16 research outputs found
Multi-path Summation for Decoding 2D Topological Codes
Fault tolerance is a prerequisite for scalable quantum computing.
Architectures based on 2D topological codes are effective for near-term
implementations of fault tolerance. To obtain high performance with these
architectures, we require a decoder which can adapt to the wide variety of
error models present in experiments. The typical approach to the problem of
decoding the surface code is to reduce it to minimum-weight perfect matching in
a way that provides a suboptimal threshold error rate, and is specialized to
correct a specific error model. Recently, optimal threshold error rates for a
variety of error models have been obtained by methods which do not use
minimum-weight perfect matching, showing that such thresholds can be achieved
in polynomial time. It is an open question whether these results can also be
achieved by minimum-weight perfect matching. In this work, we use belief
propagation and a novel algorithm for producing edge weights to increase the
utility of minimum-weight perfect matching for decoding surface codes. This
allows us to correct depolarizing errors using the rotated surface code,
obtaining a threshold of . This is larger than the threshold
achieved by previous matching-based decoders (), though
still below the known upper bound of .Comment: 19 pages, 13 figures, published in Quantum, available at
https://quantum-journal.org/papers/q-2018-10-19-102
Blind topological measurement-based quantum computation
Blind quantum computation is a novel secure quantum-computing protocol that
enables Alice, who does not have sufficient quantum technology at her disposal,
to delegate her quantum computation to Bob, who has a fully fledged quantum
computer, in such a way that Bob cannot learn anything about Alice's input,
output and algorithm. A recent proof-of-principle experiment demonstrating
blind quantum computation in an optical system has raised new challenges
regarding the scalability of blind quantum computation in realistic noisy
conditions. Here we show that fault-tolerant blind quantum computation is
possible in a topologically protected manner using the
Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is
0.0043, which is comparable to that (0.0075) of non-blind topological quantum
computation. As the error per gate of the order 0.001 was already achieved in
some experimental systems, our result implies that secure cloud quantum
computation is within reach.Comment: 17 pages, 5 figure
Topological code Autotune
Many quantum systems are being investigated in the hope of building a
large-scale quantum computer. All of these systems suffer from decoherence,
resulting in errors during the execution of quantum gates. Quantum error
correction enables reliable quantum computation given unreliable hardware.
Unoptimized topological quantum error correction (TQEC), while still effective,
performs very suboptimally, especially at low error rates. Hand optimizing the
classical processing associated with a TQEC scheme for a specific system to
achieve better error tolerance can be extremely laborious. We describe a tool
Autotune capable of performing this optimization automatically, and give two
highly distinct examples of its use and extreme outperformance of unoptimized
TQEC. Autotune is designed to facilitate the precise study of real hardware
running TQEC with every quantum gate having a realistic, physics-based error
model.Comment: 13 pages, 17 figures, version accepted for publicatio
A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)
We propose a family of local CSS stabilizer codes as possible candidates for
self-correcting quantum memories in 3D. The construction is inspired by the
classical Ising model on a Sierpinski carpet fractal, which acts as a classical
self-correcting memory. Our models are naturally defined on fractal subsets of
a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does
not imply that these models can be realised with local interactions in 3D
Euclidean space, we also discuss this possibility. The X and Z sectors of the
code are dual to one another, and we show that there exists a finite
temperature phase transition associated with each of these sectors, providing
evidence that the system may robustly store quantum information at finite
temperature.Comment: 16 pages, 6 figures. In v2, erroneous argument about embeddability
into R3 was removed. In v3, minor changes to match journal versio
Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
We consider two-dimensional lattice models that support Ising anyonic
excitations and are coupled to a thermal bath. We propose a phenomenological
model for the resulting short-time dynamics that includes pair-creation,
hopping, braiding, and fusion of anyons. By explicitly constructing topological
quantum error-correcting codes for this class of system, we use our
thermalization model to estimate the lifetime of the quantum information stored
in the encoded spaces. To decode and correct errors in these codes, we adapt
several existing topological decoders to the non-Abelian setting. We perform
large-scale numerical simulations of these two-dimensional Ising anyon systems
and find that the thresholds of these models range between 13% to 25%. To our
knowledge, these are the first numerical threshold estimates for quantum codes
without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a
misstatement about the detailed balance condition of our Metropolis
simulations. All conclusions from v1 are unaffected by this correctio