Panos Aliferis

Threshold lower bounds for Knill's Fibonacci scheme

Imagine we encode quantum computation using a