177 research outputs found
Fault-tolerant gates via homological product codes
A method for the implementation of a universal set of fault-tolerant logical
gates is presented using homological product codes. In particular, it is shown
that one can fault-tolerantly map between different encoded representations of
a given logical state, enabling the application of different classes of
transversal gates belonging to the underlying quantum codes. This allows for
the circumvention of no-go results pertaining to universal sets of transversal
gates and provides a general scheme for fault-tolerant computation while
keeping the stabilizer generators of the code sparse.Comment: 11 pages, 3 figures. v2 (published version): quantumarticle
documentclass, expanded discussion on the conditions for a fault tolerance
threshol
Error suppression via complementary gauge choices in Reed-Muller codes
Concatenation of two quantum error correcting codes with complementary sets
of transversal gates can provide a means towards universal fault-tolerant
computation. We first show that it is generally preferable to choose the inner
code with the higher pseudo-threshold in order to achieve lower logical failure
rates. We then explore the threshold properties of a wide range of
concatenation schemes. Notably, we demonstrate that the concatenation of
complementary sets of Reed-Muller codes can increase the code capacity
threshold under depolarizing noise when compared to extensions of previously
proposed concatenation models. We also analyze the properties of logical errors
under circuit level noise, showing that smaller codes perform better for all
sampled physical error rates. Our work provides new insights into the
performance of universal concatenated quantum codes for both code capacity and
circuit level noise.Comment: 11 pages + 4 appendices, 6 figures. In v2, Fig.1 was added to conform
to journal specification
Advantages of versatile neural-network decoding for topological codes
Finding optimal correction of errors in generic stabilizer codes is a
computationally hard problem, even for simple noise models. While this task can
be simplified for codes with some structure, such as topological stabilizer
codes, developing good and efficient decoders still remains a challenge. In our
work, we systematically study a very versatile class of decoders based on
feedforward neural networks. To demonstrate adaptability, we apply neural
decoders to the triangular color and toric codes under various noise models
with realistic features, such as spatially-correlated errors. We report that
neural decoders provide significant improvement over leading efficient decoders
in terms of the error-correction threshold. Using neural networks simplifies
the process of designing well-performing decoders, and does not require prior
knowledge of the underlying noise model.Comment: 11 pages, 6 figures, 2 table
Trade-off coding for universal qudit cloners motivated by the Unruh effect
A "triple trade-off" capacity region of a noisy quantum channel provides a
more complete description of its capabilities than does a single capacity
formula. However, few full descriptions of a channel's ability have been given
due to the difficult nature of the calculation of such regions---it may demand
an optimization of information-theoretic quantities over an infinite number of
channel uses. This work analyzes the d-dimensional Unruh channel, a noisy
quantum channel which emerges in relativistic quantum information theory. We
show that this channel belongs to the class of quantum channels whose capacity
region requires an optimization over a single channel use, and as such is
tractable. We determine two triple-trade off regions, the quantum dynamic
capacity region and the private dynamic capacity region, of the d-dimensional
Unruh channel. Our results show that the set of achievable rate triples using
this coding strategy is larger than the set achieved using a time-sharing
strategy. Furthermore, we prove that the Unruh channel has a distinct structure
made up of universal qudit cloning channels, thus providing a clear
relationship between this relativistic channel and the process of stimulated
emission present in quantum optical amplifiers.Comment: 26 pages, 4 figures; v2 has minor corrections to Definition 2.
Definition 4 and Remark 5 have been adde
Soft phonon modes in rutile TiO
The lattice dynamics of TiO in the rutile crystal structure was studied
by a combination of thermal diffuse scattering, inelastic x-ray scattering and
density functional perturbation theory. We experimentally confirm the existence
of an anomalous soft transverse acoustic mode with energy minimum at q = (1/2
1/2 1/4). The phonon energy landscape of this particular branch is reported and
compared to the calculation. The harmonic calculation underestimates the phonon
energies but despite this the shape of both the energy landscape and the
scattering intensities are well reproduced. We find a significant temperature
dependence in energy of this transverse acoustic mode over an extended region
in reciprocal space which is in line with a substantially anharmonic mode
potential-energy surface. The reported low energy branch is quite different
from the ferroelectric mode that softens at the Brillouin zone center and may
help explain anomalous convergence behavior in calculating TiO surface
properties
The disjointness of stabilizer codes and limitations on fault-tolerant logical gates
Stabilizer codes are a simple and successful class of quantum
error-correcting codes. Yet this success comes in spite of some harsh
limitations on the ability of these codes to fault-tolerantly compute. Here we
introduce a new metric for these codes, the disjointness, which, roughly
speaking, is the number of mostly non-overlapping representatives of any given
non-trivial logical Pauli operator. We use the disjointness to prove that
transversal gates on error-detecting stabilizer codes are necessarily in a
finite level of the Clifford hierarchy. We also apply our techniques to
topological code families to find similar bounds on the level of the hierarchy
attainable by constant depth circuits, regardless of their geometric locality.
For instance, we can show that symmetric 2D surface codes cannot have non-local
constant depth circuits for non-Clifford gates.Comment: 8+3 pages, 2 figures. Comments welcom
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