arXiv subjects

James R. Wootton

Publications and source records attributed to James R. Wootton.

At least 37 records · Page 2Linked to original sources

arXiv2020

Procedural generation using quantum computation

Quantum computation is an emerging technology that promises to be a powerful tool in many areas. Though some years likely still remain until significant quantum advantage is demonstrated, the development of the technology has led to a range of valuable resources. These include publicly available prototype quantum hardware, advanced simulators for small quantum programs and programming frameworks to test and develop quantum software. In this provocation paper we seek to demonstrate that these resources are sufficient to provide the first useful results in the field of procedural generation. This is done by introducing a proof-of-principle method: a quantum generalization of a blurring process, in which quantum interference is used to provide a unique effect. Through this we hope to show that further developments in the technology are not required before it becomes useful for procedural generation. Rather, fruitful experimentation with this new technology can begin now.

cs.ET↗

arXiv2020

A quantum procedure for map generation

Quantum computation is an emerging technology that promises a wide range of possible use cases. This promise is primarily based on algorithms that are unlikely to be viable over the coming decade. For near-term applications, quantum software needs to be carefully tailored to the hardware available. In this paper, we begin to explore whether near-term quantum computers could provide tools that are useful in the creation and implementation of computer games. The procedural generation of geopolitical maps and their associated history is considered as a motivating example. This is performed by encoding a rudimentary decision making process for the nations within a quantum procedure that is well-suited to near-term devices. Given the novelty of quantum computing within the field of procedural generation, we also provide an introduction to the basic concepts involved.

cs.AI↗

arXiv2020

Benchmarking near-term devices with quantum error correction

Now that ever more sophisticated devices for quantum computing are being developed, we require ever more sophisticated benchmarks. This includes a need to determine how well these devices support the techniques required for quantum error correction. In this paper we introduce the \texttt{topological\_codes} module of Qiskit-Ignis, which is designed to provide the tools necessary to perform such tests. Specifically, we use the \texttt{RepetitionCode} and \texttt{GraphDecoder} classes to run tests based on the repetition code and process the results. As an example, data from a 43 qubit code running on IBM's \emph{Rochester} device is presented.

quant-ph↗

arXiv2019

Universal quantum computation in the surface code using non-Abelian islands

The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are therefore required to achieve universal quantum computation. Here we propose a hybrid scheme which uses small islands of a qudit variant of the surface code to enhance the computational power of the standard surface code. This allows the non-trivial action of the non-Abelian anyons in the former to process information stored in the latter. Specifically, we show that a non-stabilizer state can be prepared, which allows universality to be achieved.

quant-ph↗

arXiv2018

Benchmarks for approximate CNOTs based on a 17-Qubit Surface Code

Scalable and fault-tolerant quantum computation will require error correction. This will demand constant measurement of many-qubit observables, implemented using a vast number of CNOT gates. Indeed, practically all operations performed by a fault-tolerant device will be these CNOTs, or equivalent two-qubit controlled operations. It is therefore important to devise benchmarks for these gates that explicitly quantify their effectiveness at this task. Here we develop such benchmarks, and demonstrate their use by applying them to a range of differently implemented controlled gates and a particular quantum error correcting code. Specifically, we consider spin qubits confined to quantum dots that are coupled either directly or via floating gates to implement the minimal 17-qubit instance of the surface code. Our results show that small differences in the gate fidelity can lead to large differences in the performance of the surface code. This shows that gate fidelity is not, in general, a good predictor of code performance.

quant-ph↗

arXiv2018

A repetition code of 15 qubits

The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of syndrome measurements, achieved using the standard quantum technique of using ancilla qubits and controlled operations. The size of the final syndrome is small enough to allow for lookup table decoding using experimentally obtained data. The results show strong evidence that the logical error rate decays exponentially with code distance, as is expected and required for the development of fault-tolerant quantum computers. The results also give insight into the nature of noise in the device.

quant-ph↗

arXiv2018

Benchmarking of quantum processors with random circuits

Quantum processors with sizes in the 10-100 qubit range are now increasingly common. However, with increased size comes increased complexity for benchmarking. The effectiveness of a given device may vary greatly between different tasks, and will not always be easy to predict from single and two qubit gate fidelities. For this reason, it is important to assess processor quality for a range of important tasks. In this work we propose and implement tests based on random quantum circuits. These are used to evaluate multiple different superconducting qubit devices, with sizes from 5 to 19 qubits, from two hardware manufacturers: IBM Research and Rigetti. The data is analyzed to give a quantitive description of how the devices perform. We also describe how it can be used for a qualititive description accessible to the layperson, by being played as a game.

