221 research outputs found
Enhanced fault-tolerant quantum computing in -level systems
Error correcting codes protect quantum information and form the basis of
fault tolerant quantum computing. Leading proposals for fault-tolerant quantum
computation require codes with an exceedingly rare property, a transverse
non-Clifford gate. Codes with the desired property are presented for -level,
qudit, systems with prime . The codes use qudits and can detect upto
errors. We quantify the performance of these codes for one approach
to quantum computation, known as magic state distillation. Unlike prior work,
we find performance is always enhanced by increasing .Comment: Author's final copy. Changes includes correction to plot in figure
Gaussification and entanglement distillation of continuous variable systems: a unifying picture
Distillation of entanglement using only Gaussian operations is an important
primitive in quantum communication, quantum repeater architectures, and
distributed quantum computing. Existing distillation protocols for continuous
degrees of freedom are only known to converge to a Gaussian state when
measurements yield precisely the vacuum outcome. In sharp contrast,
non-Gaussian states can be deterministically converted into Gaussian states
while preserving their second moments, albeit by usually reducing their degree
of entanglement. In this work - based on a novel instance of a non-commutative
central limit theorem - we introduce a picture general enough to encompass the
known protocols leading to Gaussian states, and new classes of protocols
including multipartite distillation. This gives the experimental option of
balancing the merits of success probability against entanglement produced.Comment: 4 + 4 pages, final versio
Distributed quantum information processing with minimal local resources
We present a protocol for growing graph states, the resource for one-way
quantum computing, when the available entanglement mechanism is highly
imperfect. The distillation protocol is frugal in its use of ancilla qubits,
requiring only a single ancilla qubit when the noise is dominated by one Pauli
error, and two for a general noise model. The protocol works with such scarce
local resources by never post-selecting on the measurement outcomes of
purification rounds. We find that such a strategy causes fidelity to follow a
biased random walk, and that a target fidelity is likely to be reached more
rapidly than for a comparable post-selecting protocol. An analysis is presented
of how imperfect local operations limit the attainable fidelity. For example, a
single Pauli error rate of 20% can be distilled down to times the
imperfection in local operations.Comment: 4 pages of main paper with an additional 1 page appendix, 5 figures.
Please contact me with any comment
Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation
Magic state distillation is an important primitive in fault-tolerant quantum
computation. The magic states are pure non-stabilizer states which can be
distilled from certain mixed non-stabilizer states via Clifford group
operations alone. Because of the Gottesman-Knill theorem, mixtures of Pauli
eigenstates are not expected to be magic state distillable, but it has been an
open question whether all mixed states outside this set may be distilled. In
this Letter we show that, when resources are finitely limited, non-distillable
states exist outside the stabilizer octahedron. In analogy with the bound
entangled states, which arise in entanglement theory, we call such states bound
states for magic state distillation.Comment: Published version. This paper builds on a theorem proven in "On the
Structure of Protocols for Magic State Distillation", arXiv:0908.0838. These
two papers jointly form the content of a talk entitled "Neither Magical nor
Classical?", which was presented at TQC 2009, Waterlo
Continuous-variable entanglement distillation and non-commutative central limit theorems
Entanglement distillation transforms weakly entangled noisy states into
highly entangled states, a primitive to be used in quantum repeater schemes and
other protocols designed for quantum communication and key distribution. In
this work, we present a comprehensive framework for continuous-variable
entanglement distillation schemes that convert noisy non-Gaussian states into
Gaussian ones in many iterations of the protocol. Instances of these protocols
include (a) the recursive-Gaussifier protocol, (b) the temporally-reordered
recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The
flexibility of these protocols give rise to several beneficial trade-offs
related to success probabilities or memory requirements, which that can be
adjusted to reflect experimental demands. Despite these protocols involving
measurements, we relate the convergence in this protocols to new instances of
non-commutative central limit theorems, in a formalism that we lay out in great
detail. Implications of the findings for quantum repeater schemes are
discussed.Comment: published versio
Measurement based entanglement under conditions of extreme photon loss
The act of measuring optical emissions from two remote qubits can entangle
them. By demanding that a photon from each qubit reaches the detectors, one can
ensure than no photon was lost. But the failure rate then rises quadratically
with loss probability. In [1] this resulted in 30 successes per billion
attempts. We describe a means to exploit the low grade entanglement heralded by
the detection of a lone photon: A subsequent perfect operation is quickly
achieved by consuming this noisy resource. We require only two qubits per node,
and can tolerate both path length variation and loss asymmetry. The impact of
photon loss upon the failure rate is then linear; realistic high-loss devices
can gain orders of magnitude in performance and thus support QIP.Comment: Contains an extension of the protocol that makes it robust against
asymmetries in path length and photon los
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