arXiv subjects

Naomi H. Nickerson

Publications and source records attributed to Naomi H. Nickerson.

8 recordsLinked to original sources

arXiv2021

Almost-linear time decoding algorithm for topological codes

In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of $O(n α(n))$, where $n$ is the number of physical qubits and $α$ is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, $α(n) \leq 3$. We prove that our algorithm performs optimally for errors of weight up to $(d-1)/2$ and for loss of up to $d-1$ qubits, where $d$ is the minimum distance of the code. Numerically, we obtain a threshold of $9.9\%$ for the 2d-toric code with perfect syndrome measurements and $2.6\%$ with faulty measurements.

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arXiv2019

Analysing correlated noise on the surface code using adaptive decoding algorithms

Laboratory hardware is rapidly progressing towards a state where quantum error-correcting codes can be realised. As such, we must learn how to deal with the complex nature of the noise that may occur in real physical systems. Single qubit Pauli errors are commonly used to study the behaviour of error-correcting codes, but in general we might expect the environment to introduce correlated errors to a system. Given some knowledge of structures that errors commonly take, it may be possible to adapt the error-correction procedure to compensate for this noise, but performing full state tomography on a physical system to analyse this structure quickly becomes impossible as the size increases beyond a few qubits. Here we develop and test new methods to analyse blue a particular class of spatially correlated errors by making use of parametrised families of decoding algorithms. We demonstrate our method numerically using a diffusive noise model. We show that information can be learnt about the parameters of the noise model, and additionally that the logical error rates can be improved. We conclude by discussing how our method could be utilised in a practical setting blue and propose extensions of our work to study more general error models.

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arXiv2017

Entanglement Distillation between Solid-State Quantum Network Nodes

The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. We demonstrate the heralded generation of two copies of a remote entangled state through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. In addition, this distillation protocol significantly speeds up entanglement generation compared to previous two-photon-mediated schemes. The key combination of generating, storing and processing entangled states demonstrated here opens the door to exploring and utilizing multi-particle entanglement on an extended quantum network.

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arXiv2016

Error correcting power of small topological codes

Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be possible. In doing this it will be necessary to define clear achievable metrics to measure and compare the performance of real codes. Here we consider the smallest examples of several families of topological codes: surface codes, color codes, and the gauge color code, and determine the minimum requirements to demonstrate error suppression. We use an exact decoder to compare the performance of the codes under simple models of both physical error and measurement error, and determine regions of correctability in the physical parameters for each code.

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arXiv2016

Fault-tolerant error correction with the gauge color code

The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures using a new method, known as gauge fixing, for performing the non-Clifford logical operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide encouraging preliminary data of a comparative study between the gauge color code and other promising computational architectures.

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arXiv2015

A silicon-based surface code quantum computer

Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: There is a basic conflict between nanometre separation desired for qubit-qubit interactions, and the much larger scales that would enable control and addressing in a manufacturable and fault tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid state spins, or `data qubits', that are widely separated from one another. We employ a second set of `probe' spins which are mechanically separate from the data qubits and move in-and-out of their proximity. The spin dipole-dipole interactions give rise to phase shifts; measuring a probe's total phase reveals the collective parity of the data qubits along the probe's path. We introduce a protocol to balance the systematic errors due to the spins being imperfectly located during device fabrication. Detailed simulations show that the surface code's threshold then corresponds to misalignments that are substantial on the scale of the array, indicating that it is very robust. We conclude that this simple `orbital probe' architecture overcomes many of the difficulties facing solid state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.

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arXiv2014

Freely Scalable Quantum Technologies using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links

Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters. We can regard such a system as a universal cell with diverse technological uses from communication to large-scale computing, provided that the cell is able to network with others and overcome any noise in the interlinks. Here we show that loss-tolerant entanglement purification makes quantum computing feasible with the noisy and lossy links that are realistic today: With a modestly complex cell design, and using a surface code protocol with a network noise threshold of 13.3%, we find that interlinks which attempt entanglement at a rate of 2MHz but suffer 98% photon loss can result in kilohertz computer clock speeds (i.e. rate of high fidelity stabilizer measurements). Improved links would dramatically increase the clock speed. Our simulations employed local gates of a fidelity already achieved in ion trap devices.

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arXiv2013

Topological quantum computing with a very noisy network and local error rates approaching one percent

A scalable quantum computer could be built by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. A solution is for cells to repeatedly communicate with each other and so 'purify' any imperfections; however prior studies suggest that the cells themselves must then have prohibitively low internal error rates. Here we describe a method by which even error-prone cells can perform purification: groups of cells generate shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (>=10% error rate) we find that our protocol can succeed provided that intra-cell error rates for initialisation, state manipulation and measurement are below 0.82%. This level of fidelity is already achievable in several laboratory systems.

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