arXiv subjects

Kristan Temme

Publications and source records attributed to Kristan Temme.

42 records · Page 3Linked to original sources

arXiv2012

Efficient Computation of the Permanent of Block Factorizable Matrices

We present an efficient algorithm for computing the permanent for matrices of size N that can written as a product of L block diagonal matrices with blocks of size at most 2. For fixed L, the time and space resources scale linearly in N, with a prefactor that scales exponentially in L. This class of matrices contains banded matrices with banded inverse. We show that such a factorization into a product of block diagonal matrices gives rise to a circuit acting on a Hilbert space with a tensor product structure and that the permanent is equal to the transition amplitude of this circuit and a product basis state. In this correspondence, a block diagonal matrix gives rise to one layer of the circuit, where each block to a gate acting either on a single tensor component or on two adjacent tensor components. This observation allows us to adopt matrix product states, a computational method from condensed matter physics and quantum information theory used to simulate quantum systems, to evaluate the transition amplitude.

cs.DM↗

arXiv2012

Preparing projected entangled pair states on a quantum computer

We present a quantum algorithm to prepare injective PEPS on a quantum computer, a class of open tensor networks representing quantum states. The run-time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS' parent Hamiltonian.

quant-ph↗

arXiv2010

Stochastic Matrix Product States

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the hand of the asymmetric exclusion process.

quant-ph↗

arXiv2010

Stochastic exclusion processes versus coherent transport

Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper a quantum mechanical version of a stochastic hopping process in one dimension is formulated in terms of a quantum master equation. This allows the investigation of coherent and stochastic evolution in the same formal framework. The focus lies on the non-equilibrium steady state. Two stochastic model systems are considered, the totally asymmetric exclusion process and the fully symmetric exclusion process. The steady state transport properties of these models is compared to the case with additional coherent evolution, generated by the $XX$-Hamiltonian.

quant-ph↗

arXiv2008

Graphene with geometrically induced vorticity

At half filling, the electronic structure of graphene can be modelled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field, an everywhere-real Kekule modulation of the hopping matrix elements can correspond to a non-real Higgs field with non-trivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerene-like molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekule-induced mass gap.

cond-mat.mes-hall↗

arXiv2006

Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice

The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as non-condensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components N, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610 (2004) for small atom numbers.

cond-mat.other↗