arXiv subjects

Misha Yutushui

Publications and source records attributed to Misha Yutushui.

13 recordsLinked to original sources

arXiv2026

Optimal Decoding for Measurement-Based GHZ State Preparation: The Maximum-Utility Decoder

The meticulous preparation of macroscopic Greenberger-Horne-Zeilinger (GHZ) states provides a foundational resource for quantum technologies such as metrology, cryptography, and fault-tolerant codes. While state-of-the-art measurement-based protocols offer efficient low-depth execution, their performance can be bottlenecked by conventional decoders, such as minimum weight perfect matching (MWPM) or even maximum-likelihood decoding (MLD), which optimize for $binary$ logical recovery and fail to maximize the $continuous$ long-range order characteristic of a GHZ state for two-dimensional geometries. Here we overcome this limitation by framing the decoding problem as minimum Bayesian risk inference, introducing a general paradigm that maximizes the expected ${utility}$ of the decoded state. Implementing this maximum-utility approach, we construct an algorithm that achieves the highest possible per-shot decoded quantum order and thereby establish an optimal decoding strategy for measurement-based GHZ state preparation. To improve its computational efficiency, we design a scalable two-stage decoder, which first encodes the syndromes into the edge weights of MWPM and then refines the result with a convolutional neural network trained to maximize the expected utility, at a fraction of the cost of the optimal decoder. Remarkably, we find that the first stage alone$\unicode{x2014}$which makes the matching aware of the gauge choice at no cost beyond bare MWPM$\unicode{x2014}$already performs near-optimally up to the largest sizes we study, $N=256\times256$, closing up to $87\%$ of the gap between the bare-MWPM and optimal decoding thresholds. Generalizing MWPM and MLD, the maximum-utility decoder (MUD) establishes a versatile framework that can be explicitly tailored to the operational demands of specific experiments by redefining the utility function.

quant-ph↗

arXiv2026

Interaction-driven quantum phase transitions between topological and crystalline orders of electrons

Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals can be tuned electrostatically. Applying a displacement field leads to Landau-level crossings, where the interaction potential is strongly modified due to changes in the orbital wave functions. Here, we leverage this control to investigate phase transitions between topological and crystalline orders at constant filling factors in the lowest Landau level of BLG. Using transport measurements in high-quality hBN-encapsulated devices, we study transitions as a function of displacement field near crossings of $N=0$ and $N=1$ orbitals. The enhanced Landau-level mixing near the crossing stabilizes electronic crystals at all fractional fillings, including a resistive state at $ν= \frac{1}{3}$ and a reentrant integer quantum Hall state at $ν= \frac{7}{3}$. On the $N=0$ side, the activation energies of the crystal and fractional quantum Hall liquid vanish smoothly and symmetrically at the transition, while the $N=1$ transitions out of the crystal appear discontinuous. Additionally, we observe quantized plateaus forming near the crystal transition at half filling of the $N=0$ levels, suggesting a paired composite fermion state stabilized by Landau level mixing.

cond-mat.mes-hall↗

arXiv2026

Theory of Next-Generation Even-Denominator States

Even-denominator quantum Hall states are leading candidates for realizing non-Abelian topological orders, with the $ν=\frac{5}{2}$ plateau in GaAs the first and most-studied example. Recent experiments in GaAs and bilayer graphene (BLG) have observed many `next-generation' even-denominator states at filling factors such as $ν=\frac{3}{4}$, $\frac{3}{8}$, and $\frac{3}{10}$. We develop the theory of these states, including analyses of their bulk quasiparticles, of methods for distinguishing between pairing channels in edge transport measurements, and of their trial wavefunctions. As part of this study, we derive general relations of how flux attachment affects many universal properties of states. In particular, we prove that the topological stability of interface modes is invariant under flux attachment. We compare next-generation paired states to Bonderson-Slingerland states at the same filling factors, and demonstrate that their quasiparticles carry identical charges and obey the same exchange statistics. The next-generation and Bonderson-Slingerland states still describe distinct phases, and we find that the former are energetically favored in the lowest Landau level, while the latter are favored in the first excited level.

