Microwave signal processing using an analog quantum reservoir computer

Quantum computing research has broadly focused on two approaches: building large-scale, fault-tolerant quantum computers and exploring near-term, noisy intermediate-scale quantum (NISQ) devices. While quantum computational supremacy has been demonstrated with NISQ devices, achieving quantum advantage in practically relevant applications remains challenging. Quantum machine learning, particularly with parameterized quantum circuits, faces the issue of barren plateaus in training landscapes. Quantum reservoir computing (QRC) offers a promising alternative, moving the training process to the classical domain and thus avoiding barren plateaus. Existing QRC implementations have relied on digital quantum circuits, introducing a temporal discretization bottleneck. This research investigates an analog QRC approach using a superconducting microwave circuit to directly process analog-continuous microwave signals, aiming to potentially achieve a quantum sensing-computational advantage.

Classical reservoir computing has shown success in machine learning by using a recurrent neural network with a randomly initialized recurrent layer (the reservoir) and a linear readout layer that is trained. This approach has been adapted to the quantum realm as quantum reservoir computing (QRC). Previous experimental demonstrations of QRC have primarily used digital quantum circuits, requiring the discretization of input signals in time. This discretization limits the complexity of tasks and introduces inaccuracies. Theoretical proposals for analog QRC exist, but experimental realizations have been lacking. This work addresses this gap by leveraging the continuous-time dynamics of a superconducting circuit to create an analog QRC.

The researchers used a superconducting microwave circuit consisting of a cavity resonator coupled to a transmon qubit as their quantum reservoir. The system is modeled by a qubit-oscillator Hamiltonian, incorporating nonlinear interaction strength, qubit control drive, and input signal encoding. The analog input signal, resonantly coupled to the cavity, causes a time-varying displacement of the oscillator mode. The protocol involves repeated cycles of entangling unitaries (generated by control drives) interleaved with qubit and oscillator measurements. The qubit measurements induce non-unitary dynamics. The oscillator measurements are parity measurements, projecting the oscillator state into superpositions of even or odd Fock states. The measurement outcomes are processed to create feature vectors. These feature vectors are constructed from estimates of successive central moments (up to third order) of the measurement trajectory distribution, capturing correlations in the reservoir dynamics. The feature vectors are then fed into a classical linear layer for classification. The researchers tested their analog QRC on several classification tasks: binary classification of time-independent signals, classification of radio-frequency (RF) communication modulation schemes, and classification of filtered noise signals. For time-independent signals, the unitary dynamics involved specific qubit rotations and conditional displacements that created a loop in the oscillator's phase space to encode phase information. For time-dependent signals, the closed loop was broken, and the system remained entangled before measurement. The feature vector encoding and linear layer training methods are also explained, with detailed discussions available in the supplementary information.

The analog QRC demonstrated high accuracy across all three classification tasks. In the time-independent signal classification task (binary classification of signals distributed along spiral arms in the I-Q plane), the QRC achieved >97% accuracy, outperforming a classical linear classifier. The effect of qubit coherence time was also examined, showing a significant performance decrease with reduced coherence time, only impacting performance once below the reservoir duration. In the RF modulation scheme classification task (10 different modulation schemes), the QRC achieved >90% accuracy in less than a millisecond, exceeding the performance of a classical linear classifier by a significant margin. In the filtered noise classification task (six classes of noise signals filtered with different shapes and window widths), the QRC achieved 93% accuracy. The analysis of the contribution of different moments in the feature vector showed that for signals with short coherence times, the mean dominates, while for signals with long coherence times, higher-order correlations are more important. The experiments showed the system's ability to handle both short and long-term memory aspects.

The results demonstrate the feasibility of analog QRC for microwave signal processing. The success across diverse tasks, involving both time-independent and time-dependent signals, highlights the versatility of the approach. The ability to directly process analog signals without discretization provides a significant advantage over previous digital QRC implementations. While the current system is small enough to be classically simulated, the work paves the way for future experiments with larger, more complex systems that could achieve a quantum sensing-computational advantage. The ability to effectively capture both short and long temporal correlations in the input demonstrates the robustness of the method.

This study successfully demonstrated an analog quantum reservoir computer based on a superconducting microwave circuit. High accuracy was achieved on various signal classification tasks, surpassing classical methods. Future research will focus on scaling up the system to explore the trade-offs between reservoir size, number of measurements, feature vector dimension, and required shots. Combining this analog QRC with sensitive quantum detectors could lead to quantum smart sensors capable of extracting information from extremely weak microwave signals with superior performance compared to classical systems.

The current experimental setup is small enough to be classically simulable, so it does not demonstrate a computational quantum advantage. The study primarily focused on proof-of-principle demonstrations and did not investigate the scalability and robustness of the proposed method in realistic, noisy environments. Further investigations into the expressiveness of the QRC for time-dependent signals are needed.