Figure 1 | Scientific Reports

Figure 1

From: Arrow of time and its reversal on the IBM quantum computer

Figure 1

Time reversal procedure for a Gaussian wave-packet \({\rm{\Psi }}(x,0)\propto \exp (\,-\,{x}^{2}/2{\sigma }^{2})\), \(\sigma =1(a.u.)\). The wave-packet spreads \({\rm{\Psi }}(x,0)\to {\rm{\Psi }}(x,\tau )\) according to a quadratic Hamiltonian \({\hat{p}}^{2}/2m\) during the time interval \(\tau =3m{\sigma }^{2}/\hslash \). At the moment \(\tau \) the system is exposed to the fast step-wise electromagnetic potential fluctuation v(x) (second panel). The fluctuation approximately (with the precision corresponding to the density of partitioning points) conjugates the phase of the wave-function: \(\phi (x,{\tau }^{-0})\to \tilde{\phi }(x,{\tau }^{+0})=\phi (x,{\tau }^{-0})+ev(x,\tau )\delta \tau /\hslash \) (third panel). The prepared time-reversed state \(\tilde{{\rm{\Psi }}}(x,\tau )\) then freely evolves during the same time interval \(\tau \) and arrives to the squeezed state \(\tilde{{\rm{\Psi }}}(x,2\tau )\) (fourth panel). The resulting state \(\tilde{{\rm{\Psi }}}(x,2\tau )\) has 86% overlap with the initial state \({\rm{\Psi }}(x,0)\) shown as an empty envelope curve in the fourth panel.

Back to article page