Daniel Gottesman
Title: A Simple Proof of the Threshold for Fault-Tolerant Quantum Computation

Abstract: One of the central critical results in the theory of fault-tolerant quantum computation is that arbitrarily long reliable computation is possible provided the error rate per gate and per time step is below some threshold value. This was proved by a number of groups, but the detailed published proofs are complex and furthermore only hold for concatenation of quantum error-correcting codes able to correct 2 errors per block, while typically the best estimates of the threshold value are based on the 7-qubit code, which only corrects 1 error per block. I will describe recent work by Panos Aliferis, John Preskill, and myself which substantially simplifies existing proofs and applies as well to the concatenated 7-qubit code. The new proof also provides a nice framework in which to attempt to prove relatively high values of the threshold, which so far have only emerged as estimates from simulations of fault-tolerant circuits.
Emmanuel Knill
Title: Fault-tolerant architecture for very noisy gates

Abstract: I describe some of the features of a scheme for quantum computing with gates having probabilistic and independent Pauli error probabilities of the order of 1% per gate.
Vwani Roychowdhury
Title: Fault-Tolerant Algorithmic Complexity in near-neighbor quantum computers

Abstract: We will discuss fault-tolerant architectures, related thresholds, and algorithmic complexity as they relate to near-neighbor quantum computers. In particular, we will discuss the computation of a threshold for fault-tolerant quantum computation in near-neighbor architectures, and also address the complexity issues involved in implementing quantum algorithms (e.g., the factorization algorithm).

The talk will be based on recent joint work with P. O. Boykin, T. Szkopek, H. Fan, and E. Yablonovitch.
Krysta Svore
Title: Local fault-tolerant quantum computation

Abstract: We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due to encoding. We carry out a detailed semi-numerical threshold analysis for concatenated coding using the 7-qubit CSS code in the local and `nonlocal' setting. First, we find that the threshold in the local model for the [[7,1,3]] code has a 1/r dependence, which is in correspondence with our analytical estimate. Second, the threshold, beyond the 1/r dependence, does not depend too strongly on the noise levels for transporting qubits. Beyond these results, we find that it is important to look at more than one level of concatenation in order to estimate the threshold and that it may be beneficial in certain places, like in the transportation of qubits, to do error correction only infrequently.
Daniel Lidar
Title: Fault-tolerant quantum dynamical decoupling

Abstract: We have recently introduced time-concatenated dynamical decoupling pulse sequences. Numerical and analytical results show that these pulse sequences are remarkably robust against both systematic and random control errors, thus exhibiting a rudimentary form of fault-tolerance. They super-polynomially outperform standard, periodic dynamical decoupling pulse sequences at equal cost, in the non-Markovian regime in which they apply. I will describe these results (with Kaveh Khodjasteh) in this talk. Time permitting, I will also present very recent results (with Robert Alicki and Paolo Zanardi) that point to possible internal inconsistencies in the fundamental assumptions entering into the theory of fault-tolerant quantum error correction for Markovian noise.
Panos Aliferis
Title: Quantum accuracy threshold for concatenated distance-2 codes

Abstract: I will present joint work with Daniel Gottesman and John Preskill for obtaining a proof of the threshold theorem that applies to concatenated error-detecting codes. This proof, in conjunction with the post-selected fault-tolerant architecture recently introduced by Knill, will allow us to establish rigorous lower bounds on the threshold for adversarial stochastic noise of the order of 10^{-3}.
Henry Haselgrove
Title: Noise thresholds for optical quantum computers

Abstract: I shall report on the joint work with Christopher Dawson and Michael Nielsen, to find the noise threshold for optical quantum computing. We are considering the recent proposal for combining aspects of the original KLM linear-optical scheme with that of the cluster-state model of quantum computation. I will describe how one may go about designing an efficient optical cluster-state error-correction protocol that is resistant to the combined effects of photon loss, qubit depolarisation, and inherent nondeterminism of two-qubit interactions. Threshold results based on numerical simulations will be given.
Jacob Taylor
Title: Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins

Abstract: Recently, coherent manipulation of solid-state quantum bits, analogous to well developed realisations in atomic physics, was experimentally demonstrated. However, achieving fault tolerant quantum computation entails significant mitigation of environmental couplings, which is particularly challenging in the solid-state. We develop a scalable architecture for solid-state quantum computation based on actively protected two electron spin states in quantum dots. Specifically, we find a universal set of gates for two-spin states that can be implemented using only local electrical control, with explicit suppression of hyperfine interactions, the dominant source of error. The architecture allows for a modular, hierarchical design, and includes autonomous control and non-local coupling using controlled electron transport. We present detailed analysis of quantum error correction for this architecture, and find that fault- tolerant operation appears to be achievable with present experimental methods and parameters.

The work presented is part of a collaboration with H.-A. Engel (Harvard), W. Duer (Innsbruck), A. Yacoby (Weizmann), C. M. Marcus (Harvard), and P. Zoller (Innsbruck).

Andrew Cross
Title: Accuracy threshold and architecture for trapped-ion quantum computers

Abstract: Recent experiments have demonstrated the required elements for quantum computing with trapped atomic ions. I will present a fault-tolerant system architecture that integrates these elements. The architecture is based on an array of linear traps through which ions move ballistically. Timescales for movement, gates, and measurement are related to physical limits. Networks using the [[7,1,3]] code are layed out to reduce communication distance and idle time. Finally, I will present an accuracy threshold for this architecture.

This is joint work with Tzvetan Metodiev and Isaac Chuang.

Marcus Silva
Title: A Markov chain description of error-correction

Abstract: Using symmetries inherent in the [[7,1,3]] code and circuitry used to perform fault-tolerant computation, I demonstrate how to calculate the exact error distribution in an erasure error model using Markov chains. This approach, although complex, can be automated and is an alternative to Monte Carlo simulation if the code and circuits have enough symmetry.
Debbie Leung
Title: Fault-tolerant quantum computation with graph states

Abstract: Invoking the notion of composable simulation, we provide a very simple proof why fault-tolerance and threshold analysis in graph state quantum computation require no extra technique beyond those required for the standard model. Lower bounds for the threshold thus follow from existing results.

Joint work with Panos Aliferis.