Results 1 to 10 of about 42 (41)
Graph isomorphism and Gaussian boson sampling
Special Matrices, 2021 We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties are then probed ...
Brádler Kamil +4 more
doaj +1 more source
Undecidability of the Spectral Gap
Forum of Mathematics, Pi, 2022 We construct families of translationally invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an undecidable problem.
Toby Cubitt +2 more
doaj +1 more source
Quantum algorithms for computing general discrete logarithms and orders with tradeoffs
Journal of Mathematical Cryptology, 2021 We generalize our earlier works on computing short discrete logarithms with tradeoffs, and bridge them with Seifert's work on computing orders with tradeoffs, and with Shor's groundbreaking works on computing orders and general discrete logarithms.
Ekerå Martin
doaj +1 more source
A diagrammatic calculus of fermionic quantum circuits [PDF]
Logical Methods in Computer Science, 2019 We introduce the fermionic ZW calculus, a string-diagrammatic language for fermionic quantum computing (FQC). After defining a fermionic circuit model, we present the basic components of the calculus, together with their interpretation, and show how the ...
Giovanni de Felice +2 more
doaj +1 more source
Lineal: A linear-algebraic Lambda-calculus [PDF]
Logical Methods in Computer Science, 2017 We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra.
Pablo Arrighi, Gilles Dowek
doaj +1 more source
A trade-off between classical and quantum circuit size for an attack against CSIDH
Journal of Mathematical Cryptology, 2020 We propose a heuristic algorithm to solve the underlying hard problem of the CSIDH cryptosystem (and other isogeny-based cryptosystems using elliptic curves with endomorphism ring isomorphic to an imaginary quadratic order 𝒪).
Biasse Jean-François +4 more
doaj +1 more source
EXPONENTIAL IMPROVEMENT IN PRECISION FOR SIMULATING SPARSE HAMILTONIANS
Forum of Mathematics, Sigma, 2017 We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a
DOMINIC W. BERRY +4 more
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Quantum computation of discrete logarithms in semigroups
Journal of Mathematical Cryptology, 2014 We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines.
Childs Andrew M., Ivanyos Gábor
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Introduction to Grassmann manifolds and quantum computation
Journal of Applied Mathematics, Volume 2, Issue 8, Page 371-405, 2002., 2002 Geometrical aspects of quantum computing are reviewed elementarily for nonexperts and/or graduate students who are interested in both geometry and quantum computation. We show how to treat Grassmann manifolds which are very important examples of manifolds in mathematics and physics.
Kazuyuki Fujii
wiley +1 more source
Separability criteria based on the Bloch representation of density matrices [PDF]
, 2007 15 pages, no figures.-- MSC2000 code: 81P68.MR#: MR2347059 (2008h:81016)Zbl#: Zbl 1152.81835We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix.
Vicente Majua, Julio Íñigo de
core +1 more source