arXiv subjects

Narayanan Rengaswamy

Publications and source records attributed to Narayanan Rengaswamy.

At least 19 recordsLinked to original sources

arXiv2026

Towards Block-Level Fault-Tolerant Quantum Simulation on Small High-Rate Non-CSS Codes

Small high-rate non-CSS stabilizer codes provide compact platforms for encoded quantum computation, but mixed-Pauli checks and limited native transversal logical gates complicate fault-tolerant dynamics. Block-level constructions offer an alternative by mapping an entire logical block to a physical circuit rather than compiling separately protected logical gates. We investigate this approach using the high-rate [[8,3,3]] non-CSS code and logical Trotter circuits as a testbed. We construct flagged syndrome-extraction circuits and establish a circuit-level memory pseudo-threshold near $1.5\times10^{-3}$. We then apply our symplectic-transvection construction, which maps a logical Trotter circuit to a physical circuit with the same block pattern for any stabilizer code. Although this mapping preserves the intended unitary algebraically, encoded Trotter circuits exhibit asymmetry between logical-$X$ and logical-$Z$ failure channels. Single-fault analysis identifies the mechanism: a fault on the shared parity ancilla can propagate through the uncomputation network into an undetectable logical operator, reducing the effective circuit distance in the affected sector. We evaluate flag-conditioned recovery, biased-noise decoding, CliNR resource verification, flag postselection, and asymmetric gate-noise models. These methods suppress propagated faults but do not simultaneously suppress both logical sectors in the realistic configurations studied. A diagnostic protected limit removing the identified malignant first-order locations restores pseudo-threshold behavior in both sectors, approaching memory performance. These results demonstrate the potential of block-level logical constructions for non-CSS codes without rich native transversal gate sets and the joint protection of the parity network, analog rotation, and recovery required to preserve fault-tolerant distance.

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arXiv2026

GHZ is All You Need: Quantum Sensing with VISTA

Quantum metrology holds the potential to enhance magnetic field sensing beyond current limits. However, in the presence of realistic noise, this advantage degrades to the Standard Quantum Limit. While recent algorithmic and variational techniques attempt to recover this scaling, they are hindered by stringent control requirements on the probe state that are infeasible in the near term, or by barren plateaus and interpretability issues inherent to black-box variational quantum circuits. Here, we introduce Variational Inference and Sensing with Twin Ansätze (VISTA), a closed-loop protocol that combines passive sensing, or where the probe state is left to evolve without any active control, with physics-informed variational optimization. In the VISTA framework, a probe state evolves under a Lindbladian master-equation, and is compared, via the Swap test, to a parameterized ``quantum twin", a shallow quantum circuit designed to mimic the underlying pure-state or Lindbladian master-equation dynamics. By restricting the optimization space to the physical parameters of interest, VISTA circumvents barren plateaus. We demonstrate that by coupling the protocol with a classical optimizer and high shot counts, VISTA can temporarily achieve near-Heisenberg scaling for moderately noisy qubits over a finite range of system sizes. Furthermore, we introduce a Quasi-Normalization technique that sharpens the loss gradients, enabling simultaneous extraction of both the coherent signal $θ$ and the environmental noise rate $γ$ with low absolute error. Finally, we extend VISTA to the multi-parameter vector metrology regime, enabling simultaneous parameter extraction from a transverse-magnetic-field Hamiltonian. By eliminating the need for complex, open-loop control and processing, VISTA offers a highly practical, resource-efficient framework for near- to intermediate-term quantum sensors.