cond-mat.str-el↗

arXiv2025

Orbitally tuned composite-fermion metal-to-superfluid transitions

The effective interaction between composite fermions, set entirely by the Coulomb potential and the underlying electronic Landau level orbitals, can stabilize exotic fractional quantum Hall states. In particular, half-filled Landau levels with different orbital character can host either metallic or paired phases of composite fermions. Here, we leverage experimental control over the orbital composition to realize a composite-fermion pairing transition in the first excited Landau level of bilayer graphene. Transport measurements at filling factors v = 9/2 and 11/2 reveal conductive states giving way to well-developed plateaus with increasing displacement fields. These states are insensitive to an in-plane magnetic field, indicating single-component ground states and thus pointing at non-Abelian orders. Our numerical study, based on displacement-field-dependent Landau-level wavefunctions, supports the orbital origin of the pairing transition and suggests Moore-Read or anti-Pfaffian ground states.

cond-mat.mes-hall↗

arXiv2025

Non-Abelian phases from the condensation of Abelian anyons

The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in a new Abelian phase at a different filling factor, and this process can be iterated \textit{ad infinitum}. We show that condensing clusters of the same quasiparticles into an Abelian state can instead realize non-Abelian FQH states. In particular, condensing quasiparticle pairs in the $ν=\frac{2}{3}$ Laughlin state yields the anti-Pfaffian phase at half-filling. We moreover show that the successive condensation of Laughlin quasiparticles produces quantum Hall states whose fillings coincide with the most prominent plateaus in the first excited Landau level of GaAs. More generally, such condensation can realize any non-Abelian FQH state that admits a parton representation. This surprising result is supported by an exact analysis of explicit wavefunctions, field theory arguments, conformal-field theory constructions of trial states, and numerical simulations.

cond-mat.str-el↗

arXiv2025

The numerical case for identifying paired quantum Hall phases by their daughters

Many candidate non-Abelian quantum Hall states are accompanied by nearby `daughter' states, which are proposed to identify their topological order. Combining exact diagonalization and trial wave functions, we provide numerical evidence that daughter states reliably predict the parent topological phase. In the contexts of bilayer graphene and wide GaAs quantum wells, we show that the same interactions simultaneously stabilize Pfaffian, anti-Pfaffian, and their daughters, while suppressing the Jain states. The competition between Pfaffian and anti-Pfaffian, which is decided by particle-hole symmetry-breaking interactions, can likewise be deduced from their daughters. These findings strongly support the daughter-state-based identification of non-Abelian quantum Hall phases.

cond-mat.str-el↗

arXiv2025

Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene

Even-denominator fractional quantum Hall states are promising candidates for fault-tolerant quantum computing due to their underlying non-Abelian topological orders. However, the topological order of these states remains hotly debated. Here, we report transport measurements on ultra-clean bilayer graphene heterostructures, where we observed four quarter-filled states and their corresponding Levin-Halperin daughter states, constraining their topological order. Moreover, we complete the sequence of half-filled plateaus by detecting states at v=-3/2 and v=1/2 whose daughters suggest an alternating sequence of non-Abelian orders. This pattern suggests a universal origin supporting their use in identifying topological order at even-denominator fillings, though further confirmation is needed via direct measurements. The observed quarter- and half-filled states appear in N=0 and N=1 Landau levels, respectively, and thus highlight a competition between interactions favoring paired states of either four- or two-flux composite fermions. Additionally, we observe several 'next-generation' quantum Hall states that require strong interactions between composite fermions.

cond-mat.mes-hall↗

arXiv2025

Phase diagram of compressible and paired states in the quarter-filled Landau level

Quantum Hall plateaus at quarter fillings occur in GaAs wide quantum wells, hole-doped GaAs, and bilayer graphene. However, the interactions favoring incompressible states over compressible composite-Fermi liquids at such fillings are not well understood. We devise a method of computing the trial energies for Haldane pseudopotentials via Monte Carlo sampling. Applying it to the quarter-filled lowest Landau level, we find that tuning the third and fifth pseudopotential can stabilize anti-Pfaffian, Moore-Read, and f-wave states. The smallest deviations from pure Coulomb interactions are required by anti-Pfaffian, whose presence is indicated by daughter states in recent experiments of bilayer graphene at $ν=\frac{3}{4}$.

