137 research outputs found
Resilience to time-correlated noise in quantum computation
Fault-tolerant quantum computation techniques rely on weakly correlated
noise. Here I show that it is enough to assume weak spatial correlations: time
correlations can take any form. In particular, single-shot error correction
techniques exhibit a noise threshold for quantum memories under spatially local
stochastic noise.Comment: 16 pages, v3: as accepted in journa
Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
Color codes are topological stabilizer codes with unusual transversality
properties. Here I show that their group of transversal gates is optimal and
only depends on the spatial dimension, not the local geometry. I also introduce
a generalized, subsystem version of color codes. In 3D they allow the
transversal implementation of a universal set of gates by gauge fixing, while
error-detecting measurements involve only 4 or 6 qubits.Comment: 10 pages, 6 figures, as accepted in journa
Single-shot fault-tolerant quantum error correction
Conventional quantum error correcting codes require multiple rounds of
measurements to detect errors with enough confidence in fault-tolerant
scenarios. Here I show that for suitable topological codes a single round of
local measurements is enough. This feature is generic and is related to
self-correction and confinement phenomena in the corresponding quantum
Hamiltonian model. 3D gauge color codes exhibit this single-shot feature, which
applies also to initialization and gauge-fixing. Assuming the time for
efficient classical computations negligible, this yields a topological
fault-tolerant quantum computing scheme where all elementary logical operations
can be performed in constant time.Comment: Typos corrected after publication in journal, 26 pages, 4 figure
Dimensional Jump in Quantum Error Correction
Topological stabilizer codes with different spatial dimensions have
complementary properties. Here I show that the spatial dimension can be
switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D
qubit lattice, fault-tolerant quantum computation can be achieved with constant
time overhead on the number of logical gates, up to efficient global classical
computation, using only local quantum operations. Single-shot error correction
plays a crucial role.Comment: As accepted in journal: 10 pages, 3 figure
Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
We study the resources needed to construct topological 2D stabilizer codes as
a way to estimate in part their efficiency and this leads us to perform a
comparative study of surface codes and color codes. This study clarifies the
similarities and differences between these two types of stabilizer codes. We
compute the error correcting rate for surface codes and color
codes in several instances. On the torus, typical values are and
, but we find that the optimal values are and . For
planar codes, a typical value is , while we find that the optimal values
are and . In general, a color code encodes twice as much
logical qubits as a surface code does.Comment: revtex, 6 pages, 7 figure
Topological Computation without Braiding
We show that universal quantum computation can be performed within the ground
state of a topologically ordered quantum system, which is a naturally protected
quantum memory. In particular, we show how this can be achieved using brane-net
condensates in 3-colexes. The universal set of gates is implemented without
selective addressing of physical qubits and, being fully topologically
protected, it does not rely on quasiparticle excitations or their braiding.Comment: revtex4, 4 pages, 4 figure
Topological Subsystem Codes
We introduce a family of 2D topological subsystem quantum error-correcting
codes. The gauge group is generated by 2-local Pauli operators, so that 2-local
measurements are enough to recover the error syndrome. We study the
computational power of code deformation in these codes, and show that
boundaries cannot be introduced in the usual way. In addition, we give a
general mapping connecting suitable classical statistical mechanical models to
optimal error correction in subsystem stabilizer codes that suffer from
depolarizing noise.Comment: 16 pages, 11 figures, explanations added, typos correcte
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