arXiv subjects

Adithi Udupa

Publications and source records attributed to Adithi Udupa.

12 recordsLinked to original sources

arXiv2026

Bosonic quantum error-correcting codes with finite stellar rank

Bosonic quantum error correction (QEC) relies on non-Gaussian bosonic encodings whose preparation cost is a central practical constraint. In this work, we use stellar rank as a resource measure to design and benchmark bosonic codes under finite non-Gaussian resources. For fixed cat and Gottesman--Kitaev--Preskill (GKP) code families, we show that finite stellar rank creates a trade-off among state approximability, energy, and logical protection under photon loss and photon-number dephasing, evaluated with optimal recovery. This trade-off implies that codewords with better ideal error-correction properties need not be optimal once finite-rank preparation constraints are imposed. Going beyond fixed-target codewords, we directly optimize bosonic encodings at fixed stellar rank, revealing noise-adapted code structures and concrete resource thresholds. Grid-like encodings emerge under photon loss, whereas approximately rotation-symmetric encodings arise under dephasing. In the optimized search, stellar rank k=2 suffices to surpass break-even for all dephasing strengths considered, while under photon loss the required rank increases with the loss rate. These results establish stellar rank as an operationally meaningful resource measure for bosonic QEC under practical state-preparation constraints.

quant-ph↗

arXiv2026

Error Mitigation in Bosonic Systems via Virtual Distillation

Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.

quant-ph↗

arXiv2026

Bias-Preserving Gates and Quantum Error Correction With Dual-Rail Cat Codes

Scalable fault-tolerant quantum computation requires quantum error-correcting codes that simultaneously support universal logical operations, suppress hardware-specific noise, and enable efficient handling of photon-loss errors. Bosonic encodings such as the dual-rail and cat codes each offer attractive features but also exhibit important limitations when used in isolation. The dual-rail code enables efficient single-photon-loss detection by converting leakage out of the computational subspace induced by photon-loss errors into an erasure error. In contrast, the cat code provides a resource-efficient, bias-tailored error-correction scheme with bias-preserving logical gate operations. Here, we introduce the dual-rail cat code (DRCC), a concatenated bosonic encoding that combines an inner cat code with an outer dual-rail structure, thereby inheriting and enhancing the advantages of both constituent codes. We analyse the error-correction properties of the DRCC and propose a deterministic single-photon-loss correction protocol by concatenating it with an outer repetition code. Exploiting the code's intrinsic noise bias, we construct a universal set of logical gates using only beam-splitter interactions and demonstrate that all logical operations preserve the erasure-biased noise structure. The DRCC offers several distinctive advantages, including the absence of relative geometric phases during gate operations, deterministic erasure detection and correction, and simultaneous syndrome extraction without interrupting stabilisation. These features make the DRCC a promising bosonic code for hardware-efficient, bias-preserving, and erasure-resilient fault-tolerant quantum computation.

quant-ph↗

arXiv2025

Multimode rotationally symmetric bosonic codes from group-theoretic construction

We introduce a new family of multi-mode, rotationally symmetric bosonic codes inspired by the group-theoretic framework of [Phys. Rev. Lett. 133, 240603 (2024)]. Such a construction inverts the traditional paradigm of code design by identifying codes from the requirement that a group of chosen logical gates should be implemented by means of physically simple logical operations, such as linear optics. Leveraging previously unexplored degrees of freedom within this framework, our construction preserves rotational symmetry across multiple modes, enabling linear-optics implementation of the full Pauli group. These codes exhibit improved protection against dephasing noise, outperforming both single-mode analogues and earlier multi-mode constructions. Notably, they allow exact correction of correlated dephasing and support qudit encoding in arbitrary dimensions. We analytically construct and numerically benchmark two-mode binomial codes instances, and demonstrate that, unlike single-mode rotationally symmetric bosonic codes, these exhibit no trade-off between protection against dephasing and photon loss.

quant-ph↗

arXiv2025

Performance of rotation-symmetric bosonic codes in the presence of random telegraph noise

