Quantum Reservoir Research Articles

Experimental photonic quantum memristor

Memristive devices are a class of physical systems with history-dependent dynamics characterized by signature hysteresis loops in their input–output relations. In the past few decades, memristive devices have attracted enormous interest in electronics. This is because memristive dynamics is very pervasive in nanoscale devices, and has potentially groundbreaking applications ranging from energy-efficient memories to physical neural networks and neuromorphic computing platforms. Recently, the concept of a quantum memristor was introduced by a few proposals, all of which face limited technological practicality. Here we propose and experimentally demonstrate a novel quantum-optical memristor (based on integrated photonics) that acts on single-photon states. We fully characterize the memristive dynamics of our device and tomographically reconstruct its quantum output state. Finally, we propose a possible application of our device in the framework of quantum machine learning through a scheme of quantum reservoir computing, which we apply to classical and quantum learning tasks. Our simulations show promising results, and may break new ground towards the use of quantum memristors in quantum neuromorphic architectures.

Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes

These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines provides a pedagogical introduction to the theory of non-reciprocal quantum interactions and devices. The goal is connect various approaches and concepts, including Hamiltonians encoding synthetic gauge fields, scattering descriptions, quantum master equations, and non-Hermitian Hamiltonians. The importance of having both non-trivial synthetic gauge fields and dissipation for obtaining non-reciprocal interactions is stressed. Connections to broader topics such as quantum reservoir engineering and the quantum theory of continuous-measurement based feedforward are also discussed.

Nonlinear input transformations are ubiquitous in quantum reservoir computing

Abstract The nascent computational paradigm of quantum reservoir computing presents an attractive use of near-term, noisy-intermediate-scale quantum processors. To understand the potential power and use cases of quantum reservoir computing, it is necessary to define a conceptual framework to separate its constituent components and determine their impacts on performance. In this manuscript, we utilize such a framework to isolate the input encoding component of contemporary quantum reservoir computing schemes. We find that across the majority of schemes the input encoding implements a nonlinear transformation on the input data. As nonlinearity is known to be a key computational resource in reservoir computing, this calls into question the necessity and function of further, post-input, processing. Our findings will impact the design of future quantum reservoirs, as well as the interpretation of results and fair comparison between proposed designs.

Quantum Reservoir Computing for Speckle Disorder Potentials

Quantum reservoir computing is a machine learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and fast training strategy. In this work, this technique is introduced with a quantum reservoir of spins and it is applied to find the ground state energy of an additional quantum system. The quantum reservoir computer is trained with a linear model to predict the lowest energy of a particle in the presence of different speckle disorder potentials. The performance of the task is analyzed with a focus on the observable quantities extracted from the reservoir and it is shown to be enhanced when two-qubit correlations are employed.

Natural quantum reservoir computing for temporal information processing

Reservoir computing is a temporal information processing system that exploits artificial or physical dissipative dynamics to learn a dynamical system and generate the target time-series. This paper proposes the use of real superconducting quantum computing devices as the reservoir, where the dissipative property is served by the natural noise added to the quantum bits. The performance of this natural quantum reservoir is demonstrated in a benchmark time-series regression problem and a practical problem classifying different objects based on temporal sensor data. In both cases the proposed reservoir computer shows a higher performance than a linear regression or classification model. The results indicate that a noisy quantum device potentially functions as a reservoir computer, and notably, the quantum noise, which is undesirable in the conventional quantum computation, can be used as a rich computation resource.

Learning Temporal Quantum Tomography.

Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which requires a vast number of resources. However, tomography for a quantum device with temporal processing, which is fundamentally different from standard tomography, has not been formulated. We develop a practical and approximate tomography method using a recurrent machine learning framework for this intriguing situation. The method is based on repeated quantum interactions between a system called quantum reservoir with a stream of quantum states. Measurement data from the reservoir are connected to a linear readout to train a recurrent relation between quantum channels applied to the input stream. We demonstrate our algorithms for representative quantum learning tasks, followed by the proposal of a quantum memory capacity to evaluate the temporal processing ability of near-term quantum devices.

