Implementation Of Quantum Algorithms Research Articles

A Quantum Mechanics-Based Framework for EEG Signal Feature Extraction and Classification

Quantum machine learning (QML) is an emerging research field, which is devoted to devising and implementing quantum algorithms that could enable machine learning faster than that of classical computers. In this article, a hierarchic quantum mechanics-based framework is investigated to implement both the feature extraction and classification in the electroencephalogram (EEG) signal. First, the classical EEG signal dataset is prepared as a quantum state while the sign of the data point is preserved. The prepared quantum state is then evolved with the quantum wavelet packet transformation (QWPT) and the wavelet packet energy entropy (WPEE) feature is extracted as the input of the subsequent quantum classifier. We finally propose the improved quantum support vector machine with the arbitrary nonlinear kernel, which is employed to predict the label of the EEG signal. The complexity analysis indicates that the proposed framework provides exponential speedup over the same structured classical counterpart. Besides, the quantitative experimental results verify the feasibility and validity.

Reaction: Molecular Spins as Qubits

Floriana Tuna is a Leverhulme Trust Senior Research Fellow at the University of Manchester (UoM). She holds MSc and PhD degrees in chemistry from the University of Bucharest (1989) and National Academy of Romania (1997), respectively. She worked as a visiting DAAD fellow at the University of Heidelberg (Germany), a CNRS postdoctoral fellow at ICMCB Bordeaux (France), and a Marie Curie fellow at the University of Warwick (UK) before joining UoM in 2003. She received the Romanian Academy “Ilie Murgulescu” Prize for excellence in research in 2005 and has published over 300 high-impact papers. Her major interests are in coordination chemistry, molecular magnetism, and quantum information science.

An optimized quantum circuit for converting from sign–magnitude to two’s complement

Nowadays, one of the critical issues to implement quantum algorithms is the required number of elementary gates, qubits and delay. Current quantum computers and simulators are mainly prototypes, and there is a lack of computational resources. Therefore, it is necessary to optimize the quantum operations to reduce the necessary number of gates and qubits. This work presents a novel reversible circuit which is able to convert signed binary numbers to two’s complement of N digits in a quantum environment. The depth of the circuit is O(log N). It is based on the fastest out-of-place carry look-ahead addition quantum circuit currently available. This addition circuit has been adapted to make the conversion using the minimum number of gates and qubits, being faster than other adder circuits. A robust metric has been used to measure the quantum cost, delay, ancilla inputs and garbage outputs of the proposed converter. Moreover, it has been compared with others described in the literature.

Molecular spins for quantum computation.

Spins in solids or in molecules possess discrete energy levels, and the associated quantum states can be tuned and coherently manipulated by means of external electromagnetic fields. Spins therefore provide one of the simplest platforms to encode a quantum bit (qubit), the elementary unit of future quantum computers. Performing any useful computation demands much more than realizing a robust qubit-one also needs a large number of qubits and a reliable manner with which to integrate them into a complex circuitry that can store and process information and implement quantum algorithms. This 'scalability' is arguably one of the challenges for which a chemistry-based bottom-up approach is best-suited. Molecules, being much more versatile than atoms, and yet microscopic, are the quantum objects with the highest capacity to form non-trivial ordered states at the nanoscale and to be replicated in large numbers using chemical tools.

Synthetic Hilbert Space Engineering of Molecular Qudits: Isotopologue Chemistry.

One of the most ambitious technological goals is the development of devices working under the laws of quantum mechanics. Among others, an important challenge to be resolved on the way to such breakthrough technology concerns the scalability of the available Hilbert space. Recently, proof-of-principle experiments were reported, in which the implementation of quantum algorithms (the Grover's search algorithm, iSWAP-gate, etc.) in a single-molecule nuclear spin qudit (with d = 4) known as 159 TbPc2 was described, where the nuclear spins of lanthanides are used as a quantum register to execute simple quantum algorithms. In this progress report, the goal of linear and exponential up-scalability of the available Hilbert space expressed by the qudit-dimension "d" is addressed by synthesizing lanthanide metal complexes as quantum computing hardware. The synthesis of multinuclear large-Hilbert-space complexes has to be carried out under strict control of the nuclear spin degree of freedom leading to isotopologues, whereby electronic coupling between several nuclear spin units will exponentially extend the Hilbert space available for quantum information processing. Thus, improved multilevel spin qudits can be achieved that exhibit an exponentially scalable Hilbert space to enable high-performance quantum computing and information storage.