Decoherence in quantum devices, such as qubits and resonators, is often caused by bistable fluctuators modeled as random telegraph noise (RTN), leading to significant dephasing. We analyze the impact of individual and multiple fluctuators on a bosonic mode in continuous variable systems, identifying non-Markovian behavior governed by two timescales: the fluctuator switching rate ($\xi$) and coupling strength ($\nu$). Using the Breuer-Piilo-Laine (BLP) measure, we show that for Gaussian states, squeezing and thermal fluctuations do not enhance non-Markovianity. In contrast, for non-Gaussian states, the measure becomes unbounded. For rotation-symmetric bosonic (RSB) codes, known for their error correction advantages, non-Markovianity grows linearly with code symmetry. We evaluate the performance of RSB codes under simultaneous loss and RTN dephasing. For a teleportation-based Knill error-correction circuit, the codes perform robustly in the Markovian limit. In the non-Markovian regime, the performance depends on the time the error correction is performed for a given codeword. The average gate fidelity of the error-corrected state in this case exhibits oscillations as a function of time due to the oscillatory nature of the dephasing function of the RTN noise; however, for most of the parameter ranges, the values stay above the break-even point. Extending to multiple fluctuators that produce $1/f$ noise, we observe that non-Markovianity decays with increasing fluctuator count, while the performance of RSB codes remains effective with increasing number of fluctuators.

quant-ph↗

arXiv2024

Electric field tunable edge transport in Bernal stacked trilayer graphene

This letter presents a non-local study on the electric field tunable edge transport in an hBN-encapsulated dual-gated Bernal stacked (ABA) trilayer graphene across various displacement fields ($D$) and temperatures ($T$). Our measurements revealed that the non-local resistance ($R_{NL}$) surpassed the expected classical ohmic contribution by a factor of at least two orders of magnitude. Through scaling analysis, we found that the non-local resistance scales linearly with the local resistance ($R_{L}$) only when the $D$ exceeds a critical value of $\sim0.2$ V/nm. Additionally, we observed that the scaling exponent remains constant at unity for temperatures below the bulk-band gap energy threshold ($T<25$ K). Further, the value of $R_{NL}$ decreases in a linear fashion as the channel length ($L$) increases. These experimental findings provide evidence for edge-mediated charge transport in ABA trilayer graphene under the influence of a finite displacement field. Furthermore, our theoretical calculations support these results by demonstrating the emergence of dispersive edge modes within the bulk-band gap energy range when a sufficient displacement field is applied.

cond-mat.mes-hall↗

arXiv2023

Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical point with a continuous phase transition. We compute the critical exponents $z$, $\beta$, $\gamma$ and $\nu$, and the central charge $c$ numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both $z$ and $c$ are equal to $1$, implying that the critical point is governed by a conformal field theory. The values obtained for $\beta/\nu$, $\gamma/\nu$, and $\nu$ from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. An analysis on larger systems but with open boundaries using density-matrix renormalization group calculations, however, shows that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates. A subset of these eigenstates have wave functions which are independent of $h$ and have unusual entanglement structure, suggesting that they are quantum many-body scars. The number of such states scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if $h \gg 1$ or $h \ll 1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

cond-mat.stat-mech↗

arXiv2022

Experimental observation of spin-split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructures

Proximity-induced spin-orbit coupling in graphene has led to the observation of intriguing phenomena like time-reversal invariant $\mathbb{Z}_2$ topological phase and spin-orbital filtering effects. An understanding of the effect of spin-orbit coupling on the band structure of graphene is essential if these exciting observations are to be transformed into real-world applications. In this research article, we report the experimental determination of the band structure of single-layer graphene (SLG) in the presence of strong proximity-induced spin-orbit coupling. We achieve this in high-mobility hBN-encapsulated SLG/WSe2 heterostructures through measurements of quantum oscillations. We observe clear spin-splitting of the graphene bands along with a substantial increase in the Fermi velocity. Using a theoretical model with realistic parameters to fit our experimental data, we uncover evidence of a band gap opening and band inversion in the SLG. Further, we establish that the deviation of the low-energy band structure from pristine SLG is determined primarily by the valley-Zeeman SOC and Rashba SOC, with the Kane-Mele SOC being inconsequential. Despite robust theoretical predictions and observations of band-splitting, a quantitative measure of the spin-splitting of the valence and the conduction bands and the consequent low-energy dispersion relation in SLG was missing -- our combined experimental and theoretical study fills this lacuna.

