We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query complexity of the algorithm depends only on the scaling of the measurement sensitivity with the number of distinct spin sub-ensembles. From a practical point of view, the proposed algorithm may result in an exponential speedup, compared to known quantum and classical summing algorithms. However in general, this advantage exists only if the total number of function samples is below a threshold value which depends on the measurement sensitivity.
Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensembl…
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.
We propose an effective realization of a complete set of elementary quantum gates in the solid-state quantum computer based on the multi-atomic coherent (MAC-) ensembles in the QED cavity. Here, we use the two-ensemble qubit encoding and swapping-based operations that together provide implementation of any encoded single-qubit operation by three elementary gates and the encoded controlled-NOT operation is performed in a single step. This approach simplifies a physical realization of universal quantum computing and adds the immunity to a number of errors. We also demonstrate that the proposed a…
Recently a new form of quantum memory has been proposed. The storage medium is an ensemble of electron spins, coupled to a stripline cavity and an ancillary readout system. Theoretical studies suggest that the system should be capable of storing numerous qubits within the ensemble, and an experimental proof-of-concept has already been performed. Here we show that this minimal architecture is not limited to storage but is in fact capable of full quantum processing by employing measurement-based entanglement. The technique appears to be remarkably robust against the anticipated dominant error ty…
Quantum computing with an inhomogeneously broadened ensemble of ions: Suppression of errors from detuning variations by specially adapted pulses and coherent population trapping
We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper Pair Box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.
We experimentally demonstrate quantum machine learning using NMR based on a framework of quantum reservoir computing. Reservoir computing is for exploiting natural nonlinear dynamics with large degrees of freedom, which is called a reservoir, for a machine learning purpose. Here we propose a concrete physical implementation of a quantum reservoir using controllable dynamics of a nuclear spin ensemble in a molecular solid. In this implementation, we demonstrate learning of nonlinear functions with binary or continuous variable inputs with low mean squared errors. Our implementation and demonstr…
Variational quantum algorithm (VQA), which is comprised of a classical optimizer and a parameterized quantum circuit, emerges as one of the most promising approaches for harvesting the power of quantum computers in the noisy intermediate scale quantum (NISQ) era. However, the deployment of VQAs on contemporary NISQ devices often faces considerable system and time-dependant noise and prohibitively slow training speeds. On the other hand, the expensive supporting resources and infrastructure make quantum computers extremely keen on high utilization. In this paper, we propose a virtualized way of…
We study a hybrid quantum computing system using nitrogen-vacancy center ensemble (NVE) as quantum memory, current-biased Josephson junction (CBJJ) superconducting qubit fabricated in a transmission line resonator (TLR) as quantum computing processor and the microwave photons in TLR as quantum data bus. The storage process is seriously treated by considering all kinds of decoherence mechanisms. Such a hybrid quantum device can also be used to create multi-qubit W states of NVEs through a common CBJJ. The experimental feasibility and challenge are justified using currently available technology.
Selective control of qubits in a quantum register for the purposes of quantum information processing represents a critical challenge for dense spin ensembles in solid state systems. Here we present a protocol that achieves a complete set of selective single and two-qubit gates on nuclear spins in such an ensemble in diamond facilitated by a nearby NV center. The protocol suppresses internuclear interactions as well as unwanted coupling between the NV center and other spins of the ensemble to achieve quantum gate fidelities well exceeding 99% . Notably, our method can be applied to weakly coupl…
We study experimentally demonstrated single-electron ${}^{12}$C CNT QD with significant spin-orbit interaction as a scalable quantum computer candidate. Both electron spin and orbital angular momentum can serve as a logical qubit for quantum processing. We introduce macroscopic quantum memory for the system in a form of injected either magnetic or spin carrying atomic ensemble into the nanotube. CNT provides with a stable atomic trap in finite temperature and with one-dimensional nuclear spin lattice in an external magnetic field. The electron is coupled to the atomic ensemble through either m…
In finite many-body quantum systems such as nuclei, atoms, mesoscopic systems like quantum dots and small metallic grains, interacting spin systems modeling quantum computing core and BEC, the interparticle interactions are essentially two-body in nature. Therefore, it is more appropriate to represent the complex Hamiltonian of these systems by random ensembles that incorporate the two-body nature of interactions. These ensembles are generically called embedded Gaussian ensembles (EGEs). The aim of the present thesis is to identify and systematically analyze many different physically relevant …
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects of emerging nonlinear dynamics and chaos upon the quantum averages of relevant observables and quantum probabilities are exemplified for a version of Chirikov's standard map on \mathbb{C} . Both the individual orbits and ensemble properties are addressed so that the Poincaré map for Chirikov's standard map, in the current quantum setting, is reinterpreted in …
Universidade Federal Rural de Pernambuco（伯南布哥联邦农村大学）；Universidade Federal de Pernambuco（伯南布哥联邦大学）
Through superposition, a quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning is a subfield of quantum computing that explores the potential of quantum computing to enhance machine learning algorithms. An approach of quantum machine learning named quantum ensembles of quantum classifiers consists of using superposition to build an exponentially large ensemble of classifiers to be trained with an optimization-free learning algorithm. In this work, we investigate how the quantum ensemble works with…
Spin-wave excitations in ensembles of atoms are gaining attention as a quantum information resource. However, current techniques with atomic spin waves do not achieve universal quantum information processing. We conduct a theoretical analysis of methods to create a high-capacity universal quantum processor and network node using an ensemble of laser-cooled atoms, trapped in a one-dimensional periodic potential and coupled to a ring cavity. We describe how to establish linear quantum processing using a lambda-scheme in a rubidium-atom system, calculate the expected experimental operational fide…
We report an optical one-way quantum computing experiment with stationary quantum memory involved. First we create a hybrid four-qubit cluster state with two qubits propagating as photons and the other two stationary and stored in a laser-cooled atomic-ensemble quantum memory, and characterize it with entanglement witness and quantum state tomography. Then, by making use of this cluster state and fast operations of electro-optic modulators, we realize memory-assisted feedforward operations and demonstrate deterministic single-qubit rotation as an example.
