in Disordered Systems

In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random fields is expected to prohibit any finite temperature ordering. Here, we prove that this is not necessarily true, and show rigorously that for physically relevant systems in $\mathbb{Z}^d$ with $d\ge 3$, disorder can induce ordering that is \textit{infinitely stable}, in the sense that (1) there exists ordering at arbitrarily large disorder strength and (2) the transition temperature is asymptotically nonzero in the limit of infinite disorder. Analogous results can hold in 2 dimensions provided that the underlying graph is non-planar (e.g., $\mathbb{Z}^2$ sites with nearest and next-nearest neighbor interactions).

math-ph↗

arXiv2024

Infinitely Stable Disordered Systems on Emergent Fractal Structures

In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random field is expected to prohibit any finite temperature ordering. Here, we show that this is not necessarily true. We provide physically motivated examples of systems in which disorder induces an ordering that is *infinitely stable* in the sense that: (1) there exists ordering at arbitrarily large disorder strength and (2) the transition temperature remains, asymptotically, nonzero in the limit of infinite disorder. The ordering is spatially localized on the boundary of a disorder-induced, emergent percolating fractal structure. The examples we give are most naturally described when the spatial dimension $d \ge 3$, but can also be formulated when $d=2$, provided that the underlying graph is non-planar.

cond-mat.stat-mech↗

arXiv2024

Phase sensitive information from a planar Josephson junction

Josephson tunneling across a planar junction generally depends on the relative twist angle, $θ$, between the two layers. However, if under a discrete rotation, the order parameter in one layer is odd and the other is even (as, e.g., for a $s$-wave to $d_{x^2-y^2}$-wave junction under a $π/2$ rotation) then the bulk Josephson current vanishes for all $θ$. Even in this case, we show that for a finite junction, the Josephson current, $J$, has a nonzero edge contribution that depends on $θ$ and the orientation of the junction edges in ways that can serve as an unambiguous probe of the order parameter symmetry of any time-reversal preserving system (including multiband systems and those in which spin-orbit coupling is significant). We also analyze the microscopic considerations that determine the magnitude of $J$.

cond-mat.supr-con↗

arXiv2024

Absence of Floating Phase in Superconductors with Time-reversal Symmetry Breaking on any Lattice

Due to the interplay of multi-component order parameters (e.g., a twisted bilayer superconductor with inter-layer Josephson coupling or a frustrated ($n\ge 3$)-band superconductor), a superconductor can possess a $U(1)\times \mathbb{Z}_2$ symmetry, corresponding to the superconducting $T_c$ and time-reversal symmetry breaking transition $T_\text{TRSB}$, respectively. It was then conjectured that in this class of Hamiltonians, there exists a vast parameter regime $\mathcal{O}$ such that the system exhibits vestigial TRSB, i.e., $T_\text{TRSB} > T_c$, while at the boundary $\partial \mathcal{O}$, the system possesses a single phase transition $T_\text{TRSB}=T_c$. In this paper, we provide evidence towards this conjecture by mathematically eliminating the possibility of a floating phase, i.e., $T_\text{TRSB} < T_c$, for the strong coupling regime. More specifically, we prove that the correlation functions of $U(1)$ spins are bounded above by that of $\mathbb{Z}_2$ spins for all temperatures and lattice structures (e.g., $\mathbb{Z}^d$ for all $d$). In particular, this guarantees the existence of high-$T_c$ TRSB (and consequently topological) superconductivity in a large class of Hamiltonians. Note that the same property can also be proven for a certain parameter regime ($Δ\ge 4/5$) of the generalized XY model on any lattice structure, despite belonging to an entirely distinct class of $U(1)\times \mathbb{Z}_2$ Hamiltonians.

cond-mat.stat-mech↗

arXiv2023

Exactly Solvable Model of Randomly Coupled Twisted Superconducting Bilayers

Motivated by recent experiments on twisted junctions of cuprate superconductors (SC), it was proposed [1] that at zero temperature, a random first order Josephson coupling $J_1(\textbf{r}) \cos ϕ$ generates an "effective" global second order coupling, $J_2\cos(2ϕ)$, with a sign that favors $ϕ= \pm π/2$, i.e., spontaneous breaking of time reversal symmetry (TRS). To obtain a more controlled understanding of the suggested "disorder-induced-order" mechanism, we construct an exactly solvable lattice mean field model and prove that when the disorder-average $\bar{J}_1=0$, the model exhibits a TRS breaking phase for all temperatures below the SC transition, i.e., $T_c = T_{\mathrm{TRSB}}$, regardless of the specific form of disorder. In the presence of nonzero $\bar{J}_1\ne 0$, we show that the two transitions split linearly for small $\bar{J}_1 \ll κ$ (where $κ$ is the in-plane SC stiffness), and that $T_{\mathrm{TRSB}}$ vanishes for $\bar J_1> J_c$ where $ J_c= \overline{J^2_1}/κ$ in the weak disorder limit. [1] A. C. Yuan, Y. Vituri, E. Berg, B. Spivak, and S. A. Kivelson, Inhomogeneity-induced time-reversal symmetry breaking in cuprate twist-junctions, arXiv preprint arXiv:2305.15472 (2023)

cond-mat.stat-mech↗

arXiv2023

Multiband mean-field theory of the $d+ig$ superconductivity scenario in Sr$_2$RuO$_4$

