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arXiv:2409.07886

Non-unital noise in a superconducting quantum computer as a computational resource for reservoir computing

Monzani, Francesco, Ricci, Emanuele, Nigro, Luca, Enrico Prati

Published Sep 12, 2024• 2 citations
arXivHTMLPDF

Abstract

We identify a noise model that ensures the functioning of an echo state network employing a gate-based quantum computer for reservoir computing applications. Energy dissipation induced by amplitude damping drastically improves the short-term memory capacity and expressivity of the network, by simultaneously providing fading memory and richer dynamics. There is an ideal dissipation rate that ensures the best operation of the echo state network around $γ\sim$ 0.03. Nevertheless, these beneficial effects are stable as the intensity of the applied noise increases. The improvement of the learning is confirmed by emulating a realistic noise model applied to superconducting qubits, paving the way for the application of reservoir computing methods in current non-fault-tolerant quantum computers.

DOI
10.48550/arxiv.2409.07886

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We identify a noise model that ensures the functioning of an echo state network employing a gate-based quantum computer for reservoir computing applications. Energy dissipation induced by amplitude damping drastically improves the short-term memory capacity and expressivity of the network, by simultaneously providing fading memory and richer dynamics. There is an ideal dissipation rate that ensures the best operation of the echo state network around γ∼γ\simγ∼ 0.03. Nevertheless, these beneficial effects are stable as the intensity of the applied noise increases. The improvement of the learning is confirmed by emulating a realistic noise model applied to superconducting qubits, paving the way for the application of reservoir computing methods in current non-fault-tolerant quantum computers.
Quantum reservoir computing has emerged as a promising machine learning paradigm for processing temporal data on near-term quantum devices, as it exploits the large computational capacity of qubits without suffering from typical issues arising when training variational quantum circuits. In particular, quantum gate-based echo state networks have proven effective when the evolution of the reservoir circuit is non-unital. Nonetheless, a method for ensuring a tunable and stable non-unital circuit evolution was lacking. We propose an algorithm that induces damping by applying a controlled rotation to each qubit in the reservoir. It enables tunable, circuit-level amplitude amplification of the zero state, maintaining the system away from the maximally mixed state and preventing information loss caused by repeated mid-circuit measurements. The algorithm is inherently stable over time, as it can process arbitrarily long input sequences, beyond the coherence time of individual qubits, by inducing arbitrary damping on each qubit. Moreover, we show that quantum correlations between qubits improve memory retention, underscoring the potential utility of a quantum system as a computational reservoir. We demonstrate, through standard reservoir computing benchmarks, that this algorithm enables robust and scalable quantum random computing on fault-tolerant quantum hardware.
Reservoir computing is a versatile paradigm in computational neuroscience and machine learning that uses recurrent neural networks to process time-dependent inputs. We leverage noise in gate-based quantum computers to enforce the fading memory property of a quantum circuit acting as a reservoir. We test the learning architecture on standard bench-marking tasks, such as NARMA and short-term memory tasks, by providing numerical evidence supporting the existence of an optimal noise regime that enhances predictive performances. This critical behavior indicates the presence of a regime in which several network capabilities, such as short-term memory capacity and expressivity, are maximized. Our results pave the way for the efficient use of current noisy quantum devices in quantum machine learning applications.
Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing, Scientific Reports, 13:8790, 2023] suggests that certain channels can, in appropriate regimes, improve performance by enriching the reservoir's effective dynamics. Motivated by this idea we propose a geometric mechanism to explain how non-unital noise applied together with a universal gate set leads to a faster approach to Haar-like distributions of the final states. We find that noise of this kind induces an effective volume expansion on the manifold of pure states. In order to intuitively understand this we use a minimal 1 qubit model where we take the amplitude damping channel and combine it with a renormalization rule that associates to each resulting mixed state a representative pure state. This composition defines a globally expanding nonlinear map on the space of pure states. We analytically derive the local area expansion factor and identify the global expansion threshold. Finally, we combine amplitude damping with the G3 = {H, T, CNOT} universal gate set to show how the approach to Haar-like behavior is faster in an appropriate parameter region. This leads us to propose noise as a possible resource in future quantum algorithms.
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Quantum Reservoir Computing (QRC) exploits the rich dynamics of quantum many-body systems to process time-dependent information with high-dimensional state spaces. While neutral atom arrays offer a scalable platform for this paradigm, realizing intrinsic temporal memory without relying on external classical buffering requires precise control over the relaxation dynamics of the system. We address the necessity of specific non-unitary dynamics for enforcing fading memory while overcoming the lack of separability. This study simulates and empirically identifies the specific dynamical regimes required to maximize the computational capacity of the reservoir, addressing the amount of dissipation, the effectiveness of lying at the edge of quantum chaos, and that of time-multiplexing compared to the scaling of the physical size of the system. Here we show that controlled dissipation is strictly necessary to induce echo state property, fading memory, and separability, in neutral atom arrays. Computational performance increases at the edge of quantum chaos. The counter-intuitive residual memory provided by the unital phase damping channel is justified by introducing a model based on pure outputs. The consequent implementation enables the solution of complex non-linear tasks, such as the Mackey-Glass time series, with as few as N=5N=5N=5 atoms. We establish a rigorous framework for engineering dissipative quantum reservoirs required for intrinsic temporal processing on near-term quantum devices.
While the accuracy of qubit operations has been greatly improved in the last decade, further development is demanded to achieve the ultimate goal: a fault-tolerant quantum computer that can solve real-world problems more efficiently than classical computers. With growing fidelities even subtle effects of environmental noise such as qubit–reservoir correlations and non-Markovian dynamics turn into the focus for both circuit design and control. To guide progress, we disclose, in a numerically rigorous manner, a comprehensive picture of the single-qubit dynamics in presence of a broad class of noise sources and for entire sequences of gate operations. Thermal reservoirs ranging from Ohmic to deep 1 / f ɛ -like sub-Ohmic behavior are considered to imitate realistic scenarios for superconducting qubits. Apart from dynamical features, fidelities of the qubit performance over entire sequences are analyzed as a figure of merit. The relevance of retarded feedback and long-range qubit–reservoir correlations is demonstrated on a quantitative level, thus, providing a deeper understanding of the limitations of performances for current devices and guiding the design of future ones. Published by the American Physical Society 2024