Quantum memristor with vacuum--one-photon qubits

Abstract

Quantum memristors represent a promising interface between quantum and neuromorphic computing, combining the nonlinear, memory-dependent behavior of classical memristors with the properties of quantum states. An optical quantum memristor can be realized with a vacuum--one-photon qubit entering a tunable beam splitter whose reflectivity is adapted according to the mean number of photons in the device. In this work, we report on the experimental implementation of a bulk quantum-optical memristor, working with single-rail coherent superposition states in the Fock basis, generated via a resonantly excited quantum dot single-photon source. We demonstrate that the coherence of the input state is preserved by the quantum memristor. Moreover, our modular platform allows investigating the nonlinear behavior arising from a cascade of two quantum memristors, a building block for larger networks of such devices towards the realization of complex neuromorphic quantum architectures.

Figures (3)

• Figure 1: Dynamics of a quantum memristor (QM). a) The dynamics of a QM is defined by its state variable $s(t)$, whose time behavior depends on the input variable $\hat{i}$ and on its previous state $s(t')$, where $t' < t$. b) A QM shows different hysteresis loops depending on the ratio between the input oscillation period $T_{osc}$ and the QM characteristic time $T$. c) Dual-rail encoding of vacuum--one-photon qubits. A photon impinges on a beam-splitter with tunable reflectivity and one of the two output modes is treated as an ancilla Spagnolo2022_memr. The resulting state is an entangled state in the form $\hat{\rho}_{in} = \alpha \ket{01}_{12} + \beta \ket{10}_{12}$. d) Here, a laser pulse with pulse area $A$ is used to resonantly excite a semiconductor quantum dot and generate coherent vacuum--one-photon superpositions loredo2019generation as input states to the memristor.
• Figure 2: Experimental apparatus. a) Single photons are generated through a neutral and a charged excitonic-based quantum dots (QD), excited through resonance fluorescence (RF) loredo2019generation. b) The implemented optical QM consists of two polarizing beam splitters (PBS) with a sequence of two half-waveplates (HWP) rotated by 22.5$^\circ$ and a liquid crystal (LC) in between. The feedback loop operates on the phase applied by the LC that controls the overall reflectivity of the QM. c) Input states are prepared through a variable optical attenuator (VOA) to modulate the laser pump power between 0 and $\pi$ as in Eq. \ref{['eq:in_modulation']}. The generated states are collected through a cross-polarization scheme, by using HWPs and quarter-waveplates (QWP). The generated states enter a cascade of two optical QMs, and the output is analyzed in a path-unbalanced MZI. Photons are measured through superconducting nanowire single-photon detectors (SNSPD).
• Figure 3: Experimental results compared with theoretical simulations. In panels a) to d) we show the results with a single memristor, while in panels e) to h) the ones with two concatenated memristors. a) Asymptotic regimes described in Eq. \ref{['eq:asymptotic']}, i.e., $T \ll T_{osc}$, and $T \approx T_{osc}$. In the first case we observe a quadratic response, while in the latter we observe a linear behavior. b) Hysteresis loop of a single memristor. The period of the input signal oscillation amounts to $T_{osc} \approx 400$ s. c) Experimental points and expected behavior for $\langle n_{in} \rangle$ and $\langle n_{out} \rangle$ in the time domain, for the time scale shown in panel b. Solid lines represent the theoretical trends. e) Asymptotic regimes for two concatenated memristors with the same integration windows. f) Dynamics of two concatenated memristors with different integration times, as each memristor operates independently. In the figure we called $\langle n_{in} \rangle$ the input state of the first memristor and $\langle n_{out} \rangle$ the output state of the second memristor. g) Experimental points and theoretical expectations for two concatenated memristors in the time domain, for the time scale shown in panel f. Solid lines represent the theoretical trends. With $\langle n_{mid} \rangle$ we refer to the output signal of the first memristor, which is the input signal of the second memristor. d-h) Interference fringes at two single-photon detectors (respectively green and orange) measured by sending the signal outgoing from a single (d) or a concatenation of two (h) memristors to a path-unbalanced MZI. In the background, the correspondent value of the input signal is reported (blue dots). The visibility of the fringes ranges in the interval $[0,1]$ depending on the one-photon component of the input state.