arXiv subjects

Prabha Mandayam

Publications and source records attributed to Prabha Mandayam.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Codes for Generalized Amplitude-damping Noise

Quantum error correcting (QEC) plays a crucial role in protecting quantum information against decoherence and enabling scalable, reliable quantum computing. One of the most realistic and ubiquitous sources of noise affecting quantum hardware today is generalized amplitude-damping (GAD) noise. Conventional, deterministic QEC codes struggle to correct for GAD noise because of their inherent structure, leading to fidelity losses that scale linearly with the damping strength. In this work, we introduce the framework of probabilistic approximate quantum error correction (PAQEC), that combines the flexibility of approximate QEC with the potential of post-selected recovery, enabling high-fidelity, resource-efficient error correction. We construct a five-qubit permutation-invariant code that, under probabilistic recovery, achieves a fidelity loss quadratic in the damping strength, thus outperforming existing QEC codes. Formulating PAQEC as an optimization problem, we present a numerical technique based on Charnes-Cooper and semidefinite programming to identify the optimal recovery map for any PAQEC code. Our results establish PAQEC as a powerful tool for developing resource-efficient, high-fidelity quantum codes tailored to realistic noise, with promising implications for near-term quantum devices and future fault-tolerant architectures.

quant-ph↗

arXiv2026

Universal syndrome-based recovery for noise-adapted quantum error correction

Quantum error correction (QEC) is an essential tool for quantum computing that enables reliable information processing in the presence of noise. Syndrome measurements play a central role in QEC, making it possible to unambiguously identify the location and type of errors. While syndrome extraction is natural for conventional QEC protocols, where the errors satisfy certain algebraic constraints \emph{perfectly}, this feature is largely missing in the framework of approximate or noise-adapted QEC. Rather, noise-adapted recovery maps like the Petz map are used in the latter scenario, but implementing such tailored recovery processes on the hardware can be quite challenging. Here, we address this issue by proposing an algorithmic approach to identifying error syndromes for arbitrary codes and noise processes. We then use our algorithm to develop a variant of the Petz recovery map -- a syndrome-based Petz recovery map -- which can then be implemented via syndrome measurements. We demonstrate the efficacy of our approach in the context of amplitude-damping noise, by constructing the syndrome-based Petz map for the $4$-qubit code. We execute our recovery circuits on IBM quantum hardware to successfully demonstrate break-even performance of a noise-adapted QEC protocol with upto a threefold improvement of the qubit $T_{1}$ times.

quant-ph↗

arXiv2026

Explicit attacks on differential phase shift quantum key distribution

In the well-established framework of quantum key distribution (QKD), differential phase shift (DPS) protocols have known information-theoretic security bounds defining tolerable error rates under optimal adversaries. In this work, we revisit the security of 3- and n-pulse DPS QKD by explicitly analyzing two specific, physically implementable individual attacks: minimum error discrimination (MED) and quantum cloning. Using semidefinite programming, we characterize these attacks in detail and quantify their induced quantum bit error rates (QBER) and resulting secure key rates under realistic system assumptions. The critical QBER thresholds for these attacks are approximately 20%, significantly higher than the theoretical lower bounds of 6% for individual and 4% for coherent attacks, indicating these are suboptimal adversarial strategies. This study primarily serves as a practical exercise to benchmark known attacks, providing explicit measures that aid experimental validation, protocol calibration, and risk assessment within current technological capabilities. Additionally, we explore finite-size effects and the effectiveness of phase randomization in weak coherent source-based protocols as protection against unambiguous state discrimination attacks.

