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Register a new userArithmetic on a Distributed-Memory Quantum Multicomputer
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We evaluate the performance of quantum arithmetic algorithms run on a distributed quantum computer (a quantum multicomputer). We vary the node capacity and I/O capabilities, and the network topology. The tradeoff of choosing between gates executed remotely, through ``teleported gates on entangled pairs of qubits (telegate), versus exchanging the relevant qubits via quantum teleportation, then executing the algorithm using local gates (teledata), is examined. We show that the teledata approach performs better, and that carry-ripple adders perform well when the teleportation block is decomposed so that the key quantum operations can be parallelized. A node size of only a few logical qubits performs adequately provided that the nodes have two transceiver qubits. A linear network topology performs acceptably for a broad range of system sizes and performance parameters. We therefore recommend pursuing small, high-I/O bandwidth nodes and a simple network. Such a machine will run Shors algorithm for factoring large numbers efficiently.
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The quantum multicomputer consists of a large number of small nodes and a qubus interconnect for creating entangled state between the nodes. The primary metric chosen is the performance of such a system on Shors algorithm for factoring large numbers: specifically, the quantum modular exponentiation step that is the computational bottleneck. This dissertation introduces a number of optimizations for the modular exponentiation. My algorithms reduce the latency, or circuit depth, to complete the modular exponentiation of an n-bit number from O(n^3) to O(n log^2 n) or O(n^2 log n), depending on architecture. Calculations show that these algorithms are one million times and thirteen thousand times faster, when factoring a 6,000-bit number, depending on architecture. Extending to the quantum multicomputer, five different qubus interconnect topologies are considered, and two forms of carry-ripple adder are found to be the fastest for a wide range of performance parameters. The links in the quantum multicomputer are serial; parallel links would provide only very modest improvements in system reliability and performance. Two levels of the Steane [[23,1,7]] error correction code will adequately protect our data for factoring a 1,024-bit number even when the qubit teleportation failure rate is one percent.
The paper proposes an improved quantum associative algorithm with distributed query based on model proposed by Ezhov et al. We introduce two modifications of the query that optimized data retrieval of correct multi-patterns simultaneously for any rate of the number of the recognition pattern on the total patterns. Simulation results are given.
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full use of quantum mechanical speedup, more transformation should be implemented on amplitudes. Here we propose the notion of quantum amplitude arithmetic (QAA) that intent to evolve the quantum state by performing arithmetic operations on amplitude. Based on the basic design of multiplication and addition operations, QAA can be applied to solve the black-box quantum state preparation problem and the quantum linear system problem with fairly low complexity, and evaluate nonlinear functions on amplitudes directly. QAA is expected to find applications in a variety of quantum algorithms.
We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high fidelity local unitary operations within each register, but the error probability for initialization, measurement, and entanglement generation can be very high (~5%). We demonstrate that with a reasonable time overhead our scheme can achieve deterministic non-local coupling gates between arbitrary two registers with very high fidelity, limited only by the imperfections from the local unitary operation. We estimate the clock cycle and the effective error probability for implementation of quantum registers with ion-traps or nitrogen-vacancy (NV) centers. Our new scheme capitalizes on a new efficient two-level pumping scheme that in principle can create Bell pairs with arbitrarily high fidelity. We introduce a Markov chain model to study the stochastic process of entanglement pumping and map it to a deterministic process. Finally we discuss requirements for achieving fault-tolerant operation with our register-based hybrid scheme, and also present an alternative approach to fault-tolerant preparation of GHZ states.
We demonstrate long-lived coherence in internal hyperfine states of a single Ca{43} trapped-ion qubit $[T_2=1.2(2)s]$, and in external motional states of a single Ca{40} trapped-ion qubit $[T_2=0.18(4)s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state $T_2$ time that we observe in Ca{43}, which has not previously been used as a trapped-ion qubit, is about one thousand times longer than that of physical qubits based on Ca{40} ions. Using a single spin-echo pulse to ``re-phase the internal state, we can detect no decoherence after 1s, implying an effective coherence time $T_2^{mbox{tiny SE}} gtish 45s$. This compares with timescales in this trap for single-qubit operations of ish 1us, and for two-qubit operations of ish 10us.
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