We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits are in pure states while other qubits are in mixed states. It enables a single ensemble quantum computer to perform ``single-instruction-multidata'' type of parallel computation. Parallel quantum computing can provide additional speedup in Grover's algorithm and Shor's algorithm. 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 reutilized.
We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits are in pure states while other qubits are in mixed states. It enables a single ensemble quantum computer to perform ``single-instruction-multidata'' type of parallel computation. Parallel quantum computing can provide additional speedup in Grover's algorithm and Shor's algorithm. 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 reutilized.
We propose a model for parallel quantum computing in a single ensemble quantum computer using Haskell's software transaction memory. The parallel ensemble quantum computer possesses, besides quantum parallelism, a kind of classical single-instruction-multiple-data parallelism. It explores additional speedup by making quantum computers working in parallel, as in classical computation. The whole state is prepared in such a way a subset of qubits is in a mixed state representing the communicating quantum computers while the other qubits in pure state are the proper argument registers of each quantum computer. Essentially, this particular way of structuring the state of the parallel quantum computer fits with what is well know as multithreading programming. Software transactional memory is a promising new approach to programming shared-memory parallel programs. The functional programming language Haskell elegantly implements this abstraction for concurrent communication.
Speeding up of the processing of quantum algorithms has been focused on from the point of view of an ensemble quantum computer (EQC) working in a parallel mode. As a consequence of such efforts, additional speed up has been achieved for processing both Shor’s and Grover’s algorithms. On the other hand, in the literature there is scarce concern about the quantity of entanglement contained in EQC approaches, for this reason in the present work we study such a quantity. As a first result, an upper bound on the quantity of entanglement contained in EQC is imposed. As a main result we prove that equally weighted states are not appropriate for EQC working in parallel mode. In order that our results are not exclusively purely theoretical, we exemplify the situation by discussing the entanglement on an ensemble of n1 = 3 diamond quantum computers.
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and σ(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement.
The determination of the parity of a string of N binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least N∕2 oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor 2k, with k∊1,2,…,log2(N∕2), provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.
Quantum computing makes use of wave-function superposition to provide a computational system with remarkable possibilities. A computing bit is a 0 or 1, but a quantum bit, a qubit, is a superposition of two quantum states, of, say, an atom. A number n of qubits will then be in a superposition of 2n distinct states. An operation on such a state then does 2n simultaneous operations, demonstrating quantum parallelism. The possibilities of quantum computing are demonstrated via discussion of Deutch’s problem, Shor’s period-finding algorithm, and Grover’s search algorithm. Shor’s algorithm might allow the factoring of large numbers, which might enable the decoding of many encryption schemes. Details are given for the solution of Deutch’s problem. The analysis introduces certain operators, the NOT and Hadamard, that are used in computer logic.
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.