Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary quantum states is challenging as the paradigm of efficient protocols has remained in applying specific techniques for different types of quantum states. Here we introduce a quantum state tomography platform based on the framework of reservoir computing. It forms a quantum neural network, and operates as a comprehensive device for reconstructing an arbitrary quantum state (finite dimensional or continuous variable). This is achieved with only measuring the average occupation numbers in a single physical setup, without the need of any knowledge of optimum measurement basis or correlation measurements.
To investigate the dynamical behavior of a quantum system embedded in a memory environment, it is crucial to obtain the knowledge of the reservoir spectral density. However, such knowledge is usually based on a priori assumptions about the environment. In this paper, we put forward a method to obtain key information about the reservoir spectral density of an optomechanical resonator without additional assumptions about the spectral shape. This is achieved by detecting and analysing the optical transmission rate of the emitted light. In the weak optomechanical singlephoton coupling regime, we e…
The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum information processing developed on the principle of reservoir computing that is a form of artificial neural network. A quantum reservoir processor can perform qualitative tasks like recognizing quantum states that are entangled as well as quantitative tasks like estimating a non-linear function of an input quantum state (e.g. entropy, purity or logarithmic nega…
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 transform…
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 compu…
Efficient quantum state measurement is important for maximizing the extracted information from a quantum system. For multi-qubit quantum processors in particular, the development of a scalable architecture for rapid and high-fidelity readout remains a critical unresolved problem. Here we propose reservoir computing as a resource-efficient solution to quantum measurement of superconducting multi-qubit systems. We consider a small network of Josephson parametric oscillators, which can be implemented with minimal device overhead and in the same platform as the measured quantum system. We theoreti…
Quantum machine learning represents a promising avenue for data processing, also for purposes of sequential temporal data analysis, as recently proposed in quantum reservoir computing (QRC). The possibility to operate on several platforms and noise intermediate-scale quantum devices makes QRC a timely topic. A challenge that has not been addressed yet, however, is how to efficiently include quantum measurement in realistic protocols, while retaining the reservoir memory needed for sequential time series processing and preserving the quantum advantage offered by large Hilbert spaces. In this wo…
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…
We study the quantum speed limit time for a two-qubit system interacts with indepen- dent and common reservoir. The system is initially prepared in a class of X-structure density matrix, namely the extended Werner-like states (EWL). We demonstrate that when reservoir enters to the non-Markovian regime, the quantum speed limit time de- crease more sharply in a common reservoir than independent reservoirs.
We show that the effects of decoherence on quantum steering ellipsoids can be controlled by a specific reservoir manipulating, in both Markovian and non-Markovian realms. Therefore, the so-called maximal steered coherence could be protected through reservoir engineering implemented by coupling auxiliary qubits to the reservoir.
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir computing relaxes the need for optimization of intra-network parameters, and is thus particularly attractive for near-term hardware-efficient quantum implementations. However, the complete description of practical quantum reservoir computers requires accounting for their placement in a quantum measurement chain, and its conditional evolution under measurement. C…
In this paper, we look into what happens to a quantum system under repeated measurements if it interacts with two independent reservoirs. In particular, we look at the behavior of a two-level system interacting with reservoirs consisting of harmonic oscillators. The interaction with one reservoir is weak with a dissipative-type coupling, while the interaction with the other reservoir is strong with a dephasing-type coupling. Using a polaron transformation, we show that the presence of the strongly coupled reservoir can actually reduce the decay rate of the quantum system due to the effect of t…
Quantum systems have an exponentially large degree of freedom in the number of particles and hence provide a rich dynamics that could not be simulated on conventional computers. Quantum reservoir computing is an approach to use such a complex and rich dynamics on the quantum systems as it is for temporal machine learning. In this chapter, we explain quantum reservoir computing and related approaches, quantum extreme learning machine and quantum circuit learning, starting from a pedagogical introduction to quantum mechanics and machine learning. All these quantum machine learning approaches are…
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level…
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 rese…
The non-Markovian master equations are derived to study quantum discord dynamics of two qubits coupled to a common reservoir and two independent reservoirs, respectively. We compare the dynamics under different parameters, such as reservoir spectra and resonant parameters, at high temperature and at zero temperature. The results indicate that the dynamics at these two extreme temperatures share similar characters, as well as differences.
We establish a quantum functional central limit for the dynamics of a system coupled to a Fermionic bath with a general interaction linear in the creation, annihilation and scattering of the bath reservoir. Following a quantum Markovian limit, we realize the open dynamical evolution of the system as an adapted quantum stochastic process driven by Fermionic Noise.
Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum reservoir computing is a relevant machine learning algorithm. Its simplicity of training and implementation allows to perform challenging computations on today available machines. In this Letter, we provide a criterion to select optimal quantum reservoirs, requiring few and simple gates. Our findings demonstrate that they render better results than other comm…
Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir.
Quantum Brownian motion of a rod-like particle is investigated in the frame work of system plus reservoir model. The quantum mechanical and classical limit for both translational and rotational motions are discussed. Correlation functions, fluctuation-dissipation relations and mean squared values of translational and rotational motions are obtained.
