Quantum Computing Algorithms Research Articles

Relativistic electronic structure studies on the heaviest elements

AbstractSpectacular developments in relativistic quantum theory and computational algorithms in the last two decades allowed for accurate predictions of properties of the heaviest elements and their experimental behaviour. The most recent works in this area of investigations are overviewed. Preference is given to those related to experimental research. The role of relativistic effects is elucidated.

Quantum annealing with Jarzynski equality

We show a practical application of a well-known nonequilibrium relation, the Jarzynski equality, in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. It has been disclosed that the ordinary quantum computational algorithm to solve a kind of hard optimization problems, has a bottleneck that its computational time is restricted to be extremely slow without relevant errors. However, by our novel strategy shown in the present study, we might overcome such a difficulty.

Quantum-inspired evolutionary algorithms: a survey and empirical study

Quantum-inspired evolutionary algorithms, one of the three main research areas related to the complex interaction between quantum computing and evolutionary algorithms, are receiving renewed attention. A quantum-inspired evolutionary algorithm is a new evolutionary algorithm for a classical computer rather than for quantum mechanical hardware. This paper provides a unified framework and a comprehensive survey of recent work in this rapidly growing field. After introducing of the main concepts behind quantum-inspired evolutionary algorithms, we present the key ideas related to the multitude of quantum-inspired evolutionary algorithms, sketch the differences between them, survey theoretical developments and applications that range from combinatorial optimizations to numerical optimizations, and compare the advantages and limitations of these various methods. Finally, a small comparative study is conducted to evaluate the performances of different types of quantum-inspired evolutionary algorithms and conclusions are drawn about some of the most promising future research developments in this area.

Intelligent control systems. I. Quantum computing and self-organization algorithm

The role and methodology of application of quantum computing in problems of design of robust intelligent control systems under the conditions of contingency control situations are discussed. The quantum self-organization control algorithm, which contains the self-organization control algorithm for robust knowledge bases as the particular case, is developed. The satisfaction of the introduced thermodynamic criterion (in the form of the minimum of the generalized entropy in the established relation between such qualitative control characteristics as stability, controllability, and robustness) is the goal of application of the quantum self-organization control algorithm for knowledge bases used in the control loop. The essentially nonlinear and globally unstable control object is used as the example for application of the quantum self-organization control algorithm to the solution of the vector optimization problem based on the decomposition of knowledge bases.

Real applications of quantum communications in China

The first metropolitan quantum cryptography network for government administration, which is named “QGovernment”, has recently been field tested in Wuhu, Anhui Province by researchers of Key Laboratory of Quantum Information (CAS). Based on quantum cryptography, the network can guarantee the unconditional security for information transmission in an open channel. Information security has become more and more important during the process of knowledge-based economic globalization. For both organizations and individuals, the anti-wiretapping and anti-tamper secure communication is the basic guarantee for all of the confidential solutions. However, the security of major classical cryptography realizations, including the privatekey cryptosystem and the public-key cryptosystem, is based on the computational complexity of the cipher algorithm. At present, the rapid developments of distributed computing, ASIC design and especially the quantum computer and quantum algorithm have brought out unprecedented challenges to classical cryptography. The cases of sensitive information leakage, hacking and cracking are increasing. Consequently, a brand-new generation of quantum cryptography is refined as an urgent demand of secure communication. Quantum cryptography exploits the quantum state as the information carriers, such as photons, to distribute secret keys remotely. The basic principles of quantum mechanics ensure that any attacking or tampering behavior of eavesdroppers will be perceived by legitimate users. Combined with the quantum key distribution and the “one-time pad” algorithm, quantum cryptography can establish unconditional secure communication between legal users, for now and the future. In the process of QKD industrialization, the stability of the QKD system and the network techniques are two heavy cruxes. The Wuhu quantum cryptography network implements the Faraday-Michelson Interferometer (FMI) system, a unidirectional QKD scheme with the strict proof of its security and stability, which has the proprietary intellectual property rights. The significance of the FMI system is that it can auto-compensate the influence of the birefringence in the transmitting channel that will jeopardize the performance of QKD system. Several field demonstrations including Beijing-Tianjin QKD experiment at 2004, four-port star type network in Beijing at 2007 and the Wuhu quantum cryptography network for government administration at 2009, have clearly shown that the stability and robustness of this QKD basic device is sufficient for practical implementations. Networking is a milestone for the popularization of quantum cryptography service. However, the no-clone theorem of quantum system makes data traffic difficult to route in the net while guaranteeing the security of the protocol. The Wuhu cryptography network assembles the widely-used techniques of wavelength routing, active optical switch routing and trusted relay to construct a hierarchical structure. A full-mesh backbone network is built with a quantum router in the center to supply a no-congestion communication among all the gateways, while the quantum switch based on the time multiplexing can achieve a balance for subnets between network efficiency and speed. In addition, trusted relay is a compromising method to extend the scale of the network as long as a practical quantum repeater is still missing. The whole implementation of this hierarchical framework is a key step toward the actualization of practical large-

