3,618 research outputs found
Fault-tolerant quantum computation with high threshold in two dimensions
We present a scheme of fault-tolerant quantum computation for a local
architecture in two spatial dimensions. The error threshold is 0.75% for each
source in an error model with preparation, gate, storage and measurement
errors.Comment: 4 pages, 4 figures; v2: A single 2D layer of qubits (simple square
lattice) with nearest-neighbor translation-invariant Ising interaction
suffices. Slightly improved threshol
Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes
Qubit loss and gate failure are significant problems for the development of scalable quantum computing. Recently, various schemes have been proposed for tolerating qubit loss and gate failure. These include schemes based on cluster and parity states. We show that by designing such schemes specifically to tolerate these error types we cause an exponential blowout in depolarizing noise. We discuss several examples and propose techniques for minimizing this problem. In general, this introduces a tradeoff with other undesirable effects. In some cases this is physical resource requirements, while in others it is noise rates
Entanglement and the Power of One Qubit
The "Power of One Qubit" refers to a computational model that has access to
only one pure bit of quantum information, along with n qubits in the totally
mixed state. This model, though not as powerful as a pure-state quantum
computer, is capable of performing some computational tasks exponentially
faster than any known classical algorithm. One such task is to estimate with
fixed accuracy the normalized trace of a unitary operator that can be
implemented efficiently in a quantum circuit. We show that circuits of this
type generally lead to entangled states, and we investigate the amount of
entanglement possible in such circuits, as measured by the multiplicative
negativity. We show that the multiplicative negativity is bounded by a
constant, independent of n, for all bipartite divisions of the n+1 qubits, and
so becomes, when n is large, a vanishingly small fraction of the maximum
possible multiplicative negativity for roughly equal divisions. This suggests
that the global nature of entanglement is a more important resource for quantum
computation than the magnitude of the entanglement.Comment: 22 pages, 4 figure
Quantum hashing with the icosahedral group
We study an efficient algorithm to hash any single qubit gate (or unitary
matrix) into a braid of Fibonacci anyons represented by a product of
icosahedral group elements. By representing the group elements by braid
segments of different lengths, we introduce a series of pseudo-groups. Joining
these braid segments in a renormalization group fashion, we obtain a Gaussian
unitary ensemble of random-matrix representations of braids. With braids of
length O[log(1/epsilon)], we can approximate all SU(2) matrices to an average
error epsilon with a cost of O[log(1/epsilon)] in time. The algorithm is
applicable to generic quantum compiling.Comment: 5 pages, 4 figures; revised version, to appear in Phys. Rev. Lett
A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states
We prove that universal quantum computation is possible using only (i) the
physically natural measurement on two qubits which distinguishes the singlet
from the triplet subspace, and (ii) qubits prepared in almost any three
different (potentially highly mixed) states. In some sense this measurement is
a `more universal' dynamical element than a universal 2-qubit unitary gate,
since the latter must be supplemented by measurement. Because of the rotational
invariance of the measurement used, our scheme is robust to collective
decoherence in a manner very different to previous proposals - in effect it is
only ever sensitive to the relational properties of the qubits.Comment: TR apologises for yet again finding a coauthor with a ridiculous
middle name [12
Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
We estimate the resource requirements, the total number of physical qubits
and computational time, required to compute the ground state energy of a 1-D
quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of
the system size and the numerical precision. This estimate is based on
analyzing the impact of fault-tolerant quantum error correction in the context
of the Quantum Logic Array (QLA) architecture. Our results show that due to the
exponential scaling of the computational time with the desired precision of the
energy, significant amount of error correciton is required to implement the TIM
problem. Comparison of our results to the resource requirements for a
fault-tolerant implementation of Shor's quantum factoring algorithm reveals
that the required logical qubit reliability is similar for both the TIM problem
and the factoring problem.Comment: 19 pages, 8 figure
Topological fault-tolerance in cluster state quantum computation
We describe a fault-tolerant version of the one-way quantum computer using a
cluster state in three spatial dimensions. Topologically protected quantum
gates are realized by choosing appropriate boundary conditions on the cluster.
We provide equivalence transformations for these boundary conditions that can
be used to simplify fault-tolerant circuits and to derive circuit identities in
a topological manner. The spatial dimensionality of the scheme can be reduced
to two by converting one spatial axis of the cluster into time. The error
threshold is 0.75% for each source in an error model with preparation, gate,
storage and measurement errors. The operational overhead is poly-logarithmic in
the circuit size.Comment: 20 pages, 12 figure
Quantum dynamics as a physical resource
How useful is a quantum dynamical operation for quantum information
processing? Motivated by this question we investigate several strength measures
quantifying the resources intrinsic to a quantum operation. We develop a
general theory of such strength measures, based on axiomatic considerations
independent of state-based resources. The power of this theory is demonstrated
with applications to quantum communication complexity, quantum computational
complexity, and entanglement generation by unitary operations.Comment: 19 pages, shortened by 3 pages, mainly cosmetic change
Quantum-circuit design for efficient simulations of many-body quantum dynamics
We construct an efficient autonomous quantum-circuit design algorithm for
creating efficient quantum circuits to simulate Hamiltonian many-body quantum
dynamics for arbitrary input states. The resultant quantum circuits have
optimal space complexity and employ a sequence of gates that is close to
optimal with respect to time complexity. We also devise an algorithm that
exploits commutativity to optimize the circuits for parallel execution. As
examples, we show how our autonomous algorithm constructs circuits for
simulating the dynamics of Kitaev's honeycomb model and the
Bardeen-Cooper-Schrieffer model of superconductivity. Furthermore we provide
numerical evidence that the rigorously proven upper bounds for the simulation
error here and in previous work may sometimes overestimate the error by orders
of magnitude compared to the best achievable performance for some
physics-inspired simulations.Comment: 20 Pages, 6 figure
Review article: Linear optical quantum computing
Linear optics with photon counting is a prominent candidate for practical
quantum computing. The protocol by Knill, Laflamme, and Milburn [Nature 409, 46
(2001)] explicitly demonstrates that efficient scalable quantum computing with
single photons, linear optical elements, and projective measurements is
possible. Subsequently, several improvements on this protocol have started to
bridge the gap between theoretical scalability and practical implementation. We
review the original theory and its improvements, and we give a few examples of
experimental two-qubit gates. We discuss the use of realistic components, the
errors they induce in the computation, and how these errors can be corrected.Comment: 41 pages, 37 figures, many small changes, added references, and
improved discussion on error correction and fault toleranc
- …