quant-ph↗

arXiv2026

Demonstrating Noise-adapted Quantum Error Correction With Break-Even Performance

The promise of quantum computing is closer to reality today than ever before, thanks to rapid progress in the development of quantum hardware. Even as qubit lifetimes and gate fidelities continue to improve, realizing robust, fault-tolerant quantum computers is contingent upon the successful implementation of quantum error correction (QEC). Conventional QEC schemes have rather high resource overheads and low threshold requirements, making them challenging to implement on present day hardware. Here, we use a recently developed noise-adapted 3-qubit QEC scheme to demonstrate break-even performance against native amplitude-damping (AD) noise on IBM quantum hardware. We use variational quantum circuits to construct hardware-efficient encoding and decoding circuits. This scheme is probabilistic due to the non-unitary nature of the recovery operators, which are implemented via the block-encoding technique. We demonstrate logical qubit lifetimes exceeding those of the physical qubits by performing multiple rounds of QEC. To further protect the qubits from dephasing due to crosstalk, we incorporate dynamical decoupling into our noise-adapted QEC scheme in a seamless fashion. To account for the post-selection overhead, we define a measure of gain, that allows for faithful performance benchmarking of the protocol. Our analysis suggests that the performance of our protocol is limited primarily by the measurement readout fidelity, and is bound to improve with successive generations of quantum processors.

quant-ph↗

arXiv2026

Smallest quantum codes for amplitude damping noise

We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code that corrects all the single-qubit damping errors. We generalize this construction to a family of codes that correct AD noise up to any fixed order of the damping strength. We underpin the fundamental connection between the structure of our codes and the noise structure, via a relaxed form of the Knill-Laflamme conditions, different from existing formulations of approximate QEC conditions. Although the recovery procedure for this code is non-deterministic, our codes are optimal with respect to overheads and outperform existing codes to tackle AD noise in terms of entanglement fidelity. This formulation of probabilistic QEC further leads us to new family of quantum codes tailored to AD noise and also gives rise to a noise-adapted quantum Hamming bound for AD noise. Finally, we construct a set of universal logical gates for the 3-qubit code, thus providing a potential pathway to fault tolerance via this class of codes.

quant-ph↗

arXiv2025

Expedited Noise Spectroscopy of Transmon Qubits

There has been tremendous progress in the physical realization of quantum computing hardware in recent times, bringing us closer than ever before to realizing the promise of quantum computing. However, noise continues to pose a crucial challenge when it comes to scaling up present day quantum processors. While decoherence limits the qubits ability to store information for long periods in the presence of uncontrollable noise sources, the erroneous implementation of control methods for state preparation and measurements leads to faulty implementations of quantum circuits. Conventional noise spectroscopy protocols can characterize and model environmental noise but are usually resource intensive and lengthy. Moreover, the underlying noise can vary in nature over time, making noise profile extraction futile as this new information cannot be harnessed to improve quantum error correction or dynamical decoupling protocols. In this work, we address this challenge using a machine learning-based methodology to quickly extract noise spectra of multiple qubits and demonstrate a possible noise mitigation strategy. The procedure involves implementing undemanding dynamical decoupling sequences to record coherence decays of the investigated qubits and then predict the underlying noise spectra with the help of a convolution neural network pre-trained on a synthetic dataset. While our protocol is virtually hardware-agnostic, we validate its effectiveness using superconducting qubits available on the IBM Quantum platform. We further use these rapidly obtained, yet accurate, noise spectra to design bespoke dynamic decoupling sequences and perform time-dependent noise spectroscopy.

quant-ph↗

arXiv2025

Noise-adapted qudit codes for amplitude-damping noise

Quantum error correction (QEC) plays a critical role in preventing information loss in quantum systems and provides a framework for reliable quantum computation. Identifying quantum codes with nice code parameters for physically motivated noise models remains an interesting challenge. While past work has primarily focused on qubit codes, here we identify a $[4,1]$ qudit error correcting code tailored to protect against amplitude-damping noise. We show that this four-qudit code satisfies the error correction conditions for all single-qudit and a few two-qudit damping errors up to the leading order in the damping parameter $γ$. We devise a protocol to extract syndromes that unambiguously identify this set of errors, leading to a noise-adapted recovery scheme that achieves a fidelity loss of $\mathcal{O}(γ^{2})$. For the $d=2$ case, our QEC scheme is identical to the known example of the $4$-qubit code and the associated syndrome-based recovery. We also assess the performance of this code using the Petz recovery map and note some interesting deviations from the qubit case. Finally, we generalize this construction to a family of $[2M+2, M]$ qudit codes that can approximately correct all the single-qudit and a few two-qudit amplitude-damping errors.