Robust and fast geometric quantum computation with multiqubit gates in cavity QED

A scheme is proposed for realizing geometric quantum computation with one-qubit unitary gates and $N$-qubit $(N\ensuremath{\ge}2)$ phase gates in cavity QED. In the scheme, the cavity field and excited states are virtually excited by controlling appropriately atom-field couplings and engineering adiabatic passage; thus the gate operations are insensitive to the cavity decay and the atomic spontaneous emission. Furthermore, the $N$-qubit $(N\ensuremath{\ge}2)$ geometric phase gates can be realized just by one step and the required time does not increase with the number of qubits, which can significantly reduce complexity of physical realization of practical quantum computation and quantum algorithms.

Deciphering the NMR Fingerprints of the Disordered System with Quantum Chemical Studies

Recent developments in solid-state NMR techniques helped acquire high-resolution NMR spectra for solid systems with structural disorder. But the structural origin of the observed chemical shift nonequivalence in these systems has not been revealed. We report a quantum chemical investigation of the solid-state NMR spectrum in N,N-bis(diphenylphosphino)-N-((S)-alpha-methylbenzyl)amine, where eight nonequivalent (31)P NMR chemical shifts were resolved with a range of 13.0 ppm. Results from using different quantum chemical methods, computational algorithms, intermolecular effects, and structures indicate that for the disordered system, geometry optimization gives the best accord with experimental NMR chemical shifts, which has a theory-versus-experiment correlation R(2) = 0.949 and SD = 1.1 ppm, or R(2) = 0.994 and SD = 0.4 ppm when the average of two unassigned NMR shifts for each molecule is used. In addition, these calculations indicate that the experimental chemical shift nonequivalence in this system is mainly a consequence of the different geometries around the phosphorus atoms due to disordered environments. The experimental (31)P NMR chemical shifts are well correlated (R(2) = 0.981) with two conformation angles and one bond length, each associated with one of the three bonding interactions around the phosphorus atoms. These results will facilitate the use of quantum chemical techniques in structural characterization of disordered solids and elucidation of NMR properties.

Quantum Computer Algorithm for Parity Determination Based on Quantum Counting

A new quantum computer algorithm is proposed for determining the parity of function f(x) by using quantum counting algorithm. The parity of function f(x) can be determined by counting exactly the number of satisfying f(x)=−1, which is equivalent to determine the number of solutions, M, to an N item search problem. The algorithm can be accomplished in time of order \(\Theta(\sqrt{k(N-k)})\) .