Transfer of quantum information via a dissipative protocol for data classification

We consider the equilibration dynamics of a two-level quantum system in contact with multiple structured reservoirs that carry quantum information. We develop a micromaser-like quantum master equation based on repeated interactions and show that some information is transferred from the quantum reservoir into the quantum system in the steady-state. In the results we obtained from the analytical methods we used, we have developed a clear expression of the information transferred to the two-level system in terms of information reservoir parameters and interaction coefficients of the probe qubit with the reservoirs. We propose an open quantum classifier model by developing a binary classification rule by use of these results. We also develop the analytical description of the classification process by quantum parameter estimation.

Analytical evidence of nonlinearity in qubits and continuous-variable quantum reservoir computing

The natural dynamics of complex networks can be harnessed for information processing purposes. A paradigmatic example are artificial neural networks used for machine learning. In this context, quantum reservoir computing (QRC) constitutes a natural extension of the use of classical recurrent neural networks using quantum resources for temporal information processing. Here, we explore the fundamental properties of QRC systems based on qubits and continuous variables. We provide analytical results that illustrate how nonlinearity enters the input–output map in these QRC implementations. We find that the input encoding through state initialization can serve to control the type of nonlinearity as well as the dependence on the history of the input sequences to be processed.

Machine-Learning Approach Optimizes Well Spacing

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 201698, “Finding a Trend Out of Chaos: A Machine-Learning Approach for Well-Spacing Optimization,” by Zheren Ma, Ehsan Davani, SPE, and Xiaodan Ma, SPE, Quantum Reservoir Impact, et al., prepared for the 2020 SPE Annual Technical Conference and Exhibition, originally scheduled to be held in Denver, Colorado, 5–7 October. The paper has not been peer reviewed. Data-driven decisions powered by machine-learning (ML) methods are increasing in popularity when optimizing field development in unconventional reservoirs. However, because well performance is affected by many factors, the challenge is to uncover trends within all the noise. By leveraging basin-level knowledge captured by big data sculpting, integrating private and public data with the use of uncertainty quantification, a process the authors describe as augmented artificial intelligence (AI) can provide quick, science-based answers for well spacing and fracturing optimization and can assess the full potential of an asset in unconventional reservoirs. A case study in the Midland Basin is detailed in the complete paper. Introduction Augmented AI is a process wherein ML and human expertise are coupled to improve solutions. The augmented AI work flow (Fig. 1) starts with data sculpting, which includes information retrieval; data cleaning and standardization; and smart, deep, and systematic data quality control (QC). Feature engineering generates all relevant parameters entering the ML model. More than 50 features have been generated for this work and categorized. The final step is to perform model tuning and ensemble, evaluating model robustness and generating model explanation and uncertainty quantification. Geology The complete paper provides a detailed geological background of the Permian Basin and its Wolfcamp unconventional layer, an organic-rich shale formation with tight reservoir properties. To find a solution for the multidimensional well-spacing problem in the Permian Basin, multiple sources and types of data were gathered using publicly available sources. The detailed geological attributes, including structure, petrophysics, geochemistry, basin-level features, and cultural information (such as counties or lease boundaries) have been combined in an integrated database to extract and generate features for the ML algorithm. Most attributes are available either in a limited number of wells, mostly vertical, or through the low number of available cored wells across the basin. Therefore, a significant amount of data imputation has been processed with mapping exercises using geostatistical modeling techniques. The mapping process augmented the ML attribute-generation step because these features were distributed in both vertical and lateral dimensions. All horizontal wells within the area of interest across the Permian Basin have been resampled with the logged and mapped information. The geological features also are reengineered into multiple indices to reduce the number of labeled features to include in the ML process. This feature-reduction process also has helped in ranking and selecting the most-important parameters relevant to the well-spacing problem. Here, a key attribute called the shale-oil index was introduced, which is generated for the ML-driven process and is used in understanding the level of contribution of geological sweet spots to well-spacing optimization. In addition, the initial well, reservoir, or laboratory data, including logs, have been normalized before mapping and modeling to eliminate potential bias. This study has focused on Wolfcamp layers; however, both geological and engineering attribute generation work flows used for this practical ML methodology to find optimization solutions for common problems are highly applicable to other unconventional layers, such as Bone Spring or Spraberry.

Dynamical Phase Transitions in Quantum Reservoir Computing.

Closed quantum systems exhibit different dynamical regimes, like many-body localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in quantum reservoir computing, an unconventional computing paradigm recently extended into the quantum regime that exploits dynamical systems to solve nonlinear and temporal tasks. We establish that the thermal phase is naturally adapted to the requirements of quantum reservoir computing and report an increased performance at the thermalization transition for the studied tasks. Uncovering the underlying physical mechanisms behind optimal information processing capabilities of spin networks is essential for future experimental implementations and provides a new perspective on dynamical phases.

