We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits can be in pure states while other qubits in mixed states. It enables a single ensemble quantum computer to perform $"$single-instruction-multi-data" type of parallel computation. In Grover's algorithm and Shor's algorithm, parallel quantum computing can provide additional speedup. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani, and the Cleve-DiVincenzo algorithms can be re-utilized.
Here we made an analysis of the principles of a semiconductor NMR quantum computer and its developments. The known variant of an individual-access computer (B. Kane) and alternative solid-state bulk-ensemble approach versions allowing to avoid some difficulties in implementing the first variant are considered.
In ensemble (or bulk) quantum computation, measurements of qubits in an individual computer cannot be performed. Instead, only expectation values can be measured. As a result of this limitation on the model of computation, various important algorithms cannot be processed directly on such computers, and must be modified. We provide modifications of various existing protocols, including algorithms for universal fault--tolerant computation, Shor's factorization algorithm (which can be extended to any algorithm computing an NP function), and some search algorithms to enable processing them on ense…
Problems in realization of silicon-based solid-state NMR quantum computer with ensemble addressing to qubits are considered. It is presented the extension of Kane's scheme to ensemble approach version with strip gates. For the initialization of nuclear quantum states it is proposed to use the solid-state effect in ENDOR technique whereby the nuclear spins can be practically fully polarized or, that is the same, indirect cooled to the spin temperature less than ~ 1 mK. It is suggested the possible planar silicon topology of such ensemble quantum computer and shown that the measurement with stan…
We demonstrate the implementation of a quantum algorithm for estimating the number of matching items in a search operation using a two qubit nuclear magnetic resonance (NMR) quantum computer.
Bernstein and Varizani have given the first quantum algorithm to solve parity problem in which a strong violation of the classical imformation theoritic bound comes about. In this paper, we refine this algorithm with fewer resource and implement a two qubits algorithm in a single query on an ensemble quantum computer for the first time.
We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali atoms are presented.
A unifying framework for identifying distance and holonomy for decompositions of density operators is introduced. Parallelity between quantum ensembles is defined by minimizing this distance over allowed decompositions. The minimum is a property of a pair of states and coincides with the Bures distance. The parallelity condition imposes a connection (rule for parallel transport) that results in the Uhlmann holonomy for sequences of density operators. A distance and holonomy for spectral decompositions of density operators is identified as a sub-group restriction of the full decomposition freed…
As an ensemble scheme of solid-state NMR quantum computers the extension of Kane's many-qubits silicon scheme based on the array of 31 P donor atoms are spaced lengthwise of the strip gates is considered. The possible planar topology of such ensemble quantum computer is suggested. The estimation of the output NMR signal was performed and it was shown that for the number N>=10^5 of ensemble elements involving L~10^3 qubits each, the standard NMR methods are usable. As main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance freq…
It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of P donor atoms having nuclear spin I = 1/2. It is considered here, as main mechanisms of decoherence for low temperature (< 0.1 K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity diamagnetic atoms. It was made estimations of allowed concentrations of magnetic impurities and of spin temp…
The one-dimensional homonuclear periodic array of nuclear spins I = 1/2, owing to hyperfine interaction of nuclear spins with electronic magnetic moments in antiferromagnetic structure, is considered. The neighbor nuclear spins in such array are opposite oriented and have resonant frequencies determined by hyperfine interaction constant, applied magnetic field value and interaction with the left and right nuclear neighbor spins. The resonant frequencies difference of nuclear spins, when the neighbor spins have different and the same states, is used to control the spin dynamics by means of sele…
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that prime factorization is computationally difficult. Errors limit the effectiveness of quantum computers. Because of the exponential nature of quantum com puters, simulating the effect of errors on them requires a vast amount of processing and memory resources. In this paper we describe a parallel simulator which accesses the feasibility of quantum computers. We …
We describe portable software to simulate universal quantum computers on massive parallel computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI Altix 3700 and clusters of PCs running Windows XP. We study the performance of the software by simulating quantum computers containing up to 36 qubits, using up to 4096 processors and up to 1 TB of memory. Our results demonstrate that the simulator exhibits nearly ideal scaling as a func…
The first realization of solid state quantum computer was demonstrated recently by using artificial atoms -- transmons in superconducting resonator. Here, we propose a novel architecture of flexible and scalable quantum computer based on a waveguide circuit coupling many quantum nodes of controlled atomic ensembles. For the first time, we found the optimal practically attainable parameters of the atoms and circuit for 100{%} efficiency of quantum memory for multi qubit photon fields and confirmed experimentally the predicted perfect storage. Then we revealed self modes for reversible transfer …
In this paper, we present an ensemble algorithm for selection problem to find the k-th smallest element in the unsorted database. We will search the k-th smallest element by using "divide-and-conquer" strategy. We first divide D, the domain of the database, into two parts, determine which of the two parts the object element sought belongs to, and then concentrate on that part. We repeat divide that part until object element is found. The determination of which part depends on the output of ensemble counting scheme, which outputs the number of assignments satisfying the value of the oracle quer…
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 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…
Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.