QCMPI: A parallel environment for quantum computing

QCMPI is a quantum computer (QC) simulation package written in Fortran 90 with parallel processing capabilities. It is an accessible research tool that permits rapid evaluation of quantum algorithms for a large number of qubits and for various “noise” scenarios. The prime motivation for developing QCMPI is to facilitate numerical examination of not only how QC algorithms work, but also to include noise, decoherence, and attenuation effects and to evaluate the efficacy of error correction schemes. The present work builds on an earlier Mathematica code QDENSITY, which is mainly a pedagogic tool. In that earlier work, although the density matrix formulation was featured, the description using state vectors was also provided. In QCMPI, the stress is on state vectors, in order to employ a large number of qubits. The parallel processing feature is implemented by using the Message-Passing Interface (MPI) protocol. A description of how to spread the wave function components over many processors is provided, along with how to efficiently describe the action of general one- and two-qubit operators on these state vectors. These operators include the standard Pauli, Hadamard, CNOT and CPHASE gates and also Quantum Fourier transformation. These operators make up the actions needed in QC. Codes for Grover's search and Shor's factoring algorithms are provided as examples. A major feature of this work is that concurrent versions of the algorithms can be evaluated with each version subject to alternate noise effects, which corresponds to the idea of solving a stochastic Schrödinger equation. The density matrix for the ensemble of such noise cases is constructed using parallel distribution methods to evaluate its eigenvalues and associated entropy. Potential applications of this powerful tool include studies of the stability and correction of QC processes using Hamiltonian based dynamics. Program summary Program title: QCMPI Catalogue identifier: AECS_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4866 No. of bytes in distributed program, including test data, etc.: 42 114 Distribution format: tar.gz Programming language: Fortran 90 and MPI Computer: Any system that supports Fortran 90 and MPI Operating system: developed and tested at the Pittsburgh Supercomputer Center, at the Barcelona Supercomputer (BSC/CNS) and on multi-processor Macs and PCs. For cases where distributed density matrix evaluation is invoked, the BLACS and SCALAPACK packages are needed. Has the code been vectorized or parallelized?: Yes Classification: 4.15 External routines: LAPACK, SCALAPACK, BLACS Nature of problem: Analysis of quantum computation algorithms and the effects of noise. Solution method: A Fortran 90/MPI package is provided that contains modular commands to create and analyze quantum circuits. Shor's factorization and Grover's search algorithms are explained in detail. Procedures for distributing state vector amplitudes over processors and for solving concurrent (multiverse) cases with noise effects are implemented. Density matrix and entropy evaluations are provided in both single and parallel versions. Running time: Test run takes less than 1 minute using 2 processors.

Quantum computer gate simulations

A new interactive simulator for Quantum Computation has been developed for simulation of the universal set of quantum gates and for construction of new gates of up to 3 qubits. The simulator also automatically generates an equivalent quantum circuit for any arbitrary unitary transformation on a qubit. Available quantum computer simulators attempt to emulate the various physical realisations of quantum computation, simulate existing quantum algorithms or are aimed at facilitating the development of new algorithms. However, because of the level of advancement and complexity of quantum computation algorithms, these simulators tend to be quite complex, at least from a novice's point of view. As a result of this, beginners are often at a loss when trying to interact with them. The simulator here proposed therefore is aimed at bridging the gap somewhat, making quantum computer simulation more accessible to novices in the field. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 433-446

Photonic Implementation of Quantum Computation Algorithm Based on Spatial Coding

Several implementation methods of quantum computation algorithm by conventional computer have been explored for large-scale emulation. Due to the lack of quantum effects, these methods generally require exponential growth of the size of the hardware with increase of the number of qubits. In this paper, the spatial coding, which is an effective digital optical computing technique, is studied as an efficient implementation method of quantum computation algorithms. In the proposed scheme, quantum information is represented by the intensity and the phase of elemental cells. We confirmed correct operation of the quantum teleportation algorithm by computer simulation. We also demonstrated a photonic implementation of some of the quantum gates experimentally.

Quantum phase gate through a dispersive atom-field interaction

We propose a scheme for realizing a two-qubit quantum phase gate between atoms inside a high-$Q$ optical cavity. In the scheme, the dispersive interaction between atoms and the cavity field induces photon-number Stark shift, which can yield a resonant interaction inside one selected atom-field subspace and leave the others in a highly dispersive regime. Due to the selective atom-cavity interaction, (1) the scheme only requires commonly addressing the atoms inside the optical cavity during the gate operation, and (2) it can be directly used to implement an $N$-qubit conditional phase gate. These properties can significantly reduce the number of operations for implementing quantum computation and quantum algorithms.

Joint review of "An Introduction to Quantum Computing Algorithms by Arthur O. Pittenger," Birkhäuser, ISBN: 0817641270; Quantum Computing by Mika Hirvensalo," Springer, ISBN: 3540667830; and "Classical and Quantum Computation by A. Yu. Kitaev, A. Shen, and M. N. Vyalyi," American Mathematical Society, ISBN: 082182161X

Joint review of "An Introduction to Quantum Computing Algorithms by Arthur O. Pittenger," Birkhäuser, ISBN: 0817641270; Quantum Computing by Mika Hirvensalo," Springer, ISBN: 3540667830; and "Classical and Quantum Computation by A. Yu. Kitaev, A. Shen, and M. N. Vyalyi," American Mathematical Society, ISBN: 082182161X

Solid-State Qubits with Current-Controlled Coupling

The ability to switch the coupling between quantum bits (qubits) on and off is essential for implementing many quantum-computing algorithms. We demonstrated such control with two flux qubits coupled together through their mutual inductances and through the dc superconducting quantum interference device (SQUID) that reads out their magnetic flux states. A bias current applied to the SQUID in the zero-voltage state induced a change in the dynamic inductance, reducing the coupling energy controllably to zero and reversing its sign.