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

AbstractQuantum reservoir computing and quantum extreme learning machines are two emerging approaches that have demonstrated their potential both in classical and quantum machine learning tasks. They exploit the quantumness of physical systems combined with an easy training strategy, achieving an excellent performance. The increasing interest in these unconventional computing approaches is fueled by the availability of diverse quantum platforms suitable for implementation and the theoretical progresses in the study of complex quantum systems. In this review article, recent proposals and first experiments displaying a broad range of possibilities are reviewed when quantum inputs, quantum physical substrates and quantum tasks are considered. The main focus is the performance of these approaches, on the advantages with respect to classical counterparts and opportunities.

Realising and compressing quantum circuits with quantum reservoir computing

Quantum computers require precise control over parameters and careful engineering of the underlying physical system. In contrast, neural networks have evolved to tolerate imprecision and inhomogeneity. Here, using a reservoir computing architecture we show how a random network of quantum nodes can be used as a robust hardware for quantum computing. Our network architecture induces quantum operations by optimising only a single layer of quantum nodes, a key advantage over the traditional neural networks where many layers of neurons have to be optimised. We demonstrate how a single network can induce different quantum gates, including a universal gate set. Moreover, in the few-qubit regime, we show that sequences of multiple quantum gates in quantum circuits can be compressed with a single operation, potentially reducing the operation time and complexity. As the key resource is a random network of nodes, with no specific topology or structure, this architecture is a hardware friendly alternative paradigm for quantum computation.

Threshold for a Discrete-Variable Sensor of Quantum Reservoirs

Quantum sensing employs quantum resources of a sensor to attain a smaller estimation error of physical quantities than the limit constrained by classical physics. To measure a quantum reservoir, which is significant in decoherence control, a nonunitary-encoding sensing scheme becomes necessary. However, previous studies showed that the reservoir-induced degradation to quantum resources of the sensor makes the errors divergent with the increase of encoding time. We here propose a scheme to use $N$ two-level systems as the sensor to measure a quantum reservoir. A threshold, above which the shot-noise-limited sensing error saturates or even persistently decreases with the encoding time, is uncovered. Our analysis reveals that it is due to the formation of a bound state of the total sensor-reservoir system. Solving the outstanding error-divergency problem in previous studies, our result supplies an insightful guideline in realizing a sensitive measurement of quantum reservoirs.

Ground-state cooling of mechanical resonators by quantum reservoir engineering

Ground-state cooling of multiple mechanical resonators becomes vital to employ them in various applications ranging from ultra-precise sensing to quantum information processing. Here we propose a scheme for simultaneous cooling of multiple degenerate or near-degenerate mechanical resonators to their quantum ground-state, which is otherwise a challenging goal to achieve. As opposed to standard laser cooling schemes where coherence renders the motion of a resonator to its ground-state, we consider an incoherent thermal source to achieve the same aim. The underlying physical mechanism of cooling is explained by investigating a direct connection between the laser sideband cooling and “cooling by heating”. Our advantageous scheme of cooling enabled by quantum reservoir engineering can be realized in various setups, employing parametric coupling of a cooling agent with the target systems. We also discuss using non-thermal baths to simulate ultra-high temperature thermal baths for cooling.

Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing

Quantum reservoir computing aims at harnessing the rich dynamics of quantum systems for machine-learning purposes. It can be used for online time series processing while having a remarkably low training cost. Here, we establish the potential of continuous-variable Gaussian states of linear dynamical systems for quantum reservoir computing. We prove that Gaussian resources are enough for universal reservoir computing. We find that encoding the input into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that the full potential of the proposed model can be reached by encoding to quantum fluctuations, such as squeezed vacuum, instead of classical fields or thermal fluctuations. Our results introduce a research paradigm for reservoir computing harnessing quantum systems and engineered Gaussian quantum states.