In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble consisting of finite copies of a single probabilistic machine, hence is as powerful as a probabilistic Turing machine (PTM). Then the hypothesis--that is, the SEnM can effectively simulate a general circuit model of QC--is tested by introducing an information-theoretic inequality, named readout inequality. The inequality is satisfied by the SEnM and imposes a cri…
Due to the immense potential of quantum computers and the significant computing overhead required in machine learning applications, the variational quantum classifier (VQC) has received a lot of interest recently for image classification. The performance of VQC is jeopardized by the noise in Noisy Intermediate-Scale Quantum (NISQ) computers, which is a significant hurdle. It is crucial to remember that large error rates occur in quantum algorithms due to quantum decoherence and imprecision of quantum gates. Previous studies have looked towards using ensemble learning in conventional computing …
We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity. We use the two-qubit encoding and swapping-based operations to simplify a physical realization of universal quantum computing and add the immunity to a number of errors. This approach allows to implement any encoded single-qubit operation by three elementary gates and the encoded controlled- NOT operation can be performed in a single step. The considerable a…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements leads to the generation of ensembles of random unitaries, where each random unitary is identified with a string of possible measurement results. We show that repeating an MB scheme an efficient number of times, on a simple graph state, with measurements at fixed angles and no feed-forward corrections, produces a random unitary ensemble that is an ε-approximate t…
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator provides a number of advantages when used in a fault-tolerant architecture for quantum computing, most notably that Gaussian operations suffice to implement all single- and two-qubit Clifford gates. The main drawback of the encoding is that the logical states themselves are challenging to produce. Here we present a method for generating optical GKP-encoded qubits by coupling an atomic ensemble to a squeezed state of light. Particular outcomes of a subsequent spin measurement of the ensemble herald successful generatio…
Experimental setup for the combined study of spin ensembles and superconducting quantum circuits
Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Kazan Federal University（喀山联邦大学）；Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS（俄罗斯科学院喀山科学中心联邦研究中心扎沃伊斯基物理技术研究所）
In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical prediction and uses quantum and classical computing, but it is based on a probabilistic algorithm. Let $N$ be a number of classifiers from an ensemble model and $O(T)$ be the running time of prediction on one classifier. In classical case, an ensemble model gets answers from each classifier and "averages" the result. The running time in classical case is $O…
Sampling equilibrium ensembles of dense polymer mixtures is a paradigmatically hard problem in computational physics, even in lattice-based models. Here, we develop a formalism based on interacting binary tensors that allows for tackling this problem using quantum annealing machines. Our approach is general in that properties such as self-avoidance, branching, and looping can all be specified in terms of quadratic interactions of the tensors. Microstates realizations of different lattice polymer ensembles are then seamlessly generated by solving suitable discrete energy-minimization problems. …
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins magnetically coupled to a superconducting resonator. We report on a cavity QED experiment with magnetically anisotropic Er3+:Y2SiO5 crystals and demonstrate strong coupling of rare-earth spins to a lumped element resonator. In addition, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without a…
We present a method for network-capable quantum computing that relies on holographic spin-wave excitations stored collectively in ensembles of qubits. We construct an orthogonal basis of spin waves in a one-dimensional array and show that high-fidelity universal linear controllability can be achieved using only phase shifts, applied in both momentum and position space. Neither single-site addressability nor high single-qubit cooperativity is required, and the spin waves can be read out with high efficiency into a single cavity mode for quantum computing and networking applications.
Hybrid quantum-classical systems: statistics, entropy, microcanonical ensemble and its connection to the canonical ensemble
Universidad de Zaragoza（萨拉戈萨大学）；Centro de Astropartículas y Física de Altas Energías (CAPA)（高能粒子与天体物理中心）；Universidad de Burgos（布尔戈斯大学）；Universidad Nacional de Educacion a Distancia（国家远程教育大学）；Universidad de Valladolid（巴利亚多利德大学）；Institute for Biocomputation and Physics of Complex Systems (BIFI)（生物计算与复杂系统物理研究所）；Instituto Universitario de Matemáticas y Aplicaciones (IUMA)（数学与应用大学研究所）
Affine Subcode Ensemble Decoding for Degeneracy-Aware Quantum Error Correction
Communications Engineering Lab (CEL), Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院通信工程实验室）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）