We have analyzed an efficient integration of the multi-qubit echo quantum memory into the quantum computer scheme on the atomic resonant ensembles in quantum electrodynamics cavity. Here, one atomic ensemble with controllable inhomogeneous broadening is used for the quantum memory node and other atomic ensembles characterized by the homogeneous broadening of the resonant line are used as processing nodes. We have found optimal conditions for efficient integration of multi-qubit quantum memory modified for this analyzed physical scheme and we have determined a specified shape of the self tempor…
Creation of quantum computer is outstanding fundamental and practical problem. The quantum computer could be used for execution of very complicated tasks which are not solvable with the classical computers. The first prototype of solid state quantum computer was created in 2009 with superconducting qubits. However, it suffers from the decoherent processes and it is desirable to find more practical encoding of qubits with long-lived coherence. It could be single impurity or vacancy centers in solids, but their interaction with electromagnetic radiation is rather weak. So, here, ensembles of ato…
In the framework of a model for quantum computer media, a nondigital implementation of the arithmetic of the real numbers is described. For this model, an elementary storage "cell" is an ensemble of qubits (quantum bits). It is found that to store an arbitrary real number it is sufficient to use four of these ensembles and the arithmetic operations can be implemented by fixed quantum circuits.
We discuss the issues surrounding the implementation of quantum computation in rare-earth-ion doped solids. We describe a practical scheme for two qubit gate operations which utilise experimentally available interactions between the qubits. Possibilities for a scalable quantum computer are discussed.
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, the simulation methods using parallel processing are required. We have developed a general-purpose simulator for quantum computing on the parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We have performed Shor's factoriz…
Recent years have witnessed an unprecedented increase in experiments and hybrid simulations involving quantum computers. In particular, quantum annealers. Although quantum supremacy has not been established thus far, there exist a plethora of algorithms promising to outperform classical computers in the near-term future. Here, we propose a parallel in time approach to simulate dynamical systems designed to be executed already on present-day quantum annealers. In essence, purely classical methods for solving dynamics systems are serial. Therefore, their parallelization is substantially limited.…
This paper is devoted to such a fundamental problem of quantum computing as quantum parallelism. It is well known that quantum parallelism is the basis of the ability of quantum computer to perform in polynomial time computations performed by classical computers for exponential time. Therefore better understanding of quantum parallelism is important both for theoretical and applied research, cf. e.g. David Deutsch \cite{DD}. We present a realistic interpretation based on recently developed prequantum classical statistical field theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed …
The number of qubits in current quantum computers is a major restriction on their wider application. To address this issue, Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates. In this study, we theoretically analyse the (sufficient and necessary) separability conditions of multipartite quantum gates in finite or infinite dim…
The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using Controlled NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a Controlled NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distanc…
The mapping of quantum circuits to qubits represented by ion states in a storage ring quantum computer is examined. Serial, parallel and hybrid architectures for mapping such qubits onto a storage ring quantum computer are presented. Parallelism is an important part of the SRQC architecture in terms of multiple ions, windows and lasers. A "predecessor problem" that arises in such architectures is identified and a solution is proposed. Representative numerical sizing and timing calculations are presented. The entire methodology is very general and extends to several implementation options. Open…
A revised version of the massively parallel simulator of a universal quantum computer, described in this journal eleven years ago, is used to benchmark various gate-based quantum algorithms on some of the most powerful supercomputers that exist today. Adaptive encoding of the wave function reduces the memory requirement by a factor of eight, making it possible to simulate universal quantum computers with up to 48 qubits on the Sunway TaihuLight and on the K computer. The simulator exhibits close-to-ideal weak-scaling behavior on the Sunway TaihuLight,on the K computer, on an IBM Blue Gene/Q, a…
The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are expectation values of observables, is described in detail. A filtering scheme, which effectively determines expectation values on a limited portion of the quantum state, is presented and used to locate a single item for searches involving more than one marked item. A truncated version of Grover's algorithm, requiring fewer steps than the translated standard ve…
We have proposed the construction of optical quantum computer (OQC) on regular domain structure (RDS) crystal. By using RDS crystal, we can perform all the logical operations on one RDS crystal. Moreover, RDS crystals are parctically independent to the heating effects i.e., can perform logic operations constantly without cooling the RDS crystal. Also, we have proposed the quantum parallelsim i.e., parallel coherent laser beams are injected at the input of the RDS crystals. By using the RDS crystal we can perform the reduce the requirements of the linear and nonlinear optical components.