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arXiv2026

Networked Realization of Quantum LDPC Codes

Quantum low-density parity-check (QLDPC) codes with good parameters are promising candidates for low-overhead fault-tolerant quantum computing, but their non-local stabilizers require long-range connectivity and frequent qubit movement, introducing practical challenges. Prior work has studied the networked implementation of topological codes, where each node only holds one or a few qubits of the entire code, and demonstrated competitive performance under practical constraints such as the quality of network-provided entanglement. However, since these codes are already geometrically local, such a networked setting might not be essential. In this work, we propose and study the networked implementation of better QLDPC codes, specifically bivariate bicycle codes due to their similarity to surface codes and the controlled amount of long-range connections in their stabilizers. We begin by recreating networked surface codes in Stim, with one code qubit per node, and provide additional insights into their circuit-level noise performance. We then extend this approach to bipartitions of bivariate bicycle codes, using balanced min-cut partitioning on their combined X-Z Tanner graph to identify optimal qubit splits. For stabilizers spanning nodes, we implement teleported CNOTs and vary the Bell pair fidelity enabling these gates. Through circuit-level noise simulations with BP-OSD decoding, we provide the first insights into networked realizations of these codes and compare their performance with monolithic implementations. We conclude by outlining advantages, limitations, and future directions.

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arXiv2026

Stabilizers for Compiling Logical Circuits under Hardware Constraints

To implement quantum algorithms on a quantum computer, we must overcome the twin problems of fault-tolerance -- how can we realize a relatively noiseless computation by cleverly combining noisy components? -- and compilation -- how can we realize an arbitrary quantum algorithm given the basic operations available on the quantum device at hand? We show how treating the former problem via error-correcting codes enables greater flexibility in resolving the latter. Specifically, we explicitly leverage the fact that error-correcting codes introduce redundancy which renders physically distinct operators logically indistinguishable. In terms of computation, it suffices to implement any operator logically equivalent to some target, yet from a compilation perspective, certain choices may be preferable to others. Our novel contribution is making this intuition precise in the general setting of the special unitary group. In particular, we describe how to reduce the problem of making a compilation-ideal choice to a least squares problem and provide a closed form solution thereof. Using our framework, it is possible to circumvent inserting costly swaps to adhere to hardware connectivity; instead, we could realize the logical target through a distinct physical Hamiltonian that is natively accessible. We elucidate our approach using the $[[4,2,2]]$ code. We discuss connections to compressed sensing that may pave the way to efficient compilation leveraging physical degrees of freedom.

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arXiv2026

Quantum Repeater Protocol using Quantum Error Correction for Distillation

Bell-state measurement (BSM) on entangled states shared between quantum repeaters is the fundamental operation used to route entanglement in quantum networks. Performing BSMs on Werner states shared between repeaters leads to exponential decay in the fidelity of the end-to-end Werner state with the number of repeaters, necessitating entanglement distillation. In this work, we use quantum error correcting codes for deterministic entanglement distillation to route Werner states on a chain of repeaters. To maximize the end-to-end distillable entanglement, we utilize global link-state knowledge to determine the optimal policy for scheduling distillation and BSMs at the repeaters. We observe that low-rate codes produce high-fidelity end-to-end states owing to their excellent error-correcting capability, whereas high-rate codes yield a larger number of end-to-end states but of lower fidelity. The number of quantum memories used at repeaters increases with the code rate as well as the classical computation time of the decoder.

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arXiv2026

Explaining Robust Quantum Metrology by Counting Codewords

Quantum sensing holds great promise for high-precision magnetic field measurements. However, its performance is significantly limited by noise. The investigation of active quantum error correction to address this noise led to the Hamiltonian-Not-in-Lindblad-Span (HNLS) condition. This states that Heisenberg scaling is achievable if and only if the signal Hamiltonian is orthogonal to the span of the Lindblad operators describing the noise. In this work, we consider a robust quantum metrology setting where the probe state is inspired from CSS codes for noise resilience but there is no active error correction performed. After the state picks up the signal, we measure the code's $\hat{X}$ stabilizers to infer the magnetic field parameter, $θ$. Given $N$ copies of the probe state, we derive the probability that all stabilizer measurements return $+1$, which depends on $θ$. The uncertainty in $θ$ (estimated from these measurements) is bounded by a new quantity, the \textit{Robustness Bound}, which ties the Quantum Fisher Information of the measurement to the number of weight-$2$ codewords of the dual code. Through this novel lens of coding theory, we show that for nontrivial CSS code states the HNLS condition still governs the Heisenberg scaling in our robust metrology setting. Our finding suggests fundamental limitations in the use of linear quantum codes for dephased magnetic field sensing applications both in the near-term robust sensing regime and in the long-term fault tolerant era. We also extend our results to general scenarios beyond dephased magnetic field sensing.