Realizing quantum linear regression with auxiliary qumodes

In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear regression, which utilizes both discrete and continuous quantum variables, in contrast to existing wisdoms based solely upon discrete qubits. In our framework, data information is encoded in a qubit system, while information processing is tackled using auxiliary continuous qumodes via qubit-qumode interactions. Moreover, it is also elaborated that finite squeezing is quite helpful for efficiently running the quantum algorithms in realistic setup. Comparing with an all-qubit approach, the present hybrid approach is more efficient and feasible for implementing quantum algorithms, still retaining exponential quantum speed-up.

Selective and efficient quantum process tomography in arbitrary finite dimension

The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows to acknowledge errors in the implementations of quantum algorithms; on the other, it allows to charcaterize unknown processes occurring in Nature. In previous works [Bendersky, Pastawski and Paz. Phys. Rev. Lett. 100, 190403 (2008) and Phys. Rev. A 80, 032116 (2009)] it was introduced a method to selectively and efficiently measure any given coefficient from the matrix description of a quantum channel. However, this method heavily relies on the construction of maximal sets of mutually unbiased bases (MUBs), which are known to exist only when the dimension of the Hilbert space is the power of a prime number. In this article, we lift the requirement on the dimension by presenting two variations of the method that work on arbitrary finite dimensions: one uses tensor products of maximally sets of MUBs, and the other uses a dimensional cutoff of a higher prime power dimension.

Implementing quantum algorithms on temporal photonic cluster states

Implementing quantum algorithms is essential for quantum computation. We study the implementation of three quantum algorithms by performing homodyne measurements on a two-dimensional temporal continuous-variable cluster state. We first review the generation of temporal cluster states and the implementation of gates using the measurement-based model. Alongside this we discuss methods to introduce non-Gaussianity into the cluster states. The first algorithm we consider is Gaussian Boson Sampling in which only Gaussian unitaries need to be implemented. Taking into account the fact that input states are also Gaussian, the errors due to the effect of finite squeezing can be corrected, provided a moderate amount of online squeezing is available. This helps to construct a large Gaussian Boson Sampling machine. The second algorithm is the continuous-variable Instantaneous Quantum Polynomial circuit in which one needs to implement non-Gaussian gates, such as the cubic phase gate. We discuss several methods of implementing the cubic phase gate and fit them into the temporal cluster state architecture. The third algorithm is the continuous-variable version of Grover's search algorithm, the main challenge of which is the implementation of the inversion operator. We propose a method to implement the inversion operator by injecting a resource state into a teleportation circuit. The resource state is simulated using the Strawberry Fields quantum software package.

Automated quantum operations in photonic qutrits

We report an experimental implementation of automated state transformations on spatial photonic qutrits following the theoretical proposal made by Baldij\~ao et al. [Phys. Rev. A 96, 032329 (2017)]. A qutrit state is simulated by using three Gaussian beams, and after some state operations, the transformed state is available in the end in terms of the basis state. The state transformation setup uses a spatial light modulator and a calcite-based interferometer. The results reveal the usefulness of the operation method. The experimental data show a good agreement with theoretical predictions, opening possibilities for explorations in higher dimensions and in a wide range of applications. This is a necessary step in qualifying spatial photonic qudits as a competitive setup for experimental research in the implementation of quantum algorithms which demand a large number of steps.

Recursive multiport schemes for implementing quantum algorithms with photonic integrated circuits

We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on $2d$ modes using a pair of circuits for the same operation on $d$ modes. The circuits operate on path-encoded qudits and realize $d$-dimensional unitary transformations on these states using linear optical networks with $O\left(d^2\right)$ optical elements. To evaluate the schemes against realistic errors, we ran simulations of proof-of-principle experiments using a simple fabrication model of silicon-based photonic integrated devices that employ directional couplers and thermo-optic modulators for beam splitters and phase shifters, respectively. We find that high-fidelity performance is achievable with our multiport circuits for $2$-qubit and $3$-qubit quantum Fourier transforms, and for quantum search on four-item and eight-item databases.

КВАНТОВЫЕ КОМПЬЮТЕРЫ И КВАНТОВЫЕ АЛГОРИТМЫ Часть 2. КВАНТОВЫЕ АЛГОРИТМЫ

The paper discusses principles of construction for quantum algorithms and their main features. Distinction of quantum parallelism from classical methods of high-performance computing is shown. Quantum algorithms design strategy is presented based on quantum circuits. Methods of programming for implementation of quantum algorithms using high-level languages are proposed. An approach to implement unitary transformations based on the oracle method is described.

Implementing quantum algorithms in hyperfine levels of ultracold polar molecules

Using optimal control, we implement simple quantum algorithms using hyperfine states of ultracold polar molecules. The qubits are encoded in hyperfine states of isolated 41K85Rb or 41K87Rb molecules or in hyperfine states of two neighboring molecules.