quant-ph↗

arXiv2017

Getting the public involved in Quantum Error Correction

The Decodoku project seeks to let users get hands-on with cutting-edge quantum research through a set of simple puzzle games. The design of these games is explicitly based on the problem of decoding qudit variants of surface codes. This problem is presented such that it can be tackled by players with no prior knowledge of quantum information theory, or any other high-level physics or mathematics. Methods devised by the players to solve the puzzles can then directly be incorporated into decoding algorithms for quantum computation. In this paper we give a brief overview of the novel decoding methods devised by players, and provide short postmortem for Decodoku v1.0-v4.1.

quant-ph↗

arXiv2017

Poking holes and cutting corners to achieve Clifford gates with the surface code

The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes and even by braiding engineered Majorana modes using twist defects. Here we present a unified framework to describe these methods, which can be used to better compare different schemes, and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyse ways in which different schemes can be combined, and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code without loss of distance using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.

quant-ph↗

arXiv2017

Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment

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.

quant-ph↗

arXiv2017

A proposal for a minimal surface code experiment

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 $99\%$.

quant-ph↗

arXiv2017

Conformal energy currents on the edge of a topological superconductor

The boundary of a 2D topological superconductor can be modeled by a conformal field theory. Here we demonstrate the behaviors of this high level description emerging from a microscopic model at finite temperatures. To achieve that, we analyze the low energy sector of Kitaev's honeycomb lattice model and probe its energy current. We observe that the scaling of the energy current with temperature reveals the central charge of the conformal field theory, which is in agreement with the Chern number of the bulk. Importantly, these currents can discriminate between distinct topological phases at finite temperatures. We assess the resilience of this measurement of the central charge under coupling disorder, bulk dimerisation and defects at the boundary, thus establishing it as a favorable means of experimentally probing topological superconductors.

cond-mat.str-el↗

arXiv2016

Quantum memories at finite temperature

To use quantum systems for technological applications we first need to preserve their coherence for macroscopic timescales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. Here we review the state-of-the-art developments in this field in an informative and pedagogical way. We give the main principles of self-correcting quantum memories and we analyze several milestone examples from the literature of two-, three- and higher-dimensional quantum memories.

quant-ph↗

arXiv2016

Continuous error correction for Ising anyons

Quantum gates in topological quantum computation are performed by braiding non-Abelian anyons. These braiding processes can presumably be performed with very low error rates. However, to make a topological quantum computation architecture truly scalable, even rare errors need to be corrected. Error correction for non-Abelian anyons is complicated by the fact that it needs to be performed on a continuous basis and further errors may occur while we are correcting existing ones. Here, we provide the first study of this problem and prove its feasibility, establishing non-Abelian anyons as a viable platform for scalable quantum computation. We thereby focus on Ising anyons as the most prominent example of non-Abelian anyons and show that for these a finite error rate can indeed be corrected continuously. There is a threshold error rate $p_c>0$ such that for all error rates $p<p_c$ the probability of a logical error per time-step can be made exponentially small in the distance of a logical qubit.

quant-ph↗

arXiv2015

Parafermions in a Kagome lattice of qubits for topological quantum computation

Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero modes (Ising anyons). Here we go beyond this barrier, showing that the $\mathbb{Z}_4$ parafermion model of non-Abelian anyons can be realized on a qubit lattice. Our system additionally contains the Abelian $D(\mathbb{Z}_4)$ anyons as low-energetic excitations. We show that braiding of these parafermions with each other and with the $D(\mathbb{Z}_4)$ anyons allows the entire $d=4$ Clifford group to be generated. The error correction problem for our model is also studied in detail, guaranteeing fault-tolerance of the topological operations. Crucially, since the non-Abelian anyons are engineered through defect lines rather than as excitations, non-Abelian error correction is not required. Instead the error correction problem is performed on the underlying Abelian model, allowing high noise thresholds to be realized.

quant-ph↗

arXiv2015

Active error correction for Abelian and non-Abelian anyons

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.

quant-ph↗

arXiv2015

A family of stabilizer codes for $D({\mathbb Z}_2)$ anyons and Majorana modes

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.

quant-ph↗

arXiv2015

A simple decoder for topological codes

Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both i.i.d. and spatially correlated errors and is found to compare well with existing methods.

quant-ph↗