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arXiv2026

Fault Tolerant Quantum Simulation via Symplectic Transvections

Conventional approaches to fault-tolerant quantum computing realize logical circuits gate-by-gate, synthesizing each gate independently on one or more code blocks. This incurs excess overhead and doesn't leverage common structures in quantum algorithms. In contrast, we propose a framework that enables the execution of entire logical circuit blocks at once, preserving their global structure. This whole-block approach allows for the direct implementation of logical Trotter circuits - of arbitrary rotation angles - on any stabilizer code, providing a powerful new method for fault tolerant Hamiltonian simulation within a single code block. At the heart of our approach lies a deep structural correspondence between symplectic transvections and Trotter circuits. This connection enables both logical and physical circuits to share the Trotter structure while preserving stabilizer centralization and circuit symmetry even in the presence of non-Clifford rotations. We discuss potential approaches to fault tolerance via biased noise and code concatenation. While we illustrate the key principles using a $[[8,3,3]]$ code, our simulations show that the framework applies to Hamiltonian simulation on even good quantum LDPC codes. These results open the door to new algorithm-tailored, block-level strategies for fault tolerant circuit design, especially in quantum simulation.

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arXiv2026

Transversal gates for quantum CSS codes

In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of transversal gates that induce non-trivial logical gates and logical identities. We explicitly declare the set of equations defining the groups, a key advantage and differentiator of our approach. We compute the complete set of transversal stabilizers and transversal gates for any CSS code arising from monomial codes, a family that includes decreasing monomial codes and polar codes. As a consequence, we recover and extend some results in the literature on CSS-T codes, triorthogonal codes, and divisible codes.

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arXiv2026

Adaptive Entanglement Distillation

Quantum network applications impose a variety of requirements on entanglement resources in terms of rate, fidelity, latency, and more. The repeaters in the quantum network must combine good methods for entanglement generation, effective entanglement distillation, and smart routing protocols to satisfy these application requirements. In this work, we focus on entanglement distillation in a linear chain of quantum repeaters. While conventional approaches reuse the same distillation scheme over multiple hop lengths after entanglement swaps, we propose a novel adaptive quantum error correction (QEC) scheme that boosts end-to-end metrics. Specifically, depending on the network operating point, we adapt the code used in distillation over successive rounds to monotonically increase the rate while also improving fidelity. We demonstrate the effectiveness of this strategy using three codes, with parameters [[9,1,3]], [[9,2,3]], [[9,3,3]], and a new performance metric, efficiency, that incorporates both overall rate and fidelity. Since the minimum input fidelity for QEC-based distillation is high, we then extend our study to include non-QEC-based purification protocols, specifically DEJMPS since it outperforms others. We compare the performance of end-to-end DEJMPS against adapting from DEJMPS to QEC once DEJMPS improves the initial fidelity to the threshold for QEC. Through a refined efficiency metric, we illuminate the regime where QEC is beneficial. These results provide a detailed outlook for entanglement purification and distillation in first and second generation quantum repeaters.

