TY - JOUR A1 - Barthel, Thomas A1 - Pineda, Carlos A1 - Eisert, Jens T1 - Contraction of fermionic operator circuits and the simulation of strongly correlated fermions N2 - A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented framework allows for the introduction of fermionic versions of known qudit operator circuits (QUOC), important for the simulation of strongly correlated d-dimensional systems: the multiscale entanglement renormalization ansaumltze (MERA), tree tensor networks (TTN), projected entangled pair states (PEPS), or their infinite-size versions (iPEPS etc.). After the definition of a FOC, we present a method to contract it with the same computation and memory requirements as a corresponding QUOC, for which all fermionic operators are replaced by qudit operators of identical dimension. A given scheme for contracting the QUOC relates to an analogous scheme for the corresponding fermionic circuit, where additional marginal computational costs arise only from reordering of modes for operators occurring in intermediate stages of the contraction. Our result hence generalizes efficient schemes for the simulation of d- dimensional spin systems, as MERA, TTN, or PEPS to the fermionic case. Y1 - 2009 UR - http://pra.aps.org/ U6 - https://doi.org/10.1103/Physreva.80.042333 SN - 1050-2947 ER - TY - JOUR A1 - Barthel, Thomas A1 - Schollwock, Ulrich A1 - White, Steven R. T1 - Spectral functions in one-dimensional quantum systems at finite temperature using the density matrix renormalization group N2 - We present time-dependent density matrix renormalization group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics for arbitrary temperatures. This is illustrated with spin structure factors of XX and XXX spin-1/2 chains. For the XX model we can compare against an exact solution, and for the XXX model (Heisenberg antiferromagnet) against a Bethe ansatz solution and quantum Monte Carlo data. Y1 - 2009 UR - http://prb.aps.org/ U6 - https://doi.org/10.1103/Physrevb.79.245101 SN - 1098-0121 ER - TY - JOUR A1 - Barthel, Thomas A1 - Kliesch, Martin A1 - Eisert, Jens T1 - Real-space renormalization yields finite correlations N2 - Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is further pointed out that there exist other efficiently contractible schemes violating the area law. Y1 - 2010 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.105.010502 SN - 0031-9007 ER - TY - JOUR A1 - Kliesch, Martin A1 - Barthel, Thomas A1 - Gogolin, C. A1 - Kastoryano, M. A1 - Eisert, J. T1 - Dissipative quantum church-turing theorem JF - Physical review letters N2 - We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Church-Turing theorem, since it implies that under natural assumptions, such as weak coupling to an environment, the dynamics of an open quantum system can be simulated efficiently on a quantum computer. Formally, we introduce a Trotter decomposition for Liouvillian dynamics and give explicit error bounds. This constitutes a practical tool for numerical simulations, e.g., using matrix-product operators. We also demonstrate that most quantum states cannot be prepared efficiently. Y1 - 2011 U6 - https://doi.org/10.1103/PhysRevLett.107.120501 SN - 0031-9007 VL - 107 IS - 12 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Barthel, Thomas A1 - Kliesch, Martin T1 - Quasilocality and efficient simulation of Markovian Quantum Dynamics JF - Physical review letters N2 - We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasilocal; i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. The precision increases exponentially with the diameter of the considered subsystem. Hence, time evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations in the Schrodinger picture, our result can be used to rigorously bound finite-size effects. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevLett.108.230504 SN - 0031-9007 VL - 108 IS - 23 PB - American Physical Society CY - College Park ER -