TY  - JOUR
A1  - de Beaudrap, Niel
T1  - On restricted unitary Cayley graphs and symplectic transformations modulo n
N2  - We present some observations on a restricted variant of unitary Cayley graphs modulo n, and implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs G(n), whose vertex set is the ring Z(n), and where residues a, b modulo n are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of such graphs, we show an upper bound on the number of elementary operations (symplectic scalar multiplications, symplectic row swaps, and row additions or subtractions) required to decompose a symplectic matrix over Z(n). We also characterize the conditions on n for G(n) to be a perfect graph.
Y1  - 2010
UR  - http://www.emis.de/journals/EJC/index.html
SN  - 1077-8926
ER  - 
TY  - JOUR
A1  - de Beaudrap, Niel
T1  - Unitary-circuit semantics for measurement-based computations
N2  - One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems. Is it possible to determine whether a "quantum-to-quantum" 1WQC procedure (having non-trivial input and output subsystems) performs a unitary transformation? Is it possible to describe precisely how such computations transform quantum states, by translation to a quantum circuit of comparable complexity? In this article, we present an efficient algorithm for transforming certain families of measurement-based computations into a reasonable unitary circuit model, in particular without employing the principle of deferred measurement.
Y1  - 2010
UR  - http://ejournals.wspc.com.sg/ijqi/ijqi.shtml
U6  - https://doi.org/10.1142/S0219749910006113
SN  - 0219-7499
ER  - 
TY  - JOUR
A1  - de Beaudrap, Niel
A1  - Ohliger, Matthias
A1  - Osborne, Tobias J.
A1  - Eisert, Jens
T1  - Solving frustration-free spin systems
N2  - We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground-state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models, real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean- field theory.
Y1  - 2010
UR  - http://prl.aps.org/
U6  - https://doi.org/10.1103/Physrevlett.105.060504
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - de Beaudrap, Niel
A1  - Osborne, Tobias J.
A1  - Eisert, Jens
T1  - Ground states of unfrustrated spin Hamiltonians satisfy an area law
N2  - We show that ground states of unfrustrated quantum spin-1/2 systems on general lattices satisfy an entanglement area law, provided that the Hamiltonian can be decomposed into nearest-neighbor interaction terms that have entangled excited states. The ground state manifold can be efficiently described as the image of a low-dimensional subspace of low Schmidt measure, under an efficiently contractible tree-tensor network. This structure gives rise to the possibility of efficiently simulating the complete ground space (which is in general degenerate). We briefly discuss 'non- generic' cases, including highly degenerate interactions with product eigenbases, using a relationship to percolation theory. We finally assess the possibility of using such tree tensor networks to simulate almost frustration- free spin models.
Y1  - 2010
UR  - http://iopscience.iop.org/1367-2630
U6  - https://doi.org/10.1088/1367-2630/12/9/095007
SN  - 1367-2630
ER  -