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Register a new userContinuous-variable assisted thermal quantum simulation
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Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous-variable for simulating quantum systems at finite temperatures. Our algorithm has a time complexity scaling polynomially with the inverse temperature and the desired accuracy. We demonstrate the quantum algorithm by simulating finite temperature phase diagram of the Kitaev model. It is found that the important crossover phase diagram of the Kitaev ring can be accurately simulated by a quantum computer with only a few qubits and thus the algorithm may be readily implemented on current quantum processors. We further propose a protocol implementable with superconducting or trapped ion quantum computers.
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We study the continuous-variable (CV) quantum teleportation protocol in the case that one of the two modes of the shared entangled resource is sent to the receiver through a Gaussian Quantum Brownian Motion noisy channel. We show that if the channel is engineered in a non-Markovian regime, the information backflow from the environment induces an extra dependance of the phase of the two-mode squeezing of the shared Gaussian entangled resource on the transit time along the channel of the shared mode sent to the receiver. Optimizing over the non-Markovianity dependent phase of the squeezing yields a significant enhancement of the teleportation fidelity. For short enough channel transit times, essentially unit fidelity is achieved at realistic, finite values of the squeezing amplitude for a sufficiently large degree of the channel non-Markovianity.
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We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states our results provide a theoretical justification for the use of Whites algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics.
Tensor network methods are routinely used in approximating various equilibrium and non-equilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximations to thermal states and time evolution demand a bond dimension growing with system size. To address this problem, we construct PEPOs that approximate, for all local observables, $i)$ their thermal expectation values and $ii)$ their Heisenberg time evolution. The bond dimension required does not depend on system size, but only on the temperature or time. We also show how these can be used to approximate thermal correlation functions and expectation values in quantum quenches.
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