Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland.Minimum weight perfect matching of fault-tolerant topological quantum error correction in average o(1) parallel time. Analytic asymptotic performance of topological codes. Non-markovianity through accessible information. Felipe F Fanchini, Goktug Karpat, Baris Çakmak, LK Castelano, GH Aguilar, O Jiménez Farías, SP Walborn, PH Souto Ribeiro, and MC De Oliveira.Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment. Performing quantum computing experiments in the cloud. Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill.Linear optics simulation of quantum non-markovian dynamics. Andrea Chiuri, Chiara Greganti, Laura Mazzola, Mauro Paternostro, and Paolo Mataloni.Good quantum error-correcting codes exist. Colloquium: Non-markovian dynamics in open quantum systems. Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo, and Bassano Vacchini.Measure for the degree of non-markovian behavior of quantum processes in open systems. Heinz-Peter Breuer, Elsi-Mari Laine, and Jyrki Piilo.Quantum codes on a lattice with boundary. Experimental observation of weak non-markovianity. Nadja K Bernardes, Alvaro Cuevas, Adeline Orieux, CH Monken, Paolo Mataloni, Fabio Sciarrino, and Marcelo F Santos.Approximate quantum error correction for correlated noise. Operator quantum error-correcting subsystems for self-correcting quantum memories. Quantum accuracy threshold for concatenated distance-3 codes. Panos Aliferis, Daniel Gottesman, and John Preskill.Quantum error correction fails for hamiltonian models. ACM Journal on Emerging Technologies in Computing Systems (JETC), 12(4):39, 2016. Designing a million-qubit quantum computer using a resource performance simulator. Muhammad Ahsan, Rodney Van Meter, and Jungsang Kim.Fault-tolerant quantum computation with long-range correlated noise. Dorit Aharonov, Alexei Kitaev, and John Preskill.
In Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, pages 176-188. Fault-tolerant quantum computation with constant error. Our results suggest that progressively reducing noise level in qubits and gates is as important as continuously integrating more qubits to realize scalable and reliable quantum computer. However, if instead, per-operation qubit error probability in an n-qubits long codeword is reduced O(√ n) times below the accuracy threshold, arbitrarily accurate quantum computation becomes feasible with acceptable scaling of the codeword size. We find that in the presence of noise correlation, one cannot guarantee arbitrary high computational accuracy simply by incrementing the codeword size while retaining constant noise level per qubit operation. In this noise model, the probability distribution over set of phase-flipped qubits, decays sub-exponentially in the size of the set and carries non-trivial likelihood of the occurring large numbers of qubits errors. ACM 104 or equivalent linear algebra course.We investigate the efficacy of topological quantum error-correction in correlated noise model which permits collective coupling of all the codeword qubits to the same non-Markovian environment. Prerequisites: Ph 125, Ch 125, or equivalent graduate quantum mechanics course.
Numerical renormalization group for impurity problems.Fundamentals of matrix product states, canonical forms, computation of expectation values, matrix product operators, and other basics.Emphasis will be placed on both the theoretical foundation and practical numerical implementation of a variety of 1D and 2D tensor network algorithms. This course will cover the fundamentals of tensor networks and recent algorithmic developments from a numerical perspective. Tensor networks have emerged as a powerful tool for the numerical simulation of quantum many-body systems.