2,749 research outputs found
Algorithms on ensemble 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
Experimental magic state distillation for fault-tolerant quantum computing
Any physical quantum device for quantum information processing is subject to
errors in implementation. In order to be reliable and efficient, quantum
computers will need error correcting or error avoiding methods. Fault-tolerance
achieved through quantum error correction will be an integral part of quantum
computers. Of the many methods that have been discovered to implement it, a
highly successful approach has been to use transversal gates and specific
initial states. A critical element for its implementation is the availability
of high-fidelity initial states such as |0> and the Magic State. Here we report
an experiment, performed in a nuclear magnetic resonance (NMR) quantum
processor, showing sufficient quantum control to improve the fidelity of
imperfect initial magic states by distilling five of them into one with higher
fidelity
Making Classical Ground State Spin Computing Fault-Tolerant
We examine a model of classical deterministic computing in which the ground
state of the classical system is a spatial history of the computation. This
model is relevant to quantum dot cellular automata as well as to recent
universal adiabatic quantum computing constructions. In its most primitive
form, systems constructed in this model cannot compute in an error free manner
when working at non-zero temperature. However, by exploiting a mapping between
the partition function for this model and probabilistic classical circuits we
are able to show that it is possible to make this model effectively error free.
We achieve this by using techniques in fault-tolerant classical computing and
the result is that the system can compute effectively error free if the
temperature is below a critical temperature. We further link this model to
computational complexity and show that a certain problem concerning finite
temperature classical spin systems is complete for the complexity class
Merlin-Arthur. This provides an interesting connection between the physical
behavior of certain many-body spin systems and computational complexity.Comment: 24 pages, 1 figur
What is a quantum computer, and how do we build one?
The DiVincenzo criteria for implementing a quantum computer have been seminal
in focussing both experimental and theoretical research in quantum information
processing. These criteria were formulated specifically for the circuit model
of quantum computing. However, several new models for quantum computing
(paradigms) have been proposed that do not seem to fit the criteria well. The
question is therefore what are the general criteria for implementing quantum
computers. To this end, a formal operational definition of a quantum computer
is introduced. It is then shown that according to this definition a device is a
quantum computer if it obeys the following four criteria: Any quantum computer
must (1) have a quantum memory; (2) facilitate a controlled quantum evolution
of the quantum memory; (3) include a method for cooling the quantum memory; and
(4) provide a readout mechanism for subsets of the quantum memory. The criteria
are met when the device is scalable and operates fault-tolerantly. We discuss
various existing quantum computing paradigms, and how they fit within this
framework. Finally, we lay out a roadmap for selecting an avenue towards
building a quantum computer. This is summarized in a decision tree intended to
help experimentalists determine the most natural paradigm given a particular
physical implementation
Quantum Computation in Quantum-Hall Systems
We describe a quantum information processor (quantum computer) based on the
hyperfine interactions between the conduction electrons and nuclear spins
embedded in a two-dimensional electron system in the quantum-Hall regime.
Nuclear spins can be controlled individually by electromagnetic pulses. Their
interactions, which are of the spin-exchange type, can be possibly switched on
and off pair-wise dynamically, for nearest neighbors, by controlling
impurities. We also propose the way to feed in the initial data and explore
ideas for reading off the final results.Comment: 12 pages in LaTeX + 1 PostScript figur
Quantum Computing
Quantum mechanics---the theory describing the fundamental workings of
nature---is famously counterintuitive: it predicts that a particle can be in
two places at the same time, and that two remote particles can be inextricably
and instantaneously linked. These predictions have been the topic of intense
metaphysical debate ever since the theory's inception early last century.
However, supreme predictive power combined with direct experimental observation
of some of these unusual phenomena leave little doubt as to its fundamental
correctness. In fact, without quantum mechanics we could not explain the
workings of a laser, nor indeed how a fridge magnet operates. Over the last
several decades quantum information science has emerged to seek answers to the
question: can we gain some advantage by storing, transmitting and processing
information encoded in systems that exhibit these unique quantum properties?
Today it is understood that the answer is yes. Many research groups around the
world are working towards one of the most ambitious goals humankind has ever
embarked upon: a quantum computer that promises to exponentially improve
computational power for particular tasks. A number of physical systems,
spanning much of modern physics, are being developed for this task---ranging
from single particles of light to superconducting circuits---and it is not yet
clear which, if any, will ultimately prove successful. Here we describe the
latest developments for each of the leading approaches and explain what the
major challenges are for the future.Comment: 26 pages, 7 figures, 291 references. Early draft of Nature 464, 45-53
(4 March 2010). Published version is more up-to-date and has several
corrections, but is half the length with far fewer reference
- …