Results 41 to 50 of about 15,842 (155)

Kerdock Codes Determine Unitary 2-Designs [PDF]

, 2019
The non-linear binary Kerdock codes are known to be Gray images of certain extended cyclic codes of length $N = 2^m$ over $\mathbb{Z}_4$. We show that exponentiating these $\mathbb{Z}_4$-valued codewords by $\imath \triangleq \sqrt{-1}$ produces ...
Calderbank, Robert, Can, Trung, Pfister, Henry D., Rengaswamy, Narayanan   +3 more
core   +2 more sources

Fault-tolerant additive weighted geometric spanners

, 2019
Let S be a set of n points and let w be a function that assigns non-negative weights to points in S. The additive weighted distance d_w(p, q) between two points p,q belonging to S is defined as w(p) + d(p, q) + w(q) if p \ne q and it is zero if p = q ...
A Czumaj, C Levcopoulos, G Narasimhan, I Althöfer, MA Abam, S Har-Peled, S Har-Peled, Tamás Lukovszki   +7 more
core   +1 more source

Sparse Fault-Tolerant Spanners for Doubling Metrics with Bounded Hop-Diameter or Degree [PDF]

, 2015
postprin
Chan, HTH, LI, M, NING, L
core   +1 more source

Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States [PDF]

, 2014
A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes.
Menicucci, Nicolas C.
core   +2 more sources

Fault-tolerant basis and fault-tolerant edge basis of three classes of French windmill graphs

Ain Shams Engineering Journal
A resolving set is a subset of vertices that uniquely identifies every vertex based on distances. A fault-tolerant resolving set maintains this condition under any single-vertex removal, and the minimum size of such a set is the fault-tolerant metric ...
S. Prabhu, P. Angelin Kiruba, A. Davoodi, Paul Manuel   +3 more
doaj   +1 more source

Maximum gradient embeddings and monotone clustering

, 2009
Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y ...
A. Gupta, A. Gupta, Assaf Naor, B. Brinkman, Ch. Swamy, G. Calinescu, G. Cornuéjols, I. Newman, J. R. Lee, J. R. Lee, K. Jain, K. Jain, K. Jain, M. Charikar, M. Charikar, M. Charikar, M. Elkin, M. Ledoux, M. Mendel, M. Mendel, M. R. Bridson, M. R. Korupolu, Manor Mendel, N. Alon, P. B. Mirchandani, R. Krauthgamer, S. Guha, S. Har-Peled, V. Arya, Y. Bartal, Y. Bartal, Y. Bartal, Y. Bartal, Y. Bartal, Y. Rabinovich   +34 more
core   +2 more sources

Bounding quantum gate error rate based on reported average fidelity

, 2015
Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates.
Sanders, Barry C, Sanders, Yuval R, Wallman, Joel J   +2 more
core   +1 more source

Restrictions on Transversal Encoded Quantum Gate Sets

, 2009
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block. Consequently,
B. C. Hall, Bryan Eastin, C. M. Dawson, D. Aharonov, Emanuel Knill, J. Preskill, J. R. Munkres, M. Mosca, M. R. Sepanski, P. Shor, P. W. Shor   +10 more
core   +1 more source

Long-distance quantum communication over noisy networks without long-time quantum memory

, 2015
The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky ...
A. M. Stephens, Andrzej Grudka, Anna Przysiężna, Justyna Łodyga, M. A. Nielsen, Michał Horodecki, P. Aliferis, Paweł Horodecki, Paweł Mazurek, W. Cook, Łukasz Pankowski   +10 more
core   +1 more source

Optimal Vertex Fault Tolerant Spanners (for fixed stretch)

, 2017
A $k$-spanner of a graph $G$ is a sparse subgraph $H$ whose shortest path distances match those of $G$ up to a multiplicative error $k$. In this paper we study spanners that are resistant to faults.
Bodwin, Greg, Dinitz, Michael, Parter, Merav, Williams, Virginia Vassilevska   +3 more
core   +1 more source