arXiv subjects

Pradeep Kiran Sarvepalli

Publications and source records attributed to Pradeep Kiran Sarvepalli.

At least 19 recordsLinked to original sources

arXiv2023

Universal Communication Efficient Quantum Threshold Secret Sharing Schemes

Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum secret is distributed among a number of parties where some subsets of the parties are able to recover the secret while some subsets are unable to recover the secret. In the standard $((k,n))$ quantum threshold secret sharing scheme, any subset of $k$ or more parties out of the total $n$ parties can recover the secret while other subsets have no information about the secret. But recovery of the secret incurs a communication cost of at least $k$ qudits for every qudit in the secret. Recently, a class of communication efficient QSS schemes were proposed which can improve this communication cost to $\frac{d}{d-k+1}$ by contacting $d\geq k$ parties where $d$ is fixed prior to the distribution of shares. In this paper, we propose a more general class of $((k,n))$ quantum secret sharing schemes with low communication complexity. Our schemes are universal in the sense that the combiner can contact any number of parties to recover the secret with communication efficiency i.e. any $d$ in the range $k\leq d\leq n$ can be chosen by the combiner. This is the first such class of universal communication efficient quantum threshold schemes.

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arXiv2023

Theory of Communication Efficient Quantum Secret Sharing

A $((k,n))$ quantum threshold secret sharing (QTS) scheme is a quantum cryptographic protocol for sharing a quantum secret among $n$ parties such that the secret can be recovered by any $k$ or more parties while $k-1$ or fewer parties have no information about the secret. Despite extensive research on these schemes, there has been very little study on optimizing the quantum communication cost during recovery. Recently, we initiated the study of communication efficient quantum threshold secret sharing (CE-QTS) schemes. These schemes reduce the communication complexity in QTS schemes by accessing $d\geq k$ parties for recovery; here $d$ is fixed ahead of encoding the secret. In contrast to the standard QTS schemes which require $k$ qudits for recovering each qudit in the secret, these schemes have a lower communication cost of $\frac{d}{d-k+1}$ for $d>k$. In this paper, we further develop the theory of communication efficient quantum threshold schemes. Here, we propose universal CE-QTS schemes which reduce the communication cost for all $d\geq k$ simultaneously. We provide a framework based on ramp quantum secret sharing to construct CE-QTS and universal CE-QTS schemes. We give another construction for universal CE-QTS schemes based on Staircase codes. We derived a lower bound on communication complexity and show that our constructions are optimal. Finally, an information theoretic model is developed to analyse CE-QTS schemes and the lower bound on communication complexity is proved again using this model.

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arXiv2023

Generalizations and Extensions to Lifting Constructions for Coded Caching

Coded caching is a technique for achieving increased throughput in cached networks during peak hours. Placement delivery arrays (PDAs) capture both placement and delivery scheme requirements in coded caching in a single array. Lifting is a method of constructing PDAs, where entries in a small base PDA are replaced with constituent PDAs that satisfy a property called Blackburn-compatibility. We propose two new constructions for Blackburn-compatible PDAs including a novel method for lifting Blackburn-compatible PDAs to obtain new sets of Blackburn-compatible PDAs. Both of these constructions improve upon previous tradeoffs between rate, memory and subpacketization. We generalize lifting constructions by defining partial Blackburn-compatibility between two PDAs w.r.t. a third PDA. This is a wider notion of Blackburn-compatibility making the original definition a special case. We show that some popular coded caching schemes can be defined as lifting constructions in terms of this extended notion.

cs.IT↗

arXiv2022

Concatenating Extended CSS Codes for Communication Efficient Quantum Secret Sharing

Recently, a class of quantum secret sharing schemes called communication efficient quantum threshold secret sharing schemes (CE-QTS) was introduced. These schemes reduced the communication cost during secret recovery. In this paper, we introduce a general class of communication efficient quantum secret sharing schemes (CE-QSS) which include both threshold and non-threshold schemes. We propose a framework for constructing CE-QSS schemes to generalize the earlier construction of CE-QTS schemes which was based on the staircase codes. The main component in this framework is a class of quantum codes which we call the extended Calderbank-Shor-Steane codes. These extended CSS codes could have other applications. We derive a bound on communication cost for CE-QSS schemes. Finally, we provide a construction of CE-QSS schemes meeting this bound using the proposed framework.