We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail qubit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design which we employ also demonstrates a signature for quantum parallelism which unambiguously delineates the desired quantum behavior from the merely classical. The experimental demonstration of our proposal using quantum …
Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local". It resorts a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long ra…
A new scheme is proposed which will permit electron spin resonance pulse techniques to be used to realize a quantum computer with a 100 qbits, or more. The computation is performed on effective pure states which correspond to off-diagonal blocks of the density matrix. Described is a scheme which very efficiently performs the preparation stage and which permits ``pseudo-projective measurement'' to be made on the output. With such measurements all members of the ensemble remain coherent.
The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in polynomial time on an NMR quantum computer. The NMR ensemble quantum computation is based on the quantum mechanical unitary dynamics that both a closed quantum system and its ensemble obey the same quantum mechanical unitary dynamics instead of on the pseudopure state or the effective pure state of the classical NMR quantum computation. Based on the new principle …
We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops down discontinuously as soon as a nonzero error is tolerated and the spectrum of the states is known with sufficient precision. For qubit ensembles, this feature leads to a 25% saving of memory space. Our compression protocols can be implemented efficiently on a quantum computer.
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-to…
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a composite system consisting of $N$ subsystems, where each subsystem is shared between two parties and the state of each subsystem is randomly sampled from a particular ensemble comprising the Bell states. We show that the success probability of perfectly identifying the state converges to $1$ as $N\rightarrow\infty$ if the entropy of the probability distributi…
Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translate infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the repr…
A viable approach for building large-scale quantum computers is to interlink small-scale quantum computers with a quantum network to create a larger distributed quantum computer. When designing quantum algorithms for such a distributed quantum computer, one can make use of the added parallelization and distribution abilities inherent in the system. An added difficulty to then overcome for distributed quantum computing is that a complex control system to orchestrate the various components is required. In this work, we aim to address these issues. We explicitly define what it means for a quantum…
Quantum computing represents a paradigm shift for computation requiring an entirely new computer architecture. However, there is much that can be learned from traditional classical computer engineering. In this paper, we describe the Parallel Research Kernels (PRK), a tool that was very useful for designing classical parallel computing systems. The PRK are simple kernels written to expose bottlenecks that limit classical parallel computing performance. We hypothesize that an analogous tool for quantum computing, Quantum Research Kernels (QRK), may similarly aid the co-design of software and ha…
Applicability of Rydberg atoms to quantum computers is examined from experimental point of view. In many theoretical proposals appeared recently, excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole-dipole interaction that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analyzed. We also present the results of modeling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S-37P and two-photon 37S-…
U.S. Army Research Laboratory（美国陆军研究实验室）；U.S. Military Academy（美国军事学院）；Army Cyber Institute（陆军网络研究所）
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine learning algorithms. We describe a generic mathematical model to leverage quantum parallelism to speed-up machine learning algorithms. We also apply quantum machine learning and quantum parallelism applied to a $3$-dimensional image that vary with time.
Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers
Paderborn University（帕德博恩大学）；Paderborn Center for Parallel Computing, Paderborn University（帕德博恩大学并行计算中心）；Dynamics of Condensed Matter and Institute for Sustainable Systems Design, Chair of Theoretical Chemistry, Paderborn University（帕德博恩大学凝聚态动力学与可持续系统设计研究所理论化学教席）；Department for Computer Science, Paderborn University（帕德博恩大学计算机科学系）