quant-ph↗

arXiv2025

Fault tolerance against amplitude-damping noise using Bacon-Shor codes

Designing efficient fault tolerance schemes is crucial for building useful quantum computers. Most standard schemes assume no knowledge of the underlying device noise and rely on general-purpose quantum error-correcting (QEC) codes capable of handling arbitrary errors. Biased-noise alternatives focus on only correcting a subset of some generic error basis (e.g., Pauli error basis), and lower resource needs by channeling the redundancy to dealing only with that subset. Yet, the most resource-efficient codes are expected to be those that directly target the specific noise process that afflicts the quantum device, rather than using a generic error-basis description. However, the question of whether such noise-adapted QEC protocols are amenable to fault-tolerant implementations remains largely unexplored. Here, we design a fault tolerance scheme based on the Bacon-Shor codes which can protect against amplitude-damping noise in the device. We construct a universal set of logical gadgets tolerant to multiple damping errors and estimate the fault tolerance threshold of our scheme. Our work thus establishes the possibility of achieving fault tolerance against amplitude-damping noise using noise-adapted quantum codes, while highlighting some of the unique challenges that arise in this context.

quant-ph↗

arXiv2024

Noise-adapted Quantum Error Correction for Non-Markovian Noise

We consider the problem of quantum error correction (QEC) for non-Markovian noise. Using the well known Petz recovery map, we first show that conditions for approximate QEC can be easily generalized for the case of non-Markovian noise, in the strong coupling regime where the noise map becomes non-completely-positive at intermediate times. While certain approximate QEC schemes are ineffective against quantum non-Markovian noise, in the sense that the fidelity vanishes in finite time, the Petz map adapted to non-Markovian noise uniquely safeguards the code space even at the maximum noise limit. Focusing on the case of non-Markovian amplitude damping noise, we further show that the non-Markovian Petz map also outperforms the standard, stabilizer-based QEC code. Since implementing such a non-Markovian map poses practical challenges, we also construct a Markovian Petz map that achieves similar performance, with only a slight compromise on the fidelity.

quant-ph↗

arXiv2024

Mitigating imperfections in Differential Phase Shift Measurement-Device-Independent Quantum Key Distribution via Plug-and-Play architecture

Measurement-device-independent quantum key distribution (MDI-QKD) was originally proposed as a means to address the issue of detector side-channel attacks and enable finite secure key rates over longer distances. However, the asymmetric characteristics of the channels from the two sources to the measurement device in MDI-QKD impose constraints on successfully extracting a secure key. In this work, we present a plug-and-play scheme for MDI-QKD based on differential phase shift (DPS) encoding. Specifically, we analyze the effects of pulse-width mismatch and polarization mismatch between the pulses arriving at the measurement device. The polarization mismatch is modeled with an assumption of sharing a common reference frame, and the maximum allowable mismatch is found to be 11 degrees. Furthermore, we show that a channel length asymmetry of 176.5 km results in Hong-Ou-Mandel interference visibility of 0.37, thereby leading to zero secure key rates for a polarization-based MDI-QKD protocol. We then present a plug-and-play architecture for DPS-MDI-QKD as a solution to some of these issues, thereby paving the way for practical implementations of MDI protocols.

quant-ph↗

arXiv2024

Noise-adapted recovery circuits for quantum error correction

Implementing quantum error correction (QEC) protocols is a challenging task in today's era of noisy intermediate-scale quantum devices. We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz map, which is known to achieve close-to-optimal fidelity for arbitrary codes and noise channels. While two of our circuit constructions draw upon algebraic techniques such as isometric extension and block encoding, the third approach breaks down the recovery map into a sequence of two-outcome POVMs. In each of the three cases we improve upon the resource requirements that currently exist in the literature. Apart from Petz recovery circuits, we also present circuits that can directly estimate the fidelity between the encoded state and the recovered state. As a concrete example of our circuit constructions, we implement Petz recovery circuits corresponding to the $4$-qubit QEC code tailored to protect against amplitude-damping noise. The efficacy of our noise-adapted recovery circuits is then demonstrated through ideal and noisy simulations.

quant-ph↗

arXiv2023

Pretty good measurement for bosonic Gaussian ensembles

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble (IEEE Trans. Inf. Theory, 66(9):5634-564, 2020). In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories.

