Quantum Codes From Classical Graphical Models

Roffe, Joschka; Zohren, Stefan; Horsman, Dominic; Chancellor, Nicholas

doi:10.1109/tit.2019.2938751

Cited by 7 publications

(8 citation statements)

References 34 publications

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“…While the goal of our techniques is to educate quantum non-experts on quantum computing, the primary goal of previous work is to provide more powerful tools to those who are already mathematical experts. One exception to this pattern is the graphical tool developed in Roffe et al (2019), for the design of quantum error correction codes.…”

Section: Quantum Puzzle Visualisation Toolmentioning

confidence: 99%

The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving

Nita

Smith

Chancellor

et al. 2021

Research in Science & Technological Education

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Background: Knowledge of quantum computing is arguably inaccessible to many, with knowledge of the complex mathematics involving a particular barrier to entry, creating difficulty in terms of teaching and inclusive learning for those without a high level of mathematics. Meanwhile, it is increasingly important that the knowledge of quantum technologies is accessible to those who work with real-world applications and is taught to the younger generation. Purpose: Resulting from collaborative dialogue between physicists, computer scientists, educationalists, and industrial end users, we propose the concept of quantum literacy as one means of addressing the need for transdisciplinary research in response to the complex problems that we see at the heart of issues around global sustainability. In this way, quantum literacy can contribute to UN Sustainable Development Goal 4, Quality Education. Methods: We introduce a specific puzzle visualization learning tool through which to achieve the pedagogic ends we set out with respect to quantum literacy. Visualization through puzzles can enable non-specialists to develop an intuitive, but still rigorous, understanding of universal quantum computation and provide a facility for non-specialists to discover increasingly complex and new quantum algorithms. Using the Hong-Ou-Mandel optical effect from quantum mechanics, we demonstrate how visual methods such as those made possible through the puzzle visualization tool can be very useful for understanding underlying complex processes in quantum physics and beyond and therefore support the aims of quantum literacy. Conclusion:We argue that quantum literacy, as defined here, addresses the challenges of learning within a highly bounded discipline and of access to the kind of powerful knowledge that should be more accessible to a wide group of learners. We therefore argue for the importance of addressing pedagogic issues when powerful knowledge consists of dense concepts, as well as complex and hierarchical relations between concepts, in addition to presenting a strong barrier to entry in the form of mathematics.

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Section: Quantum Puzzle Visualisation Toolmentioning

confidence: 99%

The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving

Nita

Smith

Chancellor

et al. 2021

Research in Science & Technological Education

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“…The tools of the CPC framework could help construct quantum versions of low density parity check and turbo codes. A presentation of the CPC framework in terms of classical factor graph notation can be found in [49].…”

Section: Outlook and Conclusionmentioning

confidence: 99%

Protecting quantum memories using coherent parity check codes

Roffe

Headley

Chancellor

et al. 2018

Quantum Sci. Technol.

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Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase parity checks, supplemented by cross-checks to fix the code distance. In this paper, we provide a detailed introduction to CPC codes using conventional quantum circuit notation. We demonstrate the implementation of a CPC code on real hardware, by designing a [[4, 2, 2]] detection code for the IBM 5Q superconducting qubit device. Whilst the individual gate-error rates on the IBM device are too high to realise a fault tolerant quantum detection code, our results show that the syndrome information from a full encode-decode cycle of the [[4, 2, 2]] CPC code can be used to increase the output state fidelity by post-selection. Following this, we generalise CPC codes to other quantum technologies by showing that their structure allows them to be efficiently compiled using any experimentally realistic native two-qubit gate. We introduce a threestage CPC design process for the construction of hardware-optimised quantum memories. As a proofof-concept example, we apply our design process to an idealised linear seven-qubit ion trap. In the first stage of the process, we use exhaustive search methods to find a large set of [[7, 3, 3]] codes that saturate the quantum Hamming bound for seven qubits. We then optimise over the discovered set of codes to meet the hardware and layout demands of the ion trap device. We also discuss how the CPC design process will generalise to larger-scale codes and other qubit technologies.

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“…For an m × n parity check matrix H, the two sets of nodes in G are defined as follows: 1) Data nodes V = {v j |j = 1, ..., n} corresponding to the columns of H and taking the bit-values of the error e; 2) Parity nodes U = {u i |i = 1, ..., m} corresponding to rows of H and taking the bit-values of the syndrome s = H • e. A graph edge λ ij ∈ Λ is drawn between a pair of nodes {v j , u i } if H ij = 1. Factor graphs serve as a useful visualisation of the parity check matrix with applications in code design and decoding [11,43]. Diagrammatically, factor graphs are drawn with circles representing data nodes, squares representing parity nodes and solid-lines representing the edges.…”

Section: Introductionmentioning

confidence: 99%

Decoding Across the Quantum LDPC Code Landscape

Roffe,

White,

Burton

et al. 2020

Preprint

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We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the decoder applied to three families of hypergraph product code: topological codes, fixed-rate random codes and a new class of codes that we call semi-topological codes. Our new code families share properties of both topological and random hypergraph product codes, with a construction that allows for a finely-controlled trade-off between code threshold and stabilizer locality. Our results indicate thresholds across all three families of hypergraph product code, and provide evidence of exponential suppression in the low error regime. For the Toric code, we observe a threshold in the range 9.9 ± 0.2%. This result improves upon previous quantum decoders based on belief propagation, and approaches the performance of the minimum weight perfect matching algorithm. We expect semi-topological codes to have the same threshold as Toric codes, as they are identical in the bulk, and we present numerical evidence supporting this observation.

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Quantum Codes From Classical Graphical Models

Cited by 7 publications

References 34 publications

The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving

The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving

Protecting quantum memories using coherent parity check codes

Decoding Across the Quantum LDPC Code Landscape

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