Keep your feet on the ground

Some complex problems in physics can be recast as finding the ground state of an interacting quantum system. Not getting excited along the way can be the challenging part. See Letter p.194 Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins. It is believed that the ground state of some naturally occurring spin systems can be effectively attained through a process called quantum annealing. Johnson et al. use quantum annealing to find the ground state of an artificial Ising spin system comprised of an array of eight superconducting flux qubits with programmable spin–spin couplings. With an increased number of spins, the system may provide a practical physical means to implement quantum algorithms, possibly enabling more effective approaches towards solving certain classes of hard combinatorial optimization problems.

Implementing quantum algorithms in hyperfine levels of ultracold polar molecules by optimal control

We numerically implement quantum algorithms in hyperfine levels of ultracold polar molecules. Logical operations are driven by pulses optimized by optimal control theory. All implementations take place in the lowest two rotational levels of the ground vibrational state of the ground (1)Σ(+) electronic state, exploiting the richness of the hyperfine energy structure and state mixing in static external fields. We show that it is possible to realize high fidelity complex logical operations with microsecond pulses. The possibility to run algorithms implemented on two interacting molecules is also demonstrated. (41)K(85)Rb and (41)K(87)Rb molecules are considered for the numerical simulations but the results are general and can be extended to other species.

Storing quantum information in chemically engineered nanoscale magnets

We review the implementation of quantum information processing using quantum spins and pulsed spin resonance techniques. Molecular magnets, nanoscale clusters of coupled transition metal ions, offer various potential advantages over other spin systems as the building blocks of a quantum computer. We describe the strategies which must be employed in order to implement quantum algorithms in such nanoscale magnets and explain why, when evaluating the suitability of any physical system for embodying a qubit, it is essential to determine the phase relaxation time appropriate for an individual molecular spin. Experiments utilising pulsed spin resonance techniques show that the phase relaxation times in at least some molecular magnets are long enough to permit multiple qubit operations to be performed.

Quantum Data and Control Made Easier

In this paper we define nQML, a functional quantum programming language that follows the “quantum data and control” paradigm. In comparison to Altenkirch and Grattage's QML, the control constructs of nQML are simpler and can implement quantum algorithms more directly and naturally. We avoid the unnecessary complexities of a linear type system by using types that carry the address of qubits in the quantum state. We provide a denotational semantics over density matrices and unitary transformations, inspired by Selinger's semantics for QPL. Our semantics leads naturally to an interpreter for nQML, written in Haskell. We also explore the extension of nQML with polymorphic higher-order functions.

Conscious Electromagnetic (CEMI) Field Theory

The conscious electromagnetic field theory (cemi field theory) is described which proposes that consciousness is a manifestation of the brain’s electromagnetic (em) field. The key feature of the brain’s em field is that it is capable of integrating vast quantities of information into a single physical system and it thereby accounts for the binding of consciousness. The cemi field theory is shown to be compatible with all the known facts about consciousness. Unlike quantum theories of consciousness, the cemi field theory does not require any special physical states in the brains; it is perfectly compatible with brain physiology. Nevertheless, recent work has shown that classical electromagnetic waves may be used to implement quantum algorithms; therefore the brain’s cemi field may be able to perform quantum computations (but without the requirement for quantum coherent states of matter).

Estimation of the heating rate of ions due to laser fluctuations when implementing quantum algorithms

We analyze numerically the heating of trapped ions due to laser intensity and phase fluctuations when implementing Grover's algorithm and the Quantum Fourier Transform. For a simpler analysis we assume that the stochastic processes are white noise processes and average over each noise as in [Phys. Rev. A. \textbf{57}, 3748, (1998)]. We investigate the fidelity and the heating rate for these algorithms using parameters estimated from experiments, and we can see the order of magnitude difference in the heating rate depending on the quantum algorithms.

Algorithm-based analysis of collective decoherence in quantum computation

In a quantum computer, qubits are often stored in identical two-level systems separated by a distance shorter than the characteristic wavelength of the reservoirs that are responsible for decoherence. In this case the collective qubit-reservoir interaction, rather than the individual qubit-reservoir interaction, may determine the decoherence properties. We study the collective decoherence behavior in between each step in certain quantum algorithms and propose a simple alternative of implementing quantum algorithms using a quantum trajectory that is close to a decoherence-free subspace that avoids unstable Dicke's superradiant states and Schrödinger's cat state.

Implementation of quantum algorithms with resonant interactions

We propose a scheme for implementing quantum algorithms with resonant interactions. Our scheme only requires resonant interactions between two atoms and a cavity mode, which is simple and feasible. Moreover, the implementation would be an important step towards the fabrication of quantum computers in cavity QED system.