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Trotterization-based, iterative approaches to quantum simulation (QS) are restricted to simulation times less than the coherence time of the quantum computer (QC), which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called variational fast forwarding (VFF), for decreasing the quantum circuit depth of QSs. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function’s operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. In addition, we implement VFF on Rigetti’s QC to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF.

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Recent studies using the quantum information theoretic approach to thermodynamics show that the presence of coherence in quantum systems generates corrections to classical fluctuation theorems. To explicate the physical origins and implications of such corrections, we here convert an abstract framework of an autonomous quantum Crooks relation into quantum Crooks equalities for wellknown coherent, squeezed and cat states. We further provide a proposal for a concrete experimental scenario to test these equalities. Our scheme consists of the autonomous evolution of a trapped ion and uses a position dependent AC Stark shift.Accepted in Quantum 2018-02-12, click title to verify arXiv:1806.11256v4 [quant-ph] 19 Feb 2019 1 We use the term 'coherence' in the sense of a 'superposition of states belonging to different energy eigenspaces'. Such energetic coherences are formally quantified in the thermal operations framework [12,13] and by measures such as the l1 norm of coherence [39], C l 1 (ρ) := j =k | Ej| ρ |E k |, the sum of the absolute value of the off diagonal elements of a state in the energy eigenbasis.Accepted in Quantum 2018-02-12, click title to verify