A Quantum-feedforward and classical-feedback separating structure adapted with monodirectional measurements; Blind qubit uncoupling capability and links with ICA
This paper deals with Blind Quantum Source Separation (BQSS). The proposed separating system only receives observed quantum states, each obtained after two quantum bits (qubits) were first independently initialized with values that this system does not know and then coupled according to a quantum operator involving parameter values that the separating system does not know a priori. This system aims at restoring the information contained in the initial qubit states. We previously tackled this problem by first converting the observed quantum state into data which have a classical (i.e. non-quantum) form and then only processing the latter data with classical means. We here propose a new approach, based on a separating system which uses quantum processing means (consisting of a specific unitary operator) in its feedforward path. Classical processing is only used in the feedback path of this system, to adapt its transfer function. The proposed adaptation method is based on binary-valued monodirectional output measurements and related to quantum disentanglement. We also analyze its relationships with classical Independent Component Analysis. We prove that this BQSS method partly restores the initial two-qubit states: it determines their components up to some phase and permutation indeterminacies.
This paper deals with Blind Quantum Source Separation (BQSS). The proposed separating system only receives observed quantum states, each obtained after two quantum bits (qubits) were first independently initialized with values that this system does not know and then coupled according to a quantum operator involving parameter values that the separating system does not know a priori. This system aims at restoring the information contained in the initial qubit states. We previously tackled this problem by first converting the observed quantum state into data which have a classical (i.e. non-quantum) form and then only processing the latter data with classical means. We here propose a new approach, based on a separating system which uses quantum processing means (consisting of a specific unitary operator) in its feedforward path. Classical processing is only used in the feedback path of this system, to adapt its transfer function. The proposed adaptation method is based on binary-valued monodirectional output measurements and related to quantum disentanglement. We also analyze its relationships with classical Independent Component Analysis. We prove that this BQSS method partly restores the initial two-qubit states: it determines their components up to some phase and permutation indeterminacies.
In the framework of Blind Quantum Source Separation, we investigate the adaptation of a separating system which receives coupled quantum bit (qubit) states and processes them with quantum means in its feedforward path, to uncouple them. We propose the first separation principle which ensures that the output qubit states of this system are disentangled and that they restore the non-entangled source qubit states up to limited indeterminacies. This separation principle exploits measurements of output spin components along two directions and has some links with the non-quantum Independent Component Analysis (ICA) principle. It opens the way to various practical separation criteria and algorithms, some of which are described here.
Our recent investigations of blind quantum source separation and process tomography methods for Heisenberg-coupled quantum bits (qubits) were focused on introducing a new separation principle, based on output disentanglement. We here extend them by proposing a more advanced implementation of their cost function and optimization algorithm. This leads us to move from a feedback to a feedforward adapting block, which avoids potential issues related to feedback in quantum circuits. The number of quantum source state preparations required to blindly adapt the separating system is thus strongly decreased (roughly from 107to 104), yielding much faster adaptation.
Classical, i.e. non-quantum, blind source separation (BSS) methods estimate unknown source signals by using only mixed signals obtained by transferring these source signals through a mixing transform, which typically has unknown parameter values. We developed quantum versions of BSS (called BQSS) and we extended them to the blind estimation of the unknown mixing/coupling parameters, thus achieving blind quantum process tomography (BQPT). In these investigations, the mixing parameter values remained fixed over time. We here analyze configurations where they vary. We show that the operation of our previous system may then be extended to handle BQPT and simple BQSS configurations. BQSS with rapidly evolving mixtures is more complex, because the fundamental quantum no-cloning theorem entails that each quantum state available at the output of our separating system cannot be copied so as to be used as the inputs of both (i) the subsequent quantum system which exploits it and (ii) the block of our separating system which continuously uses these states to update the separating system parameter values. We avoid this issue by introducing a quite different BQSS system, which is based on a master-slave structure and performs parallel adaptation and source state restoration. The proposed approach is thus based on spin electronics for implementing the considered quantum states, and on an original control loop in the proposed master-slave structure, which requires a specific measurement procedure, due to the quantum nature of the signals to be processed. This paper therefore bridges the gap between advanced information processing functions (especially self-learning algorithms) and the physical devices, defined at the atomic level, required for implementing such computations.
Blind Source Separation (BSS) is an active domain of Classical Information Processing, with well-identified methods and applications. The development of Quantum Information Processing has made possible the appearance of Blind Quantum Source Separation (BQSS), with a recent extension towards Blind Quantum Process Tomography (BQPT). This article investigates the use of several fundamental quantum concepts in the BQSS context and establishes properties already used without justification in that context. It mainly considers a pair of electron spins initially separately prepared in a pure state and then submitted to an undesired exchange coupling between these spins. Some consequences of the existence of the entanglement phenomenon, and of the probabilistic aspect of quantum measurements, upon BQSS solutions, are discussed. An unentanglement criterion is established for the state of an arbitrary qubit pair, expressed first with probability amplitudes and secondly with probabilities. The interest of using the concept of a random quantum state in the BQSS context is presented. It is stressed that the concept of statistical independence of the sources, widely used in classical BSS, should be used with care in BQSS, and possibly replaced by some disentanglement principle. It is shown that the coefficients of the development of any qubit pair pure state over the states of an orthonormal basis can be expressed with the probabilities of results in the measurements of well-chosen spin components.
The term “machine learning” especially refers to algorithms that derive mappings, i.e., input–output transforms, by using numerical data that provide information about considered transforms. These transforms appear in many problems related to classification/clustering, regression, system identification, system inversion, and input signal restoration/separation. We here analyze the connections between all these problems in the classical and quantum frameworks. We then focus on their most challenging versions, involving quantum data and/or quantum processing means, and unsupervised, i.e., blind, learning. We consider the general single-preparation quantum information processing (SIPQIP) framework that we have recently proposed. It involves methods that can work with a single instance of each (unknown) state, whereas usual methods are quite cumbersome because they have to very accurately create many copies of each (known) state. In our previous papers, we applied the SIPQIP approach to only one task [blind quantum process tomography (BQPT)], but it opens the way to a large range of other types of methods. In this article, we, therefore, propose various new SIPQIP methods that efficiently perform tasks related to system identification (blind Hamiltonian parameter estimation (BHPE), blind quantum channel identification/estimation, and blind phase estimation), system inversion and state estimation (blind quantum source separation (BQSS), blind quantum entangled state restoration (BQSR), and blind quantum channel equalization), and classification. Numerical tests show that our SIPQIP framework, moreover, yields much more accurate estimation than the usual multiple-preparation approach. Our methods are especially useful in aquantum computer, which we propose to more briefly call a “quamputer”: BQPT and BHPE simplify the characterization of quamputer gates; BQSS and BQSR yield quantum gates that may be used to compensate for the nonidealities that alter states stored in quantum registers and open the way to very general self-adaptive quantum gates.
Many methods for processing classical or quantum data are based on estimating some parameters, e.g. those of adaptive filters, artificial neural networks (including deep learning approaches), blind source separation systems or quantum gates. For classical signals, these methods include stochastic algorithms, such as stochastic gradient descent. We here first introduce a partly related, general, type of stochastic algorithms for quantum data and we prove the asymptotic efficiency of the proposed estimator. We then show the attractiveness of this stochastic approach for the quantum version of blind multiple-input multiple-output system identification and blind source separation: the resulting model estimation methods can operate with a single copy of each considered quantum state, whereas the previous methods require many copies of the same (unknown) states to be available and are thus "less blind". Numerical tests show that good performance is obtained with 104such quantum states.