cond-mat.mes-hall↗

arXiv2022

Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term

We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction $U$ is much larger than the hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_α,J_β,J_γ)$ on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry (TRS), $H_{eff}$ is also found to have a chiral three-spin interaction in each triangle, with the coefficient $C$ of the interaction having opposite signs on up- and down-pointing triangles. Thus periodic driving which breaks TRS can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters $(J_α,J_β,J_γ,C)$ depend on the amplitude, frequency and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (colinear and coplanar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.

cond-mat.str-el↗

arXiv2021

One-dimensional spin-orbit coupled Dirac system with extended $s$-wave superconductivity: Majorana modes and Josephson effects

Motivated by the spin-momentum locking of electrons at the boundaries of topological insulators, we study a one-dimensional system of spin-orbit coupled massless Dirac electrons with $s$-wave superconducting pairing. As a result of the spin-orbit coupling, our model has only two kinds of linearly dispersing modes, which we take to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that the $s$-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. Next we study a lattice version of a model with both Schrödinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of two $s$-wave superconductors with different phases of the pairing. Remarkably, we find that the system has a {\it single} Andreev bound state which is localized at the junction. When the pairing phase difference crosses a multiple of $2 π$, an Andreev bound state touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constant $V_0$ and a term which oscillates with a frequency $ω$. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequency $ω_J= 2eV_0/\hbar$ is a rational fraction of $ω$. We discuss experiments which can realize such junctions.

cond-mat.mes-hall↗

arXiv2019

Transport on a topological insulator surface with a time-dependent magnetic barrier

We study transport across a time-dependent magnetic barrier present on the surface of a three-dimensional topological insulator. We show that such a barrier can be implemented for Dirac electrons on the surface of a three-dimensional topological insulator by a combination of a proximate magnetic material and linearly polarized external radiation. We find that the conductance of the system can be tuned by varying the frequency and amplitude of the radiation and the energy of an electron incident on the barrier providing us optical control on the conductance of such junctions. We first study a $δ$-function barrier which shows a number of interesting features such as sharp peaks and dips in the transmission at certain angles of incidence. Approximate methods for studying the limits of small and large frequencies are presented. We then study a barrier with a finite width. This gives rise to some new features which are not present for a $δ$-function barrier, such as resonances in the conductance at certain values of the system parameters. We present a perturbation theory for studying the limit of large driving amplitude and use this to understand the resonances. Finally, we use a semiclassical approach to study transmission across a time-dependent barrier and show how this can qualitatively explain some of the results found in the earlier analysis. We discuss experiments which can test our theory.

cond-mat.mes-hall↗

arXiv2018

Transport in a thin topological insulator with potential and magnetic barriers

We study transport across either a potential or a magnetic barrier which is placed on the top surface of a three-dimensional thin topological insulator (TI). For such thin TIs, the top and bottom surfaces interact via a coupling $λ$ which influences the transport properties of junctions constructed out of them. We find that for junctions hosting a potential barrier, the differential conductance oscillates with the barrier strength. The period of these oscillations doubles as the coupling $λ$ changes from small values to a value close to the energy of the incident electrons. In contrast, for junctions with a magnetic barrier, the conductance approaches a non-zero constant as the barrier strength is increased. This feature is in contrast to the case of transport across a single TI surface where the conductance approaches zero as the strength of a magnetic barrier is increased. We also study the spin currents for these two kinds of barriers; in both cases, the spin current is found to have opposite signs on the top and bottom surfaces. Thus this system can be used to split applied charge currents to spin currents with opposite spin orientations which can be collected by applying opposite spin-polarized leads to the two surfaces. We show that several of these features of transport across finite width barriers can be understood analytically by studying the $δ$-function barrier limit. We discuss experiments which may test our theory.

cond-mat.mes-hall↗