147 research outputs found
Instruction Set Architectures for Quantum Processing Units
Progress in quantum computing hardware raises questions about how these
devices can be controlled, programmed, and integrated with existing
computational workflows. We briefly describe several prominent quantum
computational models, their associated quantum processing units (QPUs), and the
adoption of these devices as accelerators within high-performance computing
systems. Emphasizing the interface to the QPU, we analyze instruction set
architectures based on reduced and complex instruction sets, i.e., RISC and
CISC architectures. We clarify the role of conventional constraints on memory
addressing and instruction widths within the quantum computing context.
Finally, we examine existing quantum computing platforms, including the D-Wave
2000Q and IBM Quantum Experience, within the context of future ISA development
and HPC needs.Comment: To be published in the proceedings in the International Super
Computing Conference 2017 publicatio
Weighing matrices and spherical codes
Mutually unbiased weighing matrices (MUWM) are closely related to an
antipodal spherical code with 4 angles. In the present paper, we clarify the
relationship between MUWM and the spherical sets, and give the complete
solution about the maximum size of a set of MUWM of weight 4 for any order.
Moreover we describe some natural generalization of a set of MUWM from the
viewpoint of spherical codes, and determine several maximum sizes of the
generalized sets. They include an affirmative answer of the problem of Best,
Kharaghani, and Ramp.Comment: Title is changed from "Association schemes related to weighing
matrices
Efficient fault-tolerant quantum computing
Fault tolerant quantum computing methods which work with efficient quantum
error correcting codes are discussed. Several new techniques are introduced to
restrict accumulation of errors before or during the recovery. Classes of
eligible quantum codes are obtained, and good candidates exhibited. This
permits a new analysis of the permissible error rates and minimum overheads for
robust quantum computing. It is found that, under the standard noise model of
ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an
order of magnitude larger than the logical machine contained within it in order
to be reliable. For example, a scale-up by a factor of 22, with gate error rate
of order , is sufficient to permit large quantum algorithms such as
factorization of thousand-digit numbers.Comment: 21 pages plus 5 figures. Replaced with figures in new format to avoid
problem
A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field
Using the Weyl commutation relations over a finite field we introduce a
family of error-correcting quantum stabilizer codes based on a class of
symmetric matrices over the finite field satisfying certain natural conditions.
When the field is GF(2) the existence of a rich class of such symmetric
matrices is demonstrated by a simple probabilistic argument depending on the
Chernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these
symmetric matrices are assumed to be circulant it is possible to obtain
concrete examples by a computer program. The quantum codes thus obtained admit
elegant encoding circuits.Comment: 16 pages, 2 figure
Einstein metrics in projective geometry
It is well known that pseudo-Riemannian metrics in the projective class of a
given torsion free affine connection can be obtained from (and are equivalent
to) the solutions of a certain overdetermined projectively invariant
differential equation. This equation is a special case of a so-called first BGG
equation. The general theory of such equations singles out a subclass of
so-called normal solutions. We prove that non-degerate normal solutions are
equivalent to pseudo-Riemannian Einstein metrics in the projective class and
observe that this connects to natural projective extensions of the Einstein
condition.Comment: 10 pages. Adapted to published version. In addition corrected a minor
sign erro
Quantum Teleportation is a Universal Computational Primitive
We present a method to create a variety of interesting gates by teleporting
quantum bits through special entangled states. This allows, for instance, the
construction of a quantum computer based on just single qubit operations, Bell
measurements, and GHZ states. We also present straightforward constructions of
a wide variety of fault-tolerant quantum gates.Comment: 6 pages, REVTeX, 6 epsf figure
Topics in Quantum Computers
I provide an introduction to quantum computers, describing how they might be
realized using language accessible to a solid state physicist. A listing of the
minimal requirements for creating a quantum computer is given. I also discuss
several recent developments in the area of quantum error correction, a subject
of importance not only to quantum computation, but also to some aspects of the
foundations of quantum theory.Comment: 22 pages, Latex, 1 eps figure, Paper to be published in "Mesoscopic
Electron Transport", edited by L. Kowenhoven, G. Schoen and L. Sohn, NATO ASI
Series E, Kluwer Ac. Publ., Dordrecht. v2: typos in refrences fixe
Quantum optical coherence can survive photon losses: a continuous-variable quantum erasure correcting code
A fundamental requirement for enabling fault-tolerant quantum information
processing is an efficient quantum error-correcting code (QECC) that robustly
protects the involved fragile quantum states from their environment. Just as
classical error-correcting codes are indispensible in today's information
technologies, it is believed that QECC will play a similarly crucial role in
tomorrow's quantum information systems. Here, we report on the first
experimental demonstration of a quantum erasure-correcting code that overcomes
the devastating effect of photon losses. Whereas {\it errors} translate, in an
information theoretic language, the noise affecting a transmission line, {\it
erasures} correspond to the in-line probabilistic loss of photons. Our quantum
code protects a four-mode entangled mesoscopic state of light against erasures,
and its associated encoding and decoding operations only require linear optics
and Gaussian resources. Since in-line attenuation is generally the strongest
limitation to quantum communication, much more than noise, such an
erasure-correcting code provides a new tool for establishing quantum optical
coherence over longer distances. We investigate two approaches for
circumventing in-line losses using this code, and demonstrate that both
approaches exhibit transmission fidelities beyond what is possible by classical
means.Comment: 5 pages, 4 figure
Experimental Quantum Teleportation of a Two-Qubit Composite System
Quantum teleportation, a way to transfer the state of a quantum system from
one location to another, is central to quantum communication and plays an
important role in a number of quantum computation protocols. Previous
experimental demonstrations have been implemented with photonic or ionic
qubits. Very recently long-distance teleportation and open-destination
teleportation have also been realized. Until now, previous experiments have
only been able to teleport single qubits. However, since teleportation of
single qubits is insufficient for a large-scale realization of quantum
communication and computation2-5, teleportation of a composite system
containing two or more qubits has been seen as a long-standing goal in quantum
information science. Here, we present the experimental realization of quantum
teleportation of a two-qubit composite system. In the experiment, we develop
and exploit a six-photon interferometer to teleport an arbitrary polarization
state of two photons. The observed teleportation fidelities for different
initial states are all well beyond the state estimation limit of 0.40 for a
two-qubit system. Not only does our six-photon interferometer provide an
important step towards teleportation of a complex system, it will also enable
future experimental investigations on a number of fundamental quantum
communication and computation protocols such as multi-stage realization of
quantum-relay, fault-tolerant quantum computation, universal quantum
error-correction and one-way quantum computation.Comment: 16pages, 4 figure
From quantum fusiliers to high-performance networks
Our objective was to design a quantum repeater capable of achieving one
million entangled pairs per second over a distance of 1000km. We failed, but
not by much. In this letter we will describe the series of developments that
permitted us to approach our goal. We will describe a mechanism that permits
the creation of entanglement between two qubits, connected by fibre, with
probability arbitrarily close to one and in constant time. This mechanism may
be extended to ensure that the entanglement has high fidelity without
compromising these properties. Finally, we describe how this may be used to
construct a quantum repeater that is capable of creating a linear quantum
network connecting two distant qubits with high fidelity. The creation rate is
shown to be a function of the maximum distance between two adjacent quantum
repeaters.Comment: 2 figures, Comments welcom
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