Many seemingly contradictory experimental findings concerning the superconducting state in Sr$_2$RuO$_4$ can be accounted for on the basis of a conjectured accidental degeneracy between two patterns of pairing that are unrelated to each other under the $(D_{4h})$ symmetry of the crystal: a $d_{x^2-y^2}$-wave $(B_{1g})$ and a $g_{xy(x^2-y^2)}$-wave $(A_{2g})$ superconducting state. In this paper, we propose a generic multi-band model in which the $g$-wave pairing involving the $xz$ and $yz$ orbitals arises from second-nearest-neighbor interactions. Even if time-reversal symmetry is broken in a $d+ig$ state, such a superconductor remains gapless with a Bogoliubov Fermi surface that approximates a (vertical) line node. The model gives rise to a strain-dependent splitting between the critical temperature $T_c$ and the time-reversal symmetry-breaking temperature $T_\text{trsb}$ that is qualitatively similar to some of the experimental observations in Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2023

Inhomogeneity-Induced Time-Reversal Symmetry Breaking in Cuprate Twist-Junctions

The lowest order Josephson coupling, $J_1(θ)\cos(ϕ)$, between two d-wave superconductors with phase-difference $ϕ$ across the junction vanishes when their relative orientation is rotated by $θ=π/4$. However, in the presence of inhomogeneity, $J_{1}(\mathbf{r})$ is non-zero locally, with a sign that fluctuates in space. We show that such a random $J_1$ generates a global second-harmonic Josephson coupling, $J_2\cos(2ϕ)$, with a sign that favors $ϕ= \pm π/2$, i.e., spontaneous breaking of time reversal symmetry. The magnitude of $J_2$ is substantially enhanced if the spatial correlations of $J_1(\mathbf{r})$ extend over large distances, such as would be expected in the presence of large amplitude twist-angle angle disorder or significant local electronic nematicity. We argue that this effect likely accounts for the recent observations in twisted Josephson junctions between high temperature superconductors.

cond-mat.supr-con↗

arXiv2021

Strain-induced time reversal breaking and half quantum vortices near a putative superconducting tetra-critical point in Sr$_2$RuO$_4$

It has been shown [1] that many seemingly contradictory experimental findings concerning the superconducting state in Sr$_2$RuO$_4$ can be accounted for as resulting from the existence of an assumed tetra-critical point at near ambient pressure at which $d_{x^2-y^2}$ and $g_{xy(x^2-y^2)}$ superconducting states are degenerate. We perform both a Landau-Ginzburg and a microscopic mean-field analysis of the effect of spatially varying strain on such a state. In the presence of finite $xy$ shear strain, the superconducting state consists of two possible symmetry-related time-reversal symmetry (TRS) preserving states: $d \pm g$. However, at domain walls between two such regions, TRS can be broken, resulting in a $d+ig$ state. More generally, we find that various natural patterns of spatially varying strain induce a rich variety of superconducting textures, including half-quantum fluxoids. These results may resolve some of the apparent inconsistencies between the theoretical proposal and various experimental observations, including the suggestive evidence of half-quantum vortices [2]. [1] Steven A Kivelson, Andrew C Yuan, BJ Ramshaw, and Ronny Thomale, "A proposal for reconciling diverse experiments on the superconducting state in Sr$_2$RuO$_4$," npj Quantum Mater 5 (2020). [2] J Jang, DG Ferguson, V Vakaryuk, Raffi Budakian, SB Chung, PM Goldbart, and Y Maeno, "Observation of half-height magnetization steps in Sr$_2$RuO$_4$," Science 331, 186-188 (2011).

cond-mat.supr-con↗

arXiv2020

A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4

A variety of precise experiments have been carried out to establish the character of the superconducting state in Sr2RuO4. Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here, we propose that these results can be reconciled if we assume that there is a near-degeneracy between a d_{x^2-y^2} (B_{1g} in group theory nomenclature) and a g_{xy(x^2-y^2)} (A_{2g}) superconducting state. From a weak-coupling perspective, such an accidental degeneracy can occur at a point at which a balance between the on-site and nearest-neighbor repulsions triggers a d-wave to g-wave transition.

cond-mat.supr-con↗