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arXiv2025

Tailoring Fault-Tolerance to Quantum Algorithms

The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms. Hence, a universal quantum computer can likely gain from compiling such specific algorithms using tailored quantum error correction schemes. In this work, we take the first steps towards such algorithm-tailored quantum fault-tolerance. We consider Trotter circuits in quantum simulation, which is an important application of quantum computing. We develop a solve-and-stitch algorithm to systematically synthesize physical realizations of Clifford Trotter circuits on the well-known $\llbr n,n-2,2 \rrbr$ error-detecting code family. Our analysis shows that this family implements Trotter circuits with essentially optimal depth under reasonable assumptions, thereby serving as an illuminating example of tailored quantum error correction. We achieve fault-tolerance for these circuits using flag gadgets, which add minimal overhead. Importantly, the solve-and-stitch algorithm has the potential to scale beyond this specific example, as illustrated by a generalization to the four-qubit logical Clifford Trotter circuit on the $\llbr 20,4,2 \rrbr$ hypergraph product code, thereby providing a principled approach to tailored fault-tolerance in quantum computing.

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arXiv2025

Linear Time Iterative Decoders for Hypergraph-Product and Lifted-Product Codes

Quantum low-density parity-check (QLDPC) codes with asymptotically non-zero rates are prominent candidates for achieving fault-tolerant quantum computation, primarily due to their syndrome-measurement circuit's low operational depth. Numerous studies advocate for the necessity of fast decoders to fully harness the capabilities of QLDPC codes, thus driving the focus towards designing low-complexity iterative decoders. However, empirical investigations indicate that such iterative decoders are susceptible to having a high error floor while decoding QLDPC codes. The main objective of this paper is to analyze the decoding failures of the \emph{hypergraph-product} and \emph{lifted-product} codes and to design decoders that mitigate these failures, thus achieving a reduced error floor. The suboptimal performance of these codes can predominantly be ascribed to two structural phenomena: (1) stabilizer-induced trapping sets, which are subgraphs formed by stabilizers, and (2) classical trapping sets, which originate from the classical codes utilized in the construction of hypergraph-product and lifted-product codes. The dynamics of stabilizer-induced trapping sets is examined and a straightforward modification of iterative decoders is proposed to circumvent these trapping sets. Moreover, this work proposes a systematic methodology for designing decoders that can circumvent classical trapping sets in both hypergraph product and lifted product codes, from decoders capable of avoiding their trapping set in the parent classical LDPC code. When decoders that can avoid stabilizer-induced trapping sets are run in parallel with those that can mitigate the effect of classical TS, the logical error rate improves significantly in the error-floor region.

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arXiv2024

Tutorial on Quantum Error Correction for 2024 Quantum Information Knowledge (QuIK) Workshop

We provide a brief review of the fundamentals of quantum computation and quantum error correction for the participants of the first Quantum Information Knowledge (QuIK) workshop at the 2024 IEEE International Symposium on Information Theory (ISIT 2024). While this is not a comprehensive review, we provide many references for the reader to delve deeper into the concepts and research directions.

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arXiv2024

GNarsil: Splitting Stabilizers into Gauges

Quantum subsystem codes have been shown to improve error-correction performance, ease the implementation of logical operations on codes, and make stabilizer measurements easier by decomposing stabilizers into smaller-weight gauge operators. In this paper, we present two algorithms that produce new subsystem codes from a "seed" CSS code. They replace some stabilizers of a given CSS code with smaller-weight gauge operators that split the remaining stabilizers, while being compatible with the logical Pauli operators of the code. The algorithms recover the well-known Bacon-Shor code computationally as well as produce a new $\left[\left[ 9,1,2,2 \right]\right]$ rotated surface subsystem code with weight-$3$ gauges and weight-$4$ stabilizers. We illustrate using a $\left[\left[ 100,25,3 \right]\right]$ subsystem hypergraph product (SHP) code that the algorithms can produce more efficient gauge operators than the closed-form expressions of the SHP construction. However, we observe that the stabilizers of the lifted product quantum LDPC codes are more challenging to split into small-weight gauge operators. Hence, we introduce the subsystem lifted product (SLP) code construction and develop a new $\left[\left[ 775, 124, 20 \right]\right]$ code from Tanner's classical quasi-cyclic LDPC code. The code has high-weight stabilizers but all gauge operators that split stabilizers have weight $5$, except one. In contrast, the LP stabilizer code from Tanner's code has parameters $\left[\left[ 1054, 124, 20 \right]\right]$. This serves as a novel example of new subsystem codes that outperform stabilizer versions of them. Finally, based on our experiments, we share some general insights about non-locality's effects on the performance of splitting stabilizers into small-weight gauges.