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arXiv2022

Decoding Topological Subsystem Color Codes Over the Erasure Channel using Gauge Fixing

Topological subsystem color codes (TSCCs) are an important class of topological subsystem codes that allow for syndrome measurement with only 2-body measurements. It is expected that such low complexity measurements can help in fault tolerance. While TSCCs have been studied over depolarizing noise model, their performance over the erasure channel has not been studied as much. Recently, we proposed erasure decoders for TSCCs and reported a threshold of 9.7%. In this paper, we continue our study of TSCCS over the erasure channel. We propose two erasure decoders for topological subsystem color codes. These decoders use the technique of gauge fixing where some of the gauge operators of the subsystem code are promoted to stabilizers. We perform gauge fixing using 4-body and 8-body gauge operators. With partial gauge fixing we obtained a threshold of 17.7% on a TSCC derived from the square octagon lattice. Using an order maximal gauge fixing decoder we were able to improve the threshold to 44%. The previously known decoder for TSCC over the erasure channel had a threshold of 9.7%. We also study the correctability of erasures on the subsystem codes.

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arXiv2022

Lifting Constructions of PDAs for Coded Caching with Linear Subpacketization

Coded caching is a technique where multicasting and coding opportunities are utilized to achieve better rate-memory tradeoff in cached networks. A crucial parameter in coded caching is subpacketization, which is the number of parts a file is to be split into for coding purposes. The original Maddah-Ali-Niesen scheme has order-optimal rate at a subpacketization growing exponentially with the number of users. In contrast, placement and delivery schemes in coded caching, designed using placement delivery arrays (PDAs), can have linear subpacketization with a penalty in rate. In this work, we propose several constructions of efficient PDAs through lifting, where a base PDA is expanded by replacing each entry by another PDA. By proposing and using the notion of Blackburn-compatibility of PDAs, we provide multiple lifting constructions with increasing coding gains. We compare the constructed coded caching schemes with other existing schemes for moderately high number of users and show that the proposed constructions are versatile and achieve a good rate-memory tradeoff at low subpacketizations.

cs.IT↗

arXiv2022

Quantum computation with charge-and-color permuting twists in qudit color codes

Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. They are known to exhibit projective non-Abelian statistics which is exploited to perform encoded gates. In this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. To the best of our knowledge, this is the first study of twists in qudit color codes. Specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. We also present a mapping between generalized Pauli operators and strings in the lattice. Making use of the construction, we give protocols to implement generalized Clifford gates using charge-and-color-permuting twists.

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arXiv2021

Color codes with twists: construction and universal gate set implementation

Twists are defects in the lattice that can be used to perform encoded computations. Three basic types of twists can be introduced in color codes, namely, twists that permute color, charge of anyons and domino twists that permute the charge label of an anyon with a color label. In this paper, we study a subset these twists from coding theoretic viewpoint. Specifically, we discuss systematic construction of charge permuting and color permuting twists in color codes. We show that by braiding alone, Clifford gates can be realized in color codes with charge permuting twists. We also discuss implementing single qubit Clifford gates by Pauli frame update and CNOT gate by braiding holes around twists in color codes with color permuting twists. Finally, we also discuss implementing a non-Clifford gate by state injection, thus completing the realization of a universal gate set.

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arXiv2019

Decoding toric codes on three dimensional simplical complexes

Three dimensional (3D) toric codes are a class of stabilizer codes with local checks and come under the umbrella of topological codes. While decoding algorithms have been proposed for the 3D toric code on a cubic lattice, there have been very few studies on the decoding of 3D toric codes over arbitrary lattices. Color codes in 3D can be mapped to toric codes. However, the resulting toric codes are not defined on cubic lattice. They are arbitrary lattices with triangular faces. Decoding toric codes over an arbitrary lattice will help in studying the performance of color codes. Furthermore, gauge color codes can also be decoded via 3D toric codes. Motivated by this, we propose an efficient algorithm to decode 3D toric codes on arbitrary lattices (with and without boundaries). We simulated the performance of 3D toric code for cubic lattice under bit flip channel. We obtained a threshold of 12.2\% for the toric code on the cubic lattice with periodic boundary conditions.