WHAT IS QUANTUM INFORMATION?

The main purpose of this review is to deal with questions related to the nature of quantum information and particularly with quantum entanglement as an important component of quantum information and computing. We will not discuss here quantum computer algorithms, like the algorithm by Shor, or their advantages and disadvantages. We only cover the material that lies at the foundations of quantum information and computing and epistemological questions. We attempt to connect the famous debate between Einstein and Bohr on quantum entanglement to some of the latest work on qubits and quantum computing and to the mathematical theorems that form the basis of these discussions, particularly the theorem of Bell. We present a critical analysis of this material and hope that this will give the reader a better understanding of what can be said with certainty about the nature of quantum information.

QUANTUM COMPUTING, GROVER'S SEARCH ALGORITHM AND ITS APPLICATIONS IN BIOINFORMATICS

This article reviews quantum computing and quantum algorithms. Some insights into its potential in speeding up computations are covered, with emphasis on the use of Grover's Search. In the last section, we discuss applications of quantum algorithm to bioinformatics. In particular, the extension of quantum counting algorithm to protein mass spectra counting is proposed.

Neuromorphic quantum computation with energy dissipation

Real parallel computing with a quantum computer attracts vast interest due to its extreme high potential. We propose a neuromorphic quantum computation algorithm based on an adiabatic Hamiltonian evolution with energy dissipation. This algorithm can be applied to problems if a cost function can be expressed in a quadratic form. This requirement results from the fact that our Hamiltonian is designed by following a method similar to an artificial neural network (ANN). The state of an ANN is often trapped at local minima, and the network outputs an error. Since the state of a quantum system with the proposed algorithm is always in the ground state according to the adiabatic theorem, it is not necessary to be concerned that the quantum state is trapped at local minima. However, there is no guarantee that a quantum algorithm based on an adiabatic Hamiltonian evolution with degeneration or level crossing is successfully executed. We show successful numerical simulation results with the proposed algorithm by introducing energy dissipation to keep the quantum state staying in the ground state, and then we show an application to the $n$-queen problem, which is one of the combinatorial optimization problems.

Prospects for Quantum Dot Implementation of Adiabatic Quantum Computers for Intractable Problems

Schemes are examined for implementing quantum computers to solve problems that cannot be solved in polynomial time on classical computers. Special attention is given to the newly proposed adiabatic quantum computation algorithms. We explore the ways in which the latter might be easier to implement than the more conventional approach.

Ab initio study of optimal control of ammonia molecular vibrational wavepackets: Towards molecular quantum computing

Optimal control theory is applied to a molecular vibrational system in light of its possible application to quantum computing (QC). We present the numerical results of an ammonia molecular vibrational model system with two modes: a bending mode and an asymmetric stretching mode. We demonstrate logic gates fundamental to QC algorithms, namely Hadamard and controlled-NOT gates. Our results show that averages of population transfers at each gate are above 93% high fidelity. A mode that has a double-well structured potential is found to have many transfer pathways, which facilitates obtaining optimal laser pulses.

Quantum chaos algorithms and dissipative decoherence with quantum trajectories

Using the methods of quantum trajectories we investigate the effects of dissipative decoherence in a quantum computer algorithm simulating dynamics in various regimes of quantum chaos including dynamical localization, the quantum ergodic regime, and quasi-integrable motion. As an example we use the quantum sawtooth algorithm which can be implemented in a polynomial number of quantum gates. It is shown that the fidelity of quantum computation decays exponentially with time and that the decay rate is proportional to the number of qubits, number of quantum gates, and per gate dissipation rate induced by external decoherence. In the limit of strong dissipation the quantum algorithm generates a quantum attractor which may have a complex or simple structure. We also compare the effects of dissipative decoherence with the effects of static imperfections.