Currently, quantum reservoir computing is one of the most promising and experimentally accessible techniques for hybrid, quantum-classical machine learning. However, its applications are limited due to practical restrictions on the size of quantum systems and the influence of noise. Here we propose a novel approach to connect two quantum reservoirs in a network to overcome these issues and enhance their computing performance. To transfer information between quantum reservoirs, we perform optimized two-qubit non-selective measurements. We suggest a general heuristic optimization strategy based …
We investigate decoherence-free evolution (DFE) of quantum discord (QD) for two initially-correlated qubits in two finite-temperature reservoirs using an exactly solvable model. We study QD dynamics of the two qubits coupled to two independent Ohmic reservoirs when the two qubits are initially prepared in X-type quantum states. It is found that reservoir temperature significantly affects the DFE dynamics. We show that it is possible to control the DFE and to prolong the DFE time by choosing suitable parameters of the two-qubit system and 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-…
We consider a model of an optical cavity with a nonequilibrium reservoir consisting of a beam of identical two-level atom pairs (TLAPs) in the general X-state. We find that coherence of multiparticle nonequilibrium reservoir plays a central role on the potential work capability of cavity. We show that no matter whether there are quantum correlations in each TLAP (including quantum entanglement and quantum discord) or not the coherence of the TLAPs has an effect on the work capability of the cavity. Additionally, constructive and destructive interferences could be induced to influence the work …
The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects. The completely positive reduced dynamical map can be constructed in the Kraus representation. Quantum entanglement decays more slowly in the non-Markovian environment. The decoherence time for quantum entanglement can be markedly increased by the change of the memory kernel. It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reserv…
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 r…
We study dynamics of local quantum uncertainty (LQU) for a system of two cavities and two reservoirs. In the start, the cavities treated as two qubits are quantum correlated with each other, whereas reservoirs are neither correlated with each other nor with cavities. We answer two main questions in this work. First, how local quantum uncertainty decays from two quantum correlated cavities and grows among reservoirs. The second question is the examination of LQU developed among four qubits and also shed some light on its dynamics. We observe that LQU develops among reservoirs as kind of mirror …
We present a method for dealing with quantum systems coupled to a structured reservoir with any density of modes and with more than one excitation. We apply the method to a two-level atom coupled to the edge of a photonic band gap and a defect mode. Results pertaining to this system, provide the solution to the problem of two photons in the reservoir and possible generalization is discussed.
The reservoir memory effects can lead to information backflow and recurrence of the previously lost quantum correlations. We establish connections between the direction of information flow and variation of the geometric quantum discords (GQDs) measured respectively by the trace distance, the Hellinger distance, and the Bures distance for two qubits subjecting to the bosonic structured reservoirs, and unveil their dependence on a factor whose derivative signifies the (non-)Markovianity of the dynamics. By considering the reservoirs with Lorentzian and Ohmic-like spectra, we further demonstrated…
We consider a quantum Otto cycle operating between two squeezed thermal reservoirs. The influences of the squeezing degree on the optimization performance of quantum Otto heat engines and refrigerators are investigated. We demonstrate that under symmetric condition, the efficiency at maximum power (EMP) of heat engines and the coefficient of performance (COP) at maximum \c{hi} criterion of refrigerators are equal to Curzon-Ahlborn (CA) efficiency and CA COP, respectively. We also found that under asymmetric condition, the EMP of heat engines can be improved when the squeezing degree of hot the…
In this paper, the exact dynamics of open quantum systems in the presence of initial system-reservoir correlations is investigated for a photonic cavity system coupled to a general non-Markovian reservoir. The exact time-convolutionless master equation incorporating with initial system-reservoir correlations is obtained. The non-Markovian dynamics of the reservoir and the effects of the initial correlations are embedded into the time-dependent coefficients in the master equation. We show that the effects induced by the initial correlations play an important role in the non-Markovian dynamics o…
We demonstrate how an acoustic phonon bath when coupled to a quantum dot with the help of a bichromatic laser field may effectively form a quantum squeezed reservoir. This approach allows to achieve an arbitrary degree of squeezing of the effective reservoir and it incorporates the properties of the reservoir into two parameters, which can be controlled by varying the ratio of the Rabi frequencies of the bichromatic field. It is found that for unequal Rabi frequencies, the effective reservoir may appear as a quantum squeezed field of ordinary or inverted harmonic oscillators. When the Rabi fre…
Quantum reservoir networks based on decoherence-free subspaces
School of Nanoscience and Nanotechnology, Mahatma Gandhi University（马哈特玛甘地大学纳米科学与技术学院）；Space Research Institute RAS（俄罗斯科学院空间研究所）；National University of Science and Technology ’MISIS’（莫斯科国立科学技术大学 MISIS）
Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency and a Liouville space implementation of a time-discrete quantum memory, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and stru…
In this paper, we give a mechanism for controlling speedup of a single-qubit open quantum system by exclusively manipulating the system-reservoir bound states using additional non-interacting qubits. It is demonstrated that providing stronger bound states in the system-reservoir spectrum makes the single-qubit evolution with higher speed. We examine the performance of the mechanism for different spectral densities such as Lorentzian and Ohmic and find out the decisive role of bound states manipulation in speeding up of quantum evolution.
We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics processes is desired, we use concepts from collisional model to introduce a simple prototype of thermal reservoir based on $\mathcal{PT}$-symmetric Hamiltonians and study its effects under the thermalization process of a single harmonic oscillator prepared in a displaced thermal state. We verify that controlling the $\mathcal{PT}$-symmetric features of the r…