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arXiv2019

Quantum Bicyclic Hyperbolic Codes

Bicyclic codes are a generalization of the one dimensional (1D) cyclic codes to two dimensions (2D). Similar to the 1D case, in some cases, 2D cyclic codes can also be constructed to guarantee a specified minimum distance. Many aspects of these codes are yet unexplored. Motivated by the problem of constructing quantum codes, in this paper, we study some structural properties of certain bicyclic codes. We show that a primitive narrow-sense bicyclic hyperbolic code of length $n^2$ contains its dual if and only if its design distance is lower than $n-Δ$, where $Δ=\mathcal{O}(\sqrt{n})$. We extend the sufficiency condition to the non-primitive case as well. We also show that over quadratic extension fields, a primitive bicyclic hyperbolic code of length $n^2$ contains Hermitian dual if and only if its design distance is lower than $n-Δ_h$, where $Δ_h=\mathcal{O}(\sqrt{n})$. Our results are analogous to some structural results known for BCH and Reed-Solomon codes. They further our understanding of bicyclic codes. We also give an application of these results by showing that we can construct two classes of quantum bicyclic codes based on our results.

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arXiv2019

Communication Efficient Quantum Secret Sharing

In the standard model of quantum secret sharing, typically, one is interested in minimal authorized sets for the reconstruction of the secret. In such a setting, reconstruction requires the communication of all the shares of the corresponding authorized set. If we allow for non-minimal authorized sets, then we can trade off the size of the authorized sets with the amount of communication required for reconstruction. Based on the staircase codes, proposed by Bitar and El Rouayheb, we propose a class of quantum threshold secret sharing schemes that are also communication efficient. We call them $((k,2k-1,d))$ communication efficient quantum secret sharing schemes where $k\leq d\leq2k-1$. Using the proposed construction, we can recover a secret of $d-k+1$ qudits by communicating $d$ qudits whereas using the standard $((k,2k-1))$ quantum secret sharing requires $k(d-k+1)$ qudits to be communicated. In other words, to share a secret of one qudit, the standard quantum secret sharing requires $k$ qudits whereas the proposed schemes communicate only $\frac{d}{d-k+1}$ qudits per qudit in the communication complexity. Proposed schemes can reduce communication overheads by a factor $O(k)$ with respect to standard schemes, when $d$ equals $2k-1$. Further, we show that our schemes have optimal communication cost for secret reconstruction.

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arXiv2019

Neural Decoder for Topological Codes using Pseudo-Inverse of Parity Check Matrix

Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problems in the context of decoding. An important development in this regard was due to Varsamopoulos et al. who proposed a two-step decoder using neural networks. Subsequent work of Maskara et al. used the same concept for decoding for various noise models. We propose a similar two-step neural decoder using inverse parity-check matrix for topological color codes. We show that it outperforms the state-of-the-art performance of non-neural decoders for independent Pauli errors noise model on a 2D hexagonal color code. Our final decoder is independent of the noise model and achieves a threshold of $10 \%$. Our result is comparable to the recent work on neural decoder for quantum error correction by Maskara et al.. It appears that our decoder has significant advantages with respect to training cost and complexity of the network for higher lengths when compared to that of Maskara et al.. Our proposed method can also be extended to arbitrary dimension and other stabilizer codes.