Non-Markovian sensing of a quantum reservoir

Quantum sensing explores protocols using the quantum resource of sensors to achieve highly sensitive measurement of physical quantities. The conventional schemes generally use unitary dynamics to encode quantities into sensor states. In order to measure the spectral density of a quantum reservoir, which plays a vital role in controlling the reservoir-caused decoherence to microscopic systems, we propose a nonunitary-encoding optical sensing scheme. Although the nonunitary dynamics for encoding in turn degrades the quantum resource, we surprisingly find a mechanism to make the encoding time a resource to improve the precision and to make the squeezing of the sensor a resource to surpass the shot-noise limit. Our result shows that it is due to the formation of a sensor-reservoir bound state. Enriching the family of quantum sensing, our scheme gives an efficient way to measure the quantum reservoir and might supply an insightful support to decoherence control.

Quantum reservoir computing with a single nonlinear oscillator

Realizing the promise of quantum information processing remains a daunting task, given the omnipresence of noise and error. Adapting noise-resilient classical computing modalities to quantum mechanics may be a viable path towards near-term applications in the noisy intermediate-scale quantum era. Here, we propose continuous variable quantum reservoir computing in a single nonlinear oscillator. Through numerical simulation of our model we demonstrate quantum-classical performance improvement, and identify its likely source: the nonlinearity of quantum measurement. Beyond quantum reservoir computing, this result may impact the interpretation of results across quantum machine learning. We study how the performance of our quantum reservoir depends on Hilbert space dimension, how it is impacted by injected noise, and briefly comment on its experimental implementation. Our results show that quantum reservoir computing in a single nonlinear oscillator is an attractive modality for quantum computing on near-term hardware.

Predicting excited states from ground state wavefunction by supervised quantum machine learning

Excited states of molecules lie in the heart of photochemistry and chemical reactions. The recent development in quantum computational chemistry leads to inventions of a variety of algorithms that calculate the excited states of molecules on near-term quantum computers, but they require more computational burdens than the algorithms for calculating the ground states. In this study, we propose a scheme of supervised quantum machine learning which predicts the excited-state properties of molecules only from their ground state wavefunction resulting in reducing the computational cost for calculating the excited states. Our model is comprised of a quantum reservoir and a classical machine learning unit which processes the measurement results of single-qubit Pauli operators with the output state from the reservoir. The quantum reservoir effectively transforms the single-qubit operators into complicated multi-qubit ones which contain essential information of the system, so that the classical machine learning unit may decode them appropriately. The number of runs for quantum computers is saved by training only the classical machine learning unit, and the whole model requires modest resources of quantum hardware that may be implemented in current experiments. We illustrate the predictive ability of our model by numerical simulations for small molecules with and without noise inevitable in near-term quantum computers. The results show that our scheme reproduces well the first and second excitation energies as well as the transition dipole moment between the ground states and excited states only from the ground states as inputs. We expect our contribution will enhance the applications of quantum computers in the study of quantum chemistry and quantum materials.

Information Processing Capacity of Spin-Based Quantum Reservoir Computing Systems

The dynamical behaviour of complex quantum systems can be harnessed for information processing. With this aim, quantum reservoir computing (QRC) with Ising spin networks was recently introduced as a quantum version of classical reservoir computing. In turn, reservoir computing is a neuro-inspired machine learning technique that consists in exploiting dynamical systems to solve nonlinear and temporal tasks. We characterize the performance of the spin-based QRC model with the Information Processing Capacity (IPC), which allows to quantify the computational capabilities of a dynamical system beyond specific tasks. The influence on the IPC of the input injection frequency, time multiplexing, and different measured observables encompassing local spin measurements as well as correlations, is addressed. We find conditions for an optimum input driving and provide different alternatives for the choice of the output variables used for the readout. This work establishes a clear picture of the computational capabilities of a quantum network of spins for reservoir computing. Our results pave the way to future research on QRC both from the theoretical and experimental points of view.

Optimizing a quantum reservoir computer for time series prediction

Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient solving of temporal machine learning tasks such as speech recognition, time series prediction and natural language processing. Specifically, we study memory capacity and accuracy of a quantum reservoir computer based on the fully connected transverse field Ising model by investigating different forms of inter-spin interactions and computing timescales. We show that variation in inter-spin interactions leads to a better memory capacity in general, by engineering the type of interactions the capacity can be greatly enhanced and there exists an optimal timescale at which the capacity is maximized. To connect computational capabilities to physical properties of the underlaying system, we also study the out-of-time-ordered correlator and find that its faster decay implies a more accurate memory. Furthermore, as an example application on real world data, we use QRC to predict stock values.