Harnessing quantum back-action for time-series processing

Abstract

Quantum measurements affect the state of the observed systems via back-action. While projective measurements extract maximal classical information, they drastically alter the system's configuration. In contrast, indirect measurements balance information extraction with the degree of disturbance. Considering the prevalent use of projective measurements in quantum computing and communication protocols, the potential benefits of indirect measurements in these fields remain largely unexplored. In this work, we demonstrate that incorporating indirect measurements into a quantum machine-learning protocol known as quantum reservoir computing provides advantages in both execution time scaling and overall performance. We analyze different measurement settings by varying the measurement strength across two benchmarking tasks. Our results reveal that carefully optimizing both the reservoir Hamiltonian parameters and the measurement strength can significantly improve the quantum reservoir computing algorithm performance. Furthermore, our approach demonstrates improved memory performance when compared with state-of-the-art classical feedback protocols. This work provides a comprehensive and practical recipe to promote the implementation of indirect measurement-based protocols in quantum reservoir computing. Moreover, our findings motivate further exploration of experimental protocols that leverage the back-action effects of indirect measurements.

Figures (11)

• Figure 1: Quantum reservoir computing via indirect measurements. (a) Example of the reservoir's prediction (dashed lines) over the target series (solid lines) on two specific instances ($\eta = 5$) for the forward prediction task (top panel) and memory retrieval task (bottom panel) (see section \ref{['sectasks']}). (b) Schematic view of the information processing step of the QRC algorithm, the coupling strength $g$ between the measurement apparatus and the reservoir is the main parameter of this work's study. (c) Illustrative example of the effect of indirect measurement on a single spin state for different values of the measurement strength, $g$. As $g \to \infty$, the measurement becomes equivalent to a projective measurement, fully collapsing the state onto one of the measurement axes. However, as $g$ decreases, the post-measurement state is no longer collapsed along the measurement axis and is less perturbed. In this analysis, we assume measurements are performed along the $z$-axis.
• Figure 2: Performance ratio analysis for the forward prediction task (top) and for the short-term memory task (bottom). A $P_R$ in the range $[0, 1)$ shows that the unperturbed dynamics protocol is performing better than the OLP in that point of the $g$--$h$ map. A $P_R$ around 1 shows that the OLP is performing as good as the RSP, and over 1 indicates an over-performance due to the effect of back-action. The maximum $P_R$ and corresponding parameter values for each task are: forward prediction: $g^* = 0.355$, $h^* = 0.01$, $P_R = 2.178$; short-term memory: $g^* = 0.486$, $h^* = 0.01$, $P_R = 27.302$.
• Figure 3: Minimum performance ratio analysis for the forward prediction task (top) and for the short-term memory task (bottom). A $P_R^{\min}$ in the range $[0, 1)$ shows that the best performing RSP is performing better than the OLP in that point of the $g-h$ map. A $P_R^{\min}$ around 1 shows that the OLP is performing as good as the best performing RSP, and over 1 indicates an over-performance. The optimal parameters and corresponding $P_R^{\min}$ values for each task are: forward prediction — RSP: $h'^* = 0.346$; OLP: $g^* = 0.355$, $h^* = 0.273$, $P_R^{\min} = 1.006$; short-term memory — RSP: $h'^* = 0.084$; OLP $g^* = 0.256$ , $h^* = 0.066$ , $P_R^{\min} = 1.029$.
• Figure 4: Sum capacity comparison of the RSP with respect to the OLP with and without optimizing the strength of the measurement $g$. With $g^*$ we denote the $g$ value that maximizes the $P_R^{\min}$. The top panel shows the results for the forward prediction task while the bottom panel is for the short-term memory task.
• Figure 5: Capacity for different sub-tasks. The figure compares the performance in single sub-tasks of the optimal restarting protocol with respect to the optimal and non-optimal versions of the OLP. The top panel shows the results for the forward prediction task while the bottom panel is for the short-term memory task. The optimal parameters correspond to the values obtained in Figure \ref{['fig:cmaps_prmin']}, whereas the non-optimal parameters are fixed to $g = 2$ and $h = 38.88$.