quant-ph↗

arXiv2023

Quantum non-Markovianity: Overview and recent developments

In the current era of noisy intermediate-scale quantum (NISQ) devices, research in the theory of open system dynamics has a crucial role to play. In particular, understanding and quantifying memory effects in quantum systems is critical to gain a better handle on the effects of noise in quantum devices. The main focus of this review is to address the fundamental question of defining and characterizing such memory effects -- broadly referred to as quantum non-Markovianity -- from various approaches. We first discuss the two-time-parameter maps approach to open system dynamics and review the various notions of quantum non-Markovianity that arise in this paradigm. We then discuss an alternate approach to quantum stochastic processes based on the quantum combs framework, which accounts for multi-time correlations. We discuss the interconnections and differences between these two paradigms, and conclude with a discussion on necessary and sufficient conditions for quantum non-Markovianity.

quant-ph↗

arXiv2022

Unital Qubit Queue-channels: Classical Capacity and Product Decoding

Quantum queue-channels arise naturally in the context of buffering in quantum networks, wherein the noise suffered by the quantum states depends on the time spent waiting in the buffer. It has been shown that the upper-bound on the classical capacity of an additive queue-channel has a simple expression, and is achievable for the erasure and depolarizing channels [IEEE JSAIT, 1(2):432-444]. In this paper, we characterise the classical capacity for the class of unital qubit queue-channels, and show that a simple product (non-entangled) decoding strategy is capacity-achieving. As an intermediate result, we derive an explicit capacity achieving product decoding strategy for any i.i.d. unital qubit channel, which could be of independent interest. As an important special case, we also derive the capacity and optimal decoding strategies for a symmetric generalized amplitude damping (GAD) queue-channel. Our results provide useful insights towards designing practical quantum communication networks, and highlight the need to explicitly model the impact of buffering.

quant-ph↗

arXiv2022

QKD in the NISQ era: enhancing secure key rates via quantum error correction

Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness of quantum cryptographic protocols. In this work, we benchmark the performance of different QKD protocols on noisy quantum devices, with and without error correction. We obtain the secure key rates of BB84, B92 and BBM92 QKD protocols over a quantum channel that is subject to amplitude-damping noise. We demonstrate, theoretically and via implementations on the IBM quantum processors, that B92 is the optimal protocol under amplitude-damping and generalized amplitude-damping noise. We then show that the security of the noisy BBM92 protocol crucially depends on the type and the mode of distribution of an entangled pair. Finally, we implement an error-corrected BB84 protocol using dual-rail encoding on a noisy quantum processor, and show that the dual-rail BB84 implementation outperforms the conventional BB84 in the presence of noise. Our secure key rate calculation also takes into account the effects of CNOT imperfections on the error rates of the protocols.

quant-ph↗

arXiv2022

Quantum Error Correction: Noise-adapted Techniques and Applications

The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects of such noise on quantum states can be mitigated, paving the way for realising robust, scalable quantum computers. In this article we survey the current landscape of quantum error correcting (QEC) codes, focusing on recent theoretical advances in the domain of noise-adapted QEC, and highlighting some key open questions. We also discuss the interesting connections that have emerged between such adaptive QEC techniques and fundamental physics, especially in the areas of many-body physics and cosmology. We conclude with a brief review of the theory of quantum fault tolerance which gives a quantitative estimate of the physical noise threshold below which error-resilient quantum computation is possible.

quant-ph↗

arXiv2022

Equivalence of space and time-bins in DPS-QKD

Key generation efficiency, and security, in DPS-QKD improve with an increase in the number of path delays or time-bin superpositions. We demonstrate the implementation of super-position states using time-bins, and establish an equivalence with path-based superposition, thus yielding a simpler implementation of higher-order superposition states for differential phase-shift quantum key distribution (DPS-QKD). We set up DPS-QKD, over 105 km of single mode optical fiber, with a quantum bit error rate of less than 15% at a secure key rate of 2 kbps. With temporal guard bands, the QBER reduced to less than 10%, but with a 20% reduction in the key rate.

quant-ph↗

arXiv2022

Holographic spacetime, black holes and quantum error correcting codes: A review

This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation.

hep-th↗