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arXiv2018

Efficiently decoding the 3D toric codes and welded codes on cubic lattices

The recent years have seen a growing interest in quantum codes in three dimensions (3D). One of the earliest proposed 3D quantum codes is the 3D toric code. It has been shown that 3D color codes can be mapped to 3D toric codes. The 3D toric code on cubic lattice is also a building block for the welded code which has highest energy barrier to date. Although well known, the performance of the 3D toric code has not been studied extensively. In this paper, we propose efficient decoding algorithms for the 3D toric code on a cubic lattice with and without boundaries and report their performance for various quantum channels. We observe a threshold of $\gtrsim 12\%$ for the bit flip errors, $\approx 3\%$ for phase flip errors and $ 24.8\%$ for erasure channel. We also study the performance of the welded 3D toric code on the quantum erasure channel. We did not observe a threshold for the welded code over the erasure channel.

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arXiv2018

Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes

Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some subsystem codes. Later Bravyi et al. proposed a subsystem surface code. Building upon these works, we propose efficient decoding algorithms for large classes of subsystem codes on hypergraphs and surfaces. We also propose a construction of the subsystem surface codes that includes the code proposed by Bravyi et al. Our simulations for the subsystem code on the square octagon lattice resulted in a noise threshold of 1.75%. This is comparable to previous result of 2% by Bombin et al. who used a different algorithm.

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arXiv2018

On the Local Equivalence of 2D Color Codes and Surface Codes with Applications

In recent years, there have been many studies on local stabilizer codes. Under the assumption of translation and scale invariance Yoshida classified such codes. His result implies that translation invariant 2D color codes are equivalent to copies of toric codes. Independently, Bombin, Duclos-Cianci, and Poulin showed that a local translation invariant 2D topological stabilizer code is locally equivalent to a finite number of copies of Kitaev's toric code. In this paper we focus on 2D topological color codes and relax the assumption of translation invariance. Using a linear algebraic framework we show that any 2D color code (without boundaries) is locally equivalent to two copies of a related surface code. This surface code is induced by color code. We study the application of this equivalence to the decoding of 2D color codes over the bit flip channel as well as the quantum erasure channel. We report the performance of the color code on the square octagonal lattice over the quantum erasure channel. Further, we provide explicit circuits that perform the transformation between 2D color codes and surface codes. Our circuits do not require any additional ancilla qubits.

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arXiv2016

Projecting 3D color codes onto 3D toric codes

Toric codes and color codes are two important classes of topological codes. Kubica, Yoshida, and Pastawski showed that any $D$-dimensional color code can be mapped to a finite number of toric codes in $D$-dimensions. In this paper we propose an alternate map of 3D color codes to 3D toric codes with a view to decoding 3D color codes. Our approach builds on Delfosse's result for 2D color codes and exploits the topological properties of these codes. Our result reduces the decoding of 3D color codes to that of 3D toric codes. Bit flip errors are decoded by projecting on one set of 3D toric codes while phase flip errors are decoded by projecting onto another set of 3D toric codes.

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arXiv2009

Degenerate quantum codes and the quantum Hamming bound

The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether or not the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum codes. In this paper we show that Calderbank-Shor-Steane (CSS) codes with alphabet $q\geq 5$ cannot beat the quantum Hamming bound. We prove a quantum version of the Griesmer bound for the CSS codes which allows us to strengthen the Rains' bound that an $[[n,k,d]]_2$ code cannot correct more than $\floor{(n+1)/6}$ errors to $\floor{(n-k+1)/6}$. Additionally, we also show that the general quantum codes $[[n,k,d]]_q$ with $k+d\leq {(1-2eq^{-2})n}$ cannot beat the quantum Hamming bound.

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arXiv2009

Sharing classical secrets with CSS codes

In this paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum codes which can be converted to secret sharing schemes. If we are interested in sharing classical secrets using quantum information, then we show that a class of pure $[[n,1,d]]_q$ CSS codes can be converted to perfect secret sharing schemes. These secret sharing schemes are perfect in the sense the unauthorized parties do not learn anything about the secret. Gottesman had given conditions to test whether a given subset is an authorized or unauthorized set; they enable us to determine the access structure of quantum secret sharing schemes. For the secret sharing schemes proposed in this paper the access structure can be characterized in terms of minimal codewords of the classical code underlying the CSS code. This characterization of the access structure for quantum secret sharing schemes is thought to be new.

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