Thermodynamic Advantage of Quantum Time-Reversal

Abstract

Classical computations inherently require energy dissipation that increases significantly as the reliability of the computation improves. This dissipation arises when transitions between memory states are not balanced by their time-reversed counterparts. While classical memories exhibit a discrete set of possible time-reversal symmetries, quantum memory offers a continuum. This continuum enables the design of quantum memories that minimize irreversibility. As a result, quantum memory reduces energy dissipation several orders of magnitude below classical memory.

Figures (3)

• Figure 1: $N$-state erasure with error $\epsilon$ maps every state to the default state ($0$ in this case) with probability $1-\epsilon$ (highlighted with thick arrows). Every other transition (indicated with thin dashed lines) has probability $\epsilon/(|\mathcal{S}|-1)$.
• Figure 2: Time reversal on the Bloch sphere is a reflection. The state $|\gamma, \varphi \rangle$ shown in A) is reflected across the $xy$-plane to produce the time reversal in $\Theta |\gamma, \varphi \rangle=|\pi-\gamma, \varphi \rangle$ in B). C) shows a mutually unbiased basis in the Bloch sphere, where the time reversal $|0^\dagger \rangle$ has the same overlap with $|0\rangle$ as $|1 \rangle$.
• Figure 3: Entropy production decreases as QTR ambiguity increases. For two different error rates $\epsilon \in \{10^{-1},10^{-26}\}$ and five different system dimensions $|\mathcal{S}| \in \{2,3,4,20,100\}$, we plot the entropy production and QTR ambiguity of an erasure operation for 1) a classical memory (a red X), and 2) one thousand randomly sampled quantum memory bases (blue dots). Note that the QTR ambiguity $H[S^\dagger|S]$ is scaled by its maximum value $\ln |\mathcal{S}|$.