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.
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.
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, in which the mixing parameter values almost always remained fixed over time. We here show that rapidly varying mixing is much more complex to handle, because unknown quantum states cannot be cloned, i.e. copied. We avoid this issue thanks to a specific separating system based on a master-slave structure. We provide an original analytical analysis of the performance of that structure, depending on the mismatch between its master and slave inverting blocks.
System identification and inversion are two closely related problems, which lead to various configurations. In the quantum framework, system identification was only studied in the non-blind (or supervised) mode, i.e. with known input states (in addition to known output states). It is then called quantum process tomography. We here develop its blind (or unsupervised) version, operating with unknown (unentangled) input states (which are here not controlled by an automated loop). Our approach takes advantage of the blind quantum source separation (i.e. blind multi-qubit system inversion) methods based on disentanglement that we recently introduced. It is detailed for Heisenberg spin coupling and could be extended to other classes of processes. It estimates the parameter values of the Heisenberg Hamiltonian.
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.
Quantum process tomography (QPT) methods aim at identifying, i.e., estimating, a given quantum process. QPT is a major quantum information processing tool, since it especially allows one to characterize the actual behavior of quantum gates, which are the building blocks of quantum computers. However, usual QPT procedures are complicated, since they set several constraints on the quantum states used as inputs of the process to be characterized. In this paper, we extend QPT so as to avoid two such constraints. On the one hand, usual QPT methods require one to know, hence to very precisely control (i.e., prepare), the specific quantum states used as inputs of the considered quantum process, which is cumbersome. We therefore propose a blind, or unsupervised, extension of QPT (i.e., BQPT), which means that this approach uses input quantum states whose values are unknown and arbitrary, except that they are requested to meet some general known properties (and this approach exploits the output states of the considered quantum process). On the other hand, usual QPT methods require one to be able to prepare many copies of the same (known) input state, which is constraining. In contrast, we propose ``single-preparation BQPT methods'' (SBQPT) , i.e., methods which can operate with only one instance of each considered input state. These two concepts are here illustrated with practical (S)BQPT methods which are numerically validated, in the case when (i) random pure states are used as inputs and their required properties are especially related to the statistical independence of the random variables that define them and (ii) the considered quantum process is based on cylindrical-symmetry Heisenberg spin coupling. As a benchmark, we moreover introduce nonblind QPT methods dedicated to the considered Heisenberg process, we analyze their theoretical behavior (this requires the tools developed in this paper for random input states), and we numerically test their sensitivity to systematic and nonsystematic errors, which are most likely to occur in practice. This shows that, even for very low preparation errors (especially systematic ones), these nonblind QPT methods yield much lower performance than our SBQPT methods. Our blind and single-preparation QPT concepts may be extended, e.g., to a much wider class of processes and to SBQPT methods based on other quantum state properties, as outlined in this paper.
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.
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.