Abstract
Given two copies of any quantum mechanical system, one may want to prepare them in the thermofield double state for the purpose of studying thermal physics or black holes. However, the thermofield double is a unique entangled pure state and may be difficult to prepare. We propose a local interacting Hamiltonian for the combined system whose ground state is approximately the thermofield double. The energy gap for this Hamiltonian is of order the temperature. Our construction works for any quantum system satisfying the Eigenvalue Thermalization Hypothesis.
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References
P. Gao, D.L. Jafferis and A. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].
L. Susskind, Dear Qubitzers, GR=QM, arXiv:1708.03040 [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
E. Farhi, J. Goldstone and S. Gutmann, Quantum Adiabatic Evolution Algorithms versus Simulated Annealing, quant-ph/0201031.
K.L. Pudenz, G.S. Tallant, T.R. Belote and S.H. Adachi, Quantum Annealing and the Satisfiability Problem, arXiv:1612.07258.
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
B. Swingle and J. McGreevy, Renormalization group constructions of topological quantum liquids and beyond, Phys. Rev. B 93 (2016) 045127 [arXiv:1407.8203] [INSPIRE].
B. Swingle and J. McGreevy, Mixed s-sourcery: Building many-body states using bubbles of Nothing, Phys. Rev. B 94 (2016) 155125 [arXiv:1607.05753] [INSPIRE].
R. van Breukelen and K. Papadodimas, Quantum teleportation through time-shifted AdS wormholes, JHEP 08 (2018) 142 [arXiv:1708.09370] [INSPIRE].
S.E. Venegas-Andraca, W. Cruz-Santos, C. McGeoch and M. Lanzagorta, A cross-disciplinary introduction to quantum annealing-based algorithms, Contemp. Phys. 59 (2018) 174.
C. Barrett, R. Sebastiani, S. Seshia and C. Tinelli, Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications, ch. Satisfiability Modulo Theories, IOS Press (2009) [https://doi.org/10.3233/978-1-58603-929-5-825].
T. Hogg, Adiabatic quantum computing for random satisfiability problems, Phys. Rev. A 67 (2003) 022314 [quant-ph/0206059].
P. Gao and H. Liu, Regenesis and quantum traversable wormholes, arXiv:1810.01444 [INSPIRE].
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ArXiv ePrint: 1811.11528
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Cottrell, W., Freivogel, B., Hofman, D.M. et al. How to build the thermofield double state. J. High Energ. Phys. 2019, 58 (2019). https://doi.org/10.1007/JHEP02(2019)058
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DOI: https://doi.org/10.1007/JHEP02(2019)058