# James Wootton114

Feb 28 2017 14:11 UTC
Feb 28 2017 08:54 UTC
James Wootton commented on A loophole in quantum error correction

I think I was mostly reacting to where he tries to sell the importance of the work.

>Fault tolerant theorems show that an arbitrary good precision can be obtained using a limited amount of hardware...we unveil the role of an implicit assumption made in these mathematical theorems: the ability to perform quantum measurements with infinite precision.

Feb 27 2017 13:10 UTC
James Wootton commented on A loophole in quantum error correction

Do any fault-tolerance theorems claim to hold for small codes without repeated measurement, as is the case in these supposed counter examples?

The assumption that no-one ever thought about this noise before is the faulty one here.

Nov 22 2016 09:59 UTC
Nov 18 2016 09:40 UTC
Nov 17 2016 09:16 UTC
Nov 15 2016 09:39 UTC
Oct 19 2016 18:33 UTC
Sep 27 2016 02:00 UTC
Currently, the mainstream approach to quantum computing is through surface codes. One way to store and manipulate quantum information with these to create defects in the codes which can be moved and used as if they were particles. Specifically, they simulate the behaviour of exotic particles known as Majoranas, which are a kind of non-Abelian anyon. By exchanging these particles, important gates for quantum computation can be implemented. Here we investigate the simplest possible exchange operation for two surface code Majoranas. This is found to act non-trivially on only five qubits. The system is then truncated to these five qubits, so that the exchange process can be run on the IBM 5Q processor. The results demonstrate the expected effect of the exchange. This paper has been written in a style that should hopefully be accessible to both professional and amateur scientists.
Sep 14 2016 07:46 UTC

"Ni." would be slightly shorter, but some may find it offensive.

Sep 05 2016 07:47 UTC
Aug 18 2016 16:42 UTC

A video of a talk I gave this morning will be [here][1], if it ever finishes uploading.

[1]: https://youtu.be/I8cMY0AmIY0

Aug 18 2016 02:00 UTC
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major step towards fault-tolerant quantum computation. Here we propose a surface code based experiment that is the smallest, both in terms of code size and circuit depth, that would allow errors to be detected and corrected for both the $X$ and $Z$ basis of a qubit. This requires $17$ physical qubits initially prepared in a product state, on which $16$ two-qubit entangling gates are applied before a final measurement of all qubits. A platform agnostic error model is applied to give some idea of the noise levels required for success. It is found that a true demonstration of quantum error correction will require fidelities for the preparation and measurement of qubits and the entangling gates to be above $99\%$.
Jul 11 2016 08:02 UTC
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Dec 15 2015 09:15 UTC
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Nov 10 2015 09:38 UTC
Jun 02 2015 02:00 UTC
We consider a class of decoding algorithms that are applicable to error correction for both Abelian and non-Abelian anyons. This class includes multiple algorithms that have recently attracted attention, including the Bravyi-Haah RG decoder. They are applied to both the problem of single shot error correction (with perfect syndrome measurements) and that of active error correction (with noisy syndrome measurements). For Abelian models we provide a threshold proof in both cases, showing that there is a finite noise threshold under which errors can be arbitrarily suppressed when any decoder in this class is used. For non-Abelian models such a proof is found for the single shot case. The means by which decoding may be performed for active error correction of non-Abelian anyons is studied in detail. Differences with the Abelian case are discussed.
Feb 02 2015 02:00 UTC
We study and generalize the class of qubit topological stabilizer codes that arise in the Abelian phase of the honeycomb lattice model. The resulting family of codes, which we call `matching codes' realize the same anyon model as the surface codes, and so may be similarly used in proposals for quantum computation. We show that these codes are particularly well suited to engineering twist defects that behave as Majorana modes. A proof of principle system that demonstrates the braiding properties of the Majoranas is discussed that requires only three qubits.