cond-mat.str-el↗

arXiv2024

Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces

Multiple topologically distinct quantum Hall phases can occur at the same Landau level filling factor. It is a major challenge to distinguish between these phases as they only differ by the neutral modes, which do not affect the charge conductance in conventional geometries. We show that the neutral sector can be determined with coherent charge conductance in a $π$-shaped geometry that interfaces three different filling factors. Specifically, non-Abelian paired states at a half-filled Landau level and the anti-Read-Rezayi state can be identified. Interestingly, for interfaces between paired states and Jain states, the electric current in the $π$ geometry behaves as if pairs of neutral Majoranas edge modes were charge modes of Jain states.

cond-mat.str-el↗

arXiv2024

Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus

Recent quantum Hall experiments have observed `daughter states' next to several plateaus at half-integer filling factors in various platforms. These states were first proposed based on model wavefunctions for the Moore-Read state by Levin and Halperin. We show that these daughters and their parents belong to an extensive family tree that encompasses all pairing channels and permits a unified description in terms of weakly interacting composite fermions. Each daughter represents a bosonic integer quantum Hall state formed by composite-fermion pairs. The pairing of the parent dictates an additional number of filled composite-fermion Landau levels. We support our field-theoretic composite-fermion treatment by using the K-matrix formalism, analysis of trial wavefunctions, and a coupled-wire construction. Our analysis yields the topological orders, quantum numbers, and experimental signatures of all daughters of paired states at half-filling and `next-generation' even-denominators. Crucially, no two daughters share the same two parents. The unique parentage implies that Hall conductance measurements alone could pinpoint the topological order of even-denominator plateaus. Additionally, we propose a numerically suitable trial wavefunction for one daughter of the SU(2)$_2$ topological order, which arises at filling factor $ν=\frac{6}{11}$. Finally, our insights explain experimentally observed features of transitions in wide-quantum wells, such as suppression of the Jain states with the simultaneous development of half-filled and daughter states.

cond-mat.str-el↗

arXiv2024

Localization and conductance in fractional quantum Hall edges

The fractional quantum Hall (FQH) effect gives rise to abundant topological phases, presenting an ultimate platform for studying the transport of edge states. Generic FQH edge contains multiple edge modes, commonly including the counter-propagating ones. A question of the influence of Anderson localization on transport through such edges arises. Recent experimental advances in engineering novel devices with interfaces of different FQH states enable transport measurements of FQH edges and edge junctions also featuring counter-propagating modes. These developments provide an additional strong motivation for the theoretical study of the effects of localization on generic edge states. We develop a general framework for analyzing transport in various regimes that also naturally includes localization. Using a reduced field theory of the edge after localization, we derive a general formula for the conductance. We apply this framework to analyze various experimentally relevant geometries of FQH edges and edge junctions.

cond-mat.mes-hall↗

arXiv2024

Identifying non-Abelian anyons with upstream noise

Non-Abelian phases are among the most highly-sought states of matter, with those whose anyons permit universal quantum gates constituting the ultimate prize. The most promising candidate of such a phase is the fractional quantum Hall plateau at filling factors $ν=\frac{12}{5}$, which putatively facilitates Fibonacci anyons. Experimental validation of this assertion poses a major challenge and remains elusive. We present a measurement protocol that could achieve this goal with already-demonstrated experimental techniques. Interfacing the $ν=\frac{12}{5}$ state with any readily-available Abelian state yields a binary outcome of upstream noise or no noise. Judicious choices of the Abelian states can produce a sequence of yes--no outcomes that fingerprint the possible non-Abelian phase by ruling out its competitors. Crucially, this identification is insensitive to the precise value of the measured noise and can uniquely identify the anyon type at filling factors $ν=\frac{12}{5}$. In addition, it can distinguish any non-Abelian candidates at half-filling in graphene and semiconductor heterostructures.

cond-mat.str-el↗

arXiv2022

Identifying the $ν=\frac{5}{2}$ topological order through charge transport measurements

We propose an experiment to identify the topological order of the $ν=\frac{5}{2}$ state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing $ν=2, \ \frac{5}{2}$ and $3$ in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the Moore-Read and Anti-Pfaffian topological orders, which are favored by numerical calculations.

cond-mat.str-el↗