Books on Classical and Quantum Error-Correcting Codes

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Books on Classical and Quantum Error-Correcting Codes

Useful Articles and Books on Error-Correcting Codes Quantum Mechanics P. A. M. Dirac, Principles of Quantum Mechanics, Clarendon Press Oxford L. Landau and E. M. Lifshitz, Quantum Mechanics: the Non-relativistic Theory Albert Messiah, Quantum Mechanics, Dover Stephen Gasiorowicz, Quantum Mechanics, Wiley David J. Griffiths, Introduction to Quantum Mechanics, Cambridge University Press; undergraduate level J. J. Sakurai, Quantum Mechanics, (revised edition) Addison-Wesley John von Neumann, Mathematical Foundations of Quantum Mechanics", Prince- ton University Press, 1955. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics", Cambridge University Press, 1987 The Theory of Observation in Quantum Mechanics by Fritz London and Ed- mund Bauer, a set of lectures given at the Sorbonne in June 1939. Robert B. Griffiths, Consistent Quantum Theory, Cambridge University Press (2002) Yakir Aharonov and Daniel Rohrlich, Quantum Paradoxes Wiley-VCH (2005) 1 Classical Codes C. E. Shannon, A Mathematical Theory of Communication, The Bell System Technical Journal, Vol 27, 379-423, 623-656, July October 1948. Reissued De- cember 1957. LéonBrillouin, La Science et la Théoriede l'Information, Editions´ Jacques Gabay, first published in the US in 1956 as \Science and Information Theory". Thomas M. Thompson, From Error-Correcting Codes Through Sphere Packings to Simple Groups", Mathematical Association of America, 1983. R. Hill, A First Course in Coding Theory", Clarendon Press, Oxford, 1986. W Wesley Peterson and E. J. Weldon, Error-Correcting Codes, MIT Press (1961,1972) Cary Huffman and Vera Pless, Fundamentals of Error-Correcting Codes, Cam- bridge University Press (2003). Quantum Codes M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Infor- mation, Cambridge University Press (2000,2010) John Preskill's lectures on Quantum Computations http://www.theory.caltech.edu/people/preskill/ Dan Marinescu and Gabriela Marinescu, Approaching Quantum Computing, Pearson Prentice Hall (2005) Stig Stenholm and Kalle-Anti Suominen, Quantum Approach to Informatics, Wiley-Interscience (2005) Daniel Lidar and Todd Brun, Quantum Error Correction, Cambridge University Press (2013) Barbara Terhal, Quantum Error Correction for Quantum Memories, Rev. Mod. Phys. 87 (2), 207 (2015) 2.

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Achievements of the IARPA-QEO and DARPA-QAFS Programs & The
Achievements of the IARPA-QEO and DARPA-QAFS programs & The prospects for quantum enhancement with QA Elizabeth Crosson & DL, Nature Reviews Physics (2021) AQC 20201 June 22, 2021 Daniel Lidar USC A decade+ since the D‐Wave 1: where does QA stand? Numerous studies have attempted to demonstrate speedups using the D-Wave processors. Some studies have succeeded in A scaling speedup against path-integral Monte demonstrating constant-factor Carlo was claimed for quantum simulation of speedups in optimization against all geometrically frustrated magnets (scaling of classical algorithms they tried, e.g., relaxation time in escape from topological frustrated cluster-loop problems [1]. obstructions) [2]. Simulation is a natural and promising QA application. But QA was originally proposed as an optimization heuristic. No study so far has demonstrated an unequivocal scaling speedup in optimization. [1] S. Mandrà, H. Katzgraber, Q. Sci. & Tech. 3, 04LT01 (2018) [2] A. King et al., arXiv:1911.03446 What could be the reasons for the lack of scaling speedup? • Perhaps QA is inherently a poor algorithm? More on this later. • Control errors? Random errors in the final Hamiltonian (J-chaos) have a strong detrimental effect. • Such errors limit the size of QA devices that can be expected to accurately solve optimization instances without error correction/suppression [1,2]. • Decoherence? Single-qubit and ≪ anneal time. Often cited as a major problem of QA relative to the gate-model. • How important is this? Depends on weak vs strong coupling to the environment [3]. More on this later as well. [1] T. Albash, V. Martin‐Mayor, I. Hen, Q.
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The Toric Code at Finite Temperature by Christian Daniel Freeman A
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Reverse Quantum Annealing Approach to Portfolio Optimization Problems
Reverse Quantum Annealing Approach to Portfolio Optimization Problems Davide Venturelli1 Alexei Kondratyev2 1USRA Research Institute for Advanced Computer Science, Mountain View, CA 94035, USA 2Data Analytics Group, Financial Markets, Standard Chartered Bank, London EC2V 5DD, UK Abstract We investigate a hybrid quantum-classical solution method to the mean-variance port- folio optimization problems. Starting from real ﬁnancial data statistics and following the principles of the Modern Portfolio Theory, we generate parametrized samples of port- folio optimization problems that can be related to quadratic binary optimization forms programmable in the analog D-Wave Quantum Annealer 2000QTM. The instances are also solvable by an industry-established Genetic Algorithm approach, which we use as a classical benchmark. We investigate several options to run the quantum computation op- timally, ultimately discovering that the best results in terms of expected time-to-solution as a function of number of variables for the hardest instances set are obtained by seed- ing the quantum annealer with a solution candidate found by a greedy local search and then performing a reverse annealing protocol. The optimized reverse annealing proto- col is found to be more than 100 times faster than the corresponding forward quantum annealing on average. Keywords: Portfolio Optimization, Quadratic Unconstrained Binary Optimization, Quantum Annealing, Genetic Algorithm, arXiv:1810.08584v2 [quant-ph] 25 Oct 2018 Reverse Quantum Annealing JEL classiﬁcation: C61, C63, G11 1 1 Introduction One reason behind the current massive investment in quantum computing is that this computational paradigm has access to resources and techniques that are able to circumvent several bottlenecks of state-of-the-art digital algorithms.
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