Now showing 1 - 7 of 7
  • Placeholder Image
    Publication
    Decoding topological subsystem color codes and generalized subsystem surface codes
    (15-01-2019)
    Gayatri, Vinuta V.
    ;
    Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. In this paper we study two classes of topological subsystem codes with an emphasis on decoding them. First, we generalize the two step decoding algorithm of Suchara et al. to all topological subsystem color codes. Then, we propose a construction of subsystem surface codes and develop decoders for them generalizing the results of Bravyi et al. Our simulations for the topological subsystem color code derived from the square octagon lattice resulted in a noise threshold of 1.75%. This is comparable to the previous result of 1.95% by Bombin et al., who used a different algorithm.
  • Placeholder Image
    Publication
    Subpacketization in coded caching with demand privacy
    (01-02-2020)
    Aravind, V. R.
    ;
    ;
    Coded caching is a technique where we utilize multi-casting opportunities to reduce rate in cached networks. One limitation of coded caching schemes is that they reveal the demands of all users to their peers. In this work, we consider coded caching schemes that assure privacy for user demands with a particular focus on reducing subpacketization. For the 2-user, 2-file case, we present a new linear demand-private scheme with the lowest possible subpacketization. This is done by presenting the scheme explicitly and proving impossibility results under lower subpacketization. When only partial privacy is required, we show that subpacketization can be significantly reduced when there are a large number of files.
  • Placeholder Image
    Publication
    Universal communication efficient quantum threshold secret sharing schemes
    (11-04-2021)
    Senthoor, Kaushik
    ;
    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 d/d− k+1 by contacting d ≥ 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. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.
  • Placeholder Image
    Publication
    Correcting erasures with topological subsystem color codes
    (11-04-2021)
    Solanki, Hiteshvi Manish
    ;
    Qubit loss is one of the forms of noise encountered in some quantum technologies. Such noise is modeled using the quantum erasure channel. Unlike the depolarizing noise, it is much more tractable, yet the performance of many quantum codes over the erasure channel has not been studied as extensively. In this paper, we study the performance of topological subsystem color codes (TSCCs) over the quantum erasure channel. It is the first such study of TSCCs over the erasure channel. We propose multiple decoding algorithms for TSCC and obtain the highest threshold of about 9.7% for the subsystem color code derived from the square octagon lattice.
  • Placeholder Image
    Publication
    Quantum codes and symplectic matroids
    (01-01-2014)
    The correspondence between linear codes and representable matroids is well known. But a similar correspondence between quantum codes and matroids is not known. We show that representable symplectic matroids over a finite field F q correspond to Fq-linear quantum codes. This connection is straightforward but it does not appear to have been made earlier in literature. This correspondence is made through isotropic subspaces. We show that Calderbank-Shor-Steane (CSS) codes correspond to homogenous symplectic matroids while graph states, which figure so prominently in measurement based quantum computation, correspond to a special class of symplectic matroids, namely Lagrangian matroids. This association is useful in that it enables the study of symplectic matroids in terms of quantum codes and vice versa. Furthermore, it has application in the study of quantum secret sharing schemes. © 2014 IEEE.
  • Placeholder Image
    Publication
    Performance of Nonbinary Cubic Codes
    (08-03-2019)
    Moncy, Arun John
    ;
    Cubic codes were proposed by Haah as candidates for self-error correction in three dimensions (3D). While these codes are not self-correcting, Bravyi and Haah showed that they are partially self-correcting. In this paper we are interested in generalizations of the cubic code to prime alphabet. Kim initiated the study of such codes over prime alphabet. Haah also proposed a framework based on modules that enables the study of cubic codes over higher alphabet. However, there are many open questions remaining, especially those pertaining to the performance of nonbinary cubic codes. Building on Bravyi and Haah's decoder, we study the performance of nonbinary cubic codes over the quantum erasure and depolarizing channels. This is the first such study of nonbinary cubic codes.
  • Placeholder Image
    Publication
    Equivalence of 2D color codes (without translational symmetry) to surface codes
    (28-09-2015)
    Bhagoji, Arjun
    ;
    In a recent work, Bombin, Duclos-Cianci, and Poulin showed that every local translationally invariant 2D topological stabilizer code is locally equivalent to a finite number of copies of Kitaev's toric code. For 2D color codes, Delfosse relaxed the constraint on translation invariance and mapped a 2D color code onto three surface codes. In this paper, we propose an alternate map based on linear algebra. We show that any 2D color code can be mapped onto exactly two copies of a related surface code. The surface code in our map is induced by the color code and easily derived from the color code. Furthermore, our map does not require any ancilla qubits for the surface codes.