Quantum chip predicts time series with a feedback loop

Nearly four decades passed between the 1971 postulation of the memristor and its eventual demonstration in 2008. The memristor functions as the primary example of neuromorphic components due to its ability to retain memory through hysteresis, mirroring how synapses function in the human brain. This work explores integrating the memristor with quantum computing to create more efficient machine learning platforms.

Photonic Quantum Memristor Enables Neuromorphic Computing The implementation of a quantum reservoir computing system using single photon states marks a first for the field, according to work detailed in a recent publication. Researchers designed the device to update its internal phase via feedback based on measurements at one output mode. The reservoir’s output then undergoes processing by a linear regression model, calculating a weighted sum to produce a final result. To test the system’s efficacy, the team addressed four distinct tasks: predicting a smooth nonlinear function and forecasting three random time series, NARMA, Mackey-Glass and Santa Fe, with vowel recognition also numerically simulated. These benchmarks allowed for a direct comparison of performance with and without the quantum memristor’s dynamic enhancements. The photonic quantum memristor itself is modeled as a tunable Mach-Zehnder interferometer, with its internal phase updated by a feedback rule dependent on measurement outcomes. The researchers employed a unitary representation of the memristor action, adaptively updated based on previous outcomes, with coefficients serving as hyperparameters within the model. For time-series prediction, they fixed certain parameters, focusing on the memory decay rate as an adjustable hyperparameter. This design allows the system to exploit the feedback mechanism to implement nonlinear operations on input states and use short-term memory, effectively demonstrating a proof-of-principle quantum reservoir computing system.

The team encoded classical data using one-qubit states in the path degree of freedom of a single photon. The reservoir itself consists of a sequence of three unitaries operating on three spatial modes, creating a complex network for information processing. Randomness is introduced through unitary operations both before and after the memristor, further enhancing the system’s capacity for handling diverse data sets. The study distinguishes between nonlinearity originating from the quantum memristor itself and that introduced by the input encoding, providing a detailed analysis of the system’s behavior. “In all of the considered tasks, we show that the dynamics of the photonic quantum memristor enhances the performance, with respect to the case where no feedback loop is implemented,” the researchers report. This improvement suggests that the quantum properties of the memristor are actively contributing to the system’s ability to solve complex problems. Beyond the immediate performance gains, the work lays the groundwork for further exploration of nonlinearities achievable on photonic platforms, potentially advancing the field of optical computing. This is particularly relevant given that hybrid optical-electronic artificial neural networks have already demonstrated lower energy consumption compared to standard architectures. “The memristor could be employed to constitute the activation function layer of quantum neural networks,” the team suggests, envisioning a future where this technology could even unlock the possibility of implementing spiking optical neural networks. The present work demonstrates how a quantum system, specifically, a photonic quantum memristor, can tackle tasks previously addressed with classical architectures, but with substantially fewer resources. This advancement, the researchers believe, “paves the way to efficient machine learning models and to the possibility of exploring neuromorphic architectures applied to quantum tasks.” The implications extend beyond immediate applications, hinting at a future where quantum systems play a more prominent role in the development of energy-efficient and powerful machine learning solutions.

Reservoir Computing Model: Quantum & Classical Integration A hybrid quantum/classical algorithm uses a photonic quantum memristor to enhance nonlinearity and implement classical memory within a reservoir computing model, offering a potential pathway toward more efficient machine learning. This approach combines the quantum system for generating nonlinearity with a classical linear regression model for training. This distinction is important for scalability and practical application. The model’s architecture features input encoding performed using quantum states, followed by a nonlinear quantum reservoir, and concludes with the classical linear regression unit, requiring only the final stage to undergo a training phase. Numerical simulations demonstrate the model’s performance, revealing that it features only one adjustable element, with reported mean squared error values ranging from 0.92 to 2.76 depending on the task. Researchers also investigated extending the output space of the quantum reservoir by either employing multiple parallel units or multiplexing data from different time steps during classical post-processing. These explorations, detailed in supplemental materials, aim to optimize the model’s capacity and efficiency. “These machine learning models work by injecting input data into a fixed random quantum reservoir, whose memory and nonlinearity is mainly given by a photonic quantum memristor, equipped with a feedback loop, which is then followed by a classical linear regression model,” the study explains. The versatility of this approach, allowing operation mode selection based on context and task, distinguishes it from existing optical-based reservoir computing schemes, which often struggle to adapt to the single-photon regime. After quantum processing, a classical linear regression model was applied to determine the best prediction for each task. This final regression stage adds no further nonlinearity or memory to the system, isolating the quantum component’s contribution.

