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Quantum computing by color-code lattice surgery
Andrew Landahl University of New Mexico
PIRSA:14070006 -
Quantum Error Correction for Ising Anyon Systems
PIRSA:14070005 -
Fault-Tolerant Quantum Computation with Constant Overhead
Daniel Gottesman University of Maryland, College Park
PIRSA:14070004 -
Spin glass reflection of the decoding transition for space-time codes
Alexey Kovalev University of California, Riverside
PIRSA:14070003 -
Maximum likelihood decoding threshold as a phase transition
Leonid Pryadko University of California, Riverside
PIRSA:14070002 -
Overview of the theory of spin glasses and its applications to quantum codes
Hidetoshi Nishimori Tokyo Institute of Technology
PIRSA:14070001 -
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Free Discussion
PIRSA:14060038 -
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Nuclear spin precession of noble gases in ultra low magnetic fields
Lutz Trahms Physikalisch-Technische Bundesanstalt (PTB)
PIRSA:14060033
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Injectivity radius bounds on the minimum distance of quantum LDPC codes
PIRSA:14070007Only a rare number of constructions of quantum LDPC codes are equipped with an unbounded minimum distance. Most of them are inspired by Kitaev toric codes constructed from the a tiling of the torus such as, color codes which are based on 3-colored tilings of surfaces, hyperbolic codes which are defined from hyperbolic tilings, or codes based on higher dimensional manifolds. These constructions are based on tilings of surfaces or manifolds and their parameters depend on the homology of the tiling.
In the first part of this talk, we recall homological bounds on the parameters of these quantum LDPC codes. In particular, the injectivity radius of the tiling provides a general lower bound on the minimum distance of these quantum LDPC codes.
Then, we extend the injectivity radius method to bound the minimum distance of a family of quantum LDPC codes based on Cayley graphs.
Finally, we improve these results by studying a notion of expansion of these Cayley graphs.
This talk is based on a joint work with Alain Couvreur and Gilles Zémor, and a joint work with Zhentao Li and Stephan Tommassé. -
Quantum computing by color-code lattice surgery
Andrew Landahl University of New Mexico
PIRSA:14070006In this talk, I will explain how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, I will also show how to improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits and the same time or less than associated defect-braiding methods. Per code distance, color-code lattice surgery uses approximately half the qubits and the same time or less than surface-code lattice surgery. Color-code lattice surgery can also implement the Hadamard and phase gates in a single transversal step—much faster than surface-code lattice surgery can. I will show that against uncorrelated circuit-level depolarizing noise, color-code lattice surgery uses fewer qubits to achieve the same degree of fault-tolerant error suppression as surface-code lattice-surgery when the noise rate is low enough and the error suppression demand is high enough. -
Quantum Error Correction for Ising Anyon Systems
PIRSA:14070005We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath, and we propose a phenomenological model to describe the resulting short-time dynamics, including pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of quantum information stored in the code space. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting: one based on Edmond's perfect matching algorithm and one based on the renormalization group. These decoders provably run in polynomial time, and one of them has a provable threshold against a simple iid noise model. Using numerical simulations, we find that the error correction thresholds for these codes/decoders are comparable to similar values for the toric code (an Abelian sub-model consisting of a restricted set of allowed anyons). To our knowledge, these are the first threshold results for quantum codes without explicit Pauli algebraic structure. Joint work with Courtney Brell, Simon Burton, Guillaum Dauphinais, and David Poulin, arXiv:1311.0019. -
Fault-Tolerant Quantum Computation with Constant Overhead
Daniel Gottesman University of Maryland, College Park
PIRSA:14070004The threshold theorem for fault tolerance tells us that it is possible to build arbitrarily large reliable quantum computers provided the error rate per physical gate or time step is below some threshold value. Most research on the threshold theorem so far has gone into optimizing the tolerable error rate under various assumptions, with other considerations being secondary. However, for the foreseeable future, the number of qubits may be an even greater restriction than error rates. The overhead, the ratio of physical qubits to logical qubits, determines how expensive (in qubits) a fault-tolerant computation is. Earlier results on fault tolerance used a large overhead which grows (albeit slowly) with the size of the computation. I show that using quantum LDPC codes, it is possible in principle to do fault-tolerant quantum computation with low overhead, and with the overhead constant in the size of the computation. -
Spin glass reflection of the decoding transition for space-time codes
Alexey Kovalev University of California, Riverside
PIRSA:14070003We introduce space-time quantum code construction which is based on repeating the layers of an arbitrary quantum error correcting code. The error threshold of such space-time construction is shown to be related to the fault tolerant error threshold of the original quantum error correcting code in the presence of errors in syndrome measurements. The decoding transition for space-time codes can be further mapped to random-bond Wegner spin models.
Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette Z2 gauge models) as well as unexplored earlier and generally non-local disordered spin models with non-trivial phase diagrams that include the spin glass phase.
We apply this construction to the simplest examples of recently discovered hypergraph-product codes and numerically find the fault tolerant threshold in excess of 5% by employing Monte-Carlo simulations. -
Maximum likelihood decoding threshold as a phase transition
Leonid Pryadko University of California, Riverside
PIRSA:14070002In maximum likelihood (ML) decoding, we are trying to find the most likely error given the measured syndrome. While this is hardly ever practical, such a decoder is expected to have the highest threshold.
I will discuss the mapping between the ML threshold for an infinite family of stabilizer codes and a phase transition in an associated family of Ising models with bond disorder [1]. This is a generalization of the map between the toric codes and the square lattice Ising model. Quantum LDPC codes produce generally non-local spin models with few-body interactions. A relatively simple Monte Carlo simulation of such a model can give an upper bound on the decoding threshold for the original code family. This can be used to compare code families irrespectively of decoders, and to establish an absolute measure of decoder performance.
[1] A. A. Kovalev and L. P. Pryadko, "Spin glass reflection of the decoding transition for quantum error correcting codes," unpublished,
arXiv:1311.7688 (2013). -
Overview of the theory of spin glasses and its applications to quantum codes
Hidetoshi Nishimori Tokyo Institute of Technology
PIRSA:14070001I will review the theory of spin glasses with an emphasis on gauge symmetry. A number of exact results will be shown to be derived, some of which are useful to discuss the properties of quantum LDPC codes. Also will be explained is the combination of gauge symmetry, replica method, and duality argument to predict the precise location of a multicritical point, which is equivalent to the error-tolerance limit of toric code. -
An introduction to quantum LDPC code
David Poulin Université de Sherbrooke
PIRSA:14070000In this talk, I will cover some basic notions of quantum LDPC codes, focusing on the similarities and distinctions with their classical cousins. Topics will include definitions of stabilizer quantum LDPC codes (CSS and general), iterative decoding algorithms, dual spin models, and obstructions caused by error degeneracy. The talk will be informal and a good occasion to ask questions. -
Free Discussion
PIRSA:14060038 -
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Atomic magnetometers for precision measurements
Mike Romalis Princeton University
PIRSA:14060034Atomic magnetometers have a long history in tests of Standard Model since they provide sensitive constraints on new spin interactions. I will review recent progress in magnetometry using electron and nuclear spins, describe some of the limits set on new physics and discuss ideas for future experiments. -
Nuclear spin precession of noble gases in ultra low magnetic fields
Lutz Trahms Physikalisch-Technische Bundesanstalt (PTB)
PIRSA:14060033In the low energy re¬gime, precision measurements of spin precession have gained increased attention as an alternative pathway to physics beyond the standard model. These measurements aim at the detection of minute frequency changes superimposed on low Larmor frequencies at extremely weak magnetic fields. Such measurements require an effective shielding against the magnetic field of the Earth and other perturbations. For measuring the precession frequency with high precision, a long lifetime of the precessing nuclear magnetization is required, thus the homogeneity of the applied field is a crucial parameter. In addition, criteria are needed that unambiguously distinguish magnetic artifacts from the non-magnetic exotic interactions that we search for. This can be accomplished by the concept of co-magnetometry, i.e., by simultaneous measuring the precession of two nuclear species such as 3He and 129Xe. Yet another kind of co-magnetometry is the use of SQUIDs for monitoring the spin precession. SQUIDs are magnetic field detectors of their own kind, which can measure the oscillating magnetic field generated by the precessing nuclear magnetic moment as well as the magnetic dc background field. In this presentation, I will report on the current state of the art in our lab in measurements of nuclear spin precession of noble gases.