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arXiv2024

Entanglement Purification with Quantum LDPC Codes and Iterative Decoding

Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is a challenging one. Given the practical difficulty in building a monolithic architecture for quantum computers based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected quantum processors. In such a setting, all syndrome measurements and logical operations must be performed using high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond DQC since entanglement purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder for distilling $3$-qubit GHZ states using a rate $0.118$ family of lifted product QLDPC codes and obtain an input threshold of $\approx 0.7974$ under i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield of $0.118$ for any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of $3$-qubit GHZ states to construct a scalable GHZ purification protocol.

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arXiv2023

Describing quantum metrology with erasure errors using weight distributions of classical codes

Quantum sensors are expected to be a prominent use-case of quantum technologies, but in practice, noise easily degrades their performance. Quantum sensors can for instance be afflicted with erasure errors. Here, we consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance $d \geq t+1$. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field after at most $t$ qubits of the quantum probe state are erased. We show that the quantum Fisher information is proportional to the variances of the weight distributions of the corresponding $2^t$ shortened codes. If the shortened codes of a fixed code with $d \geq t+1$ have a non-trivial weight distribution, then the probe states obtained by concatenating this code with repetition codes of increasing length enable asymptotically optimal field-sensing that passively tolerates up to $t$ erasure errors.

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arXiv2022

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable GottesmanKitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder - a hardware-friendly min-sum algorithm (MSA) - utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.

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arXiv2022

Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors

Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the iterative decoders for decoding quantum low-density parity-check (QLDPC) codes. Syndrome-based iterative belief propagation decoders are modified to utilize the syndrome-soft information to successfully correct both data and syndrome errors simultaneously, without repeated measurements. We demonstrate the advantages of extracting the soft information from the syndrome in our improved decoders, not only in terms of comparison of thresholds and logical error rates for quasi-cyclic lifted-product QLDPC code families, but also for faster convergence of iterative decoders. In particular, the new BP decoder with noisy syndrome performs as good as the standard BP decoder under ideal syndrome.

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arXiv2022

Distilling GHZ States using Stabilizer Codes

Entanglement distillation is a well-studied problem in quantum information, where one typically starts with $n$ noisy Bell pairs and distills $k$ Bell pairs of higher fidelity. While distilling Bell pairs is the canonical setting, it is important to study the distillation of multipartite entangled states because these can be useful for realizing distributed algorithms on quantum networks. In this paper, we study the distillation of GHZ states using quantum error correcting codes (QECCs). Using the stabilizer formalism, we begin by explaining the QECC-based Bell pair distillation protocol in arXiv:0708.3699, which relies particularly on the transpose symmetry between Alice's and Bob's qubits in Bell states. Extending this idea, we show that, given $n$ GHZ states, performing a matrix on Alice's qubits is equivalent to performing a "stretched" version of the transpose of the matrix on the qubits of Bob and Charlie. We call this mapping to the stretched version of the matrix the GHZ-map, and show that it is an algebra homomorphism. Using this property, we show that Alice projecting her qubits onto an $[[n,k]]$ stabilizer code implies the simultaneous projection of Bob's and Charlie's qubits onto an induced $[[2n,k]]$ stabilizer code. Guided by this insight, we develop a GHZ distillation protocol based on local operations and classical communication that uses any stabilizer code. Inspired by stabilizer measurements on GHZ states, we also develop a new algorithm to generate logical Pauli operators of any stabilizer code and use it in the protocol. Since quantum codes with finite rate and almost linear minimum distance have recently been discovered, this paper paves the way for high-rate high-output-fidelity GHZ distillation. We provide simulation results on the $5$-qubit perfect code to emphasize the importance of the placement of a certain local Clifford operation in the protocol.

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