Quantum Memristor Implementation via Mach-Zehnder Interferometer A Mach-Zehnder interferometer, adapted with a feedback loop, now functions as a photonic quantum memristor, demonstrating a device capable of both enhancing nonlinearity and implementing classical memory within a single system. This implementation bypasses a common limitation in artificial neural networks, arising from the increasing number of parameters needed to train complex models on large datasets. These photon pairs, created by a 775 nm pump laser, are then directed through polarizing beam splitters and dichroic mirrors, ultimately collected via optical fibers. The quantum component of the model, therefore, encompasses the encoding of classical data and the reservoir. Although the current implementation employs single photon inputs, the researchers note that equivalent output statistics could be achieved using a coherent light source. To quantify performance, the team used the mean squared error, calculated by comparing target and predicted values across data points. In tests involving the prediction of monomials, three scenarios were compared: a system with the quantum memristor, a system without memory (no feedback loop), and a system without a reservoir. Results, detailed in Table I, demonstrate that the model featuring the quantum memristor outperformed both classical models, even when the classical model had access to past inputs. The final prediction is generated by a polynomial function of current and previous inputs, with the quantum memristor model achieving superior results despite having fewer free parameters, three compared to the classical model’s nine.

The team’s work builds on prior explorations of quantum memristors across various platforms, including optical, superconducting, trapped-ion, and bosonic systems, with extensions to digital quantum simulations and related quantum memory elements. Their implementation, based on the Mach-Zehnder interferometer equipped with a feedback loop, has been proven to exhibit memristive behavior.

Feedback Loop Enhances Memory & Nonlinear Dynamics The coefficients governing this feedback rule are hyperparameters, allowing for fine-tuning of the system’s behavior and optimization for specific tasks. The implementation features a single physical node, realized through the Mach-Zehnder interferometer, which, combined with the feedback loop, functions as a quantum memristor, mirroring the behavior of biological synapses. This approach contrasts with traditional quantum reservoir computing architectures that rely on numerous randomly connected nodes to create intrinsic memory and historical nonlinearity, offering a potentially more resource-efficient pathway to complex computation. The ability of the feedback loop to enhance nonlinearity is particularly noteworthy. Even without it, some nonlinear behavior arises from the initial encoding of inputs, but the loop significantly amplifies this effect and improves overall algorithmic performance. Specifically, the team found that the feedback loop induces a dependence of the measurement operator on the previous output state, resulting in a nonlinear output even after a single processing step, and establishing a memory of prior states. This memory is not inherent to the quantum processing itself, but is introduced through the feedback mechanism, and is then augmented by a subsequent classical linear regression used to refine predictions. To systematically quantify the nonlinearity, the researchers encoded inputs and varied rotation parameters, observing that a proper choice of these parameters, combined with the feedback loop, maximized the nonlinear behavior of the model.

The team also benchmarked their system against scenarios without a feedback loop and without a quantum reservoir, revealing that the quantum memristor consistently outperformed these classical approaches. For the prediction of monomials, the performance improvement was clearly demonstrated, with the inset of a figure showing the difference in mean squared error between the system with and without the feedback loop across different parameter settings. This highlights the hybrid nature of the approach, combining the strengths of both quantum and classical computation. The researchers also note that during the classical linear regression phase, no additional nonlinearity or memory is introduced, emphasising the importance of the quantum memristor and its feedback loop in establishing these key properties. The ability to achieve comparable or superior performance with a simplified, single-node quantum system opens up possibilities for building more scalable and energy-efficient quantum devices. 👉 More information🗞 Experimental Neuromorphic Computing Based on Quantum Memristor✍️ Mirela Selimović et al.🧠 DOI: http://link.aps.org/doi/10.1103/jknv-3tx7 More like thisQuantum SecurityA 0.11 threshold defines secure quantum data for learningQuantum HardwareDRDO and startup build 20 mK refrigerator for quantum computersQuantum ApplicationsIonQ tests quantum model on real satellite radar dataPhysicsRice University images show how graphene wrinkles affect flowStay currentSee today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals. Tags: