Implement both time evolution and time reversal evolution operations to a quantum state on IBM Q device
Description
Due to the time symmetry of Schrodinger equation in quantum mechanics. If an initial state is evolved forward in time by a Hamiltonian. One could use the same Hamiltonian to construct a time reversal operator such that when evolving the evolved state forward in time with this operator, one will restore the evolved state back to its original initial state.
We can simulate dynamics of a quantum system on IBM devices in a way similar to Ref. [1]. For demonstration of the results we first need to
Encode quantum state and dynamics under some specific Hamiltonian in qubit state
Implement corresponding time reversal operator (complex conjugation and time reversal unitary operation)
By demonstrating time reversal operator we could gain insight of how time reversal works and perhaps have some idea on how to come up with a time reversal algorithm to construct time reversal operators of arbitrary circuits.
Ref.
[1] Lesovik, G.B., Sadovskyy, I.A., Suslov, M.V. et al. Arrow of time and its reversal on the IBM quantum computer. Sci Rep 9, 4396 (2019).
Abstract
Implement both time evolution and time reversal evolution operations to a quantum state on IBM Q device
Description
Due to the time symmetry of Schrodinger equation in quantum mechanics. If an initial state is evolved forward in time by a Hamiltonian. One could use the same Hamiltonian to construct a time reversal operator such that when evolving the evolved state forward in time with this operator, one will restore the evolved state back to its original initial state. We can simulate dynamics of a quantum system on IBM devices in a way similar to Ref. [1]. For demonstration of the results we first need to
By demonstrating time reversal operator we could gain insight of how time reversal works and perhaps have some idea on how to come up with a time reversal algorithm to construct time reversal operators of arbitrary circuits.
Ref. [1] Lesovik, G.B., Sadovskyy, I.A., Suslov, M.V. et al. Arrow of time and its reversal on the IBM quantum computer. Sci Rep 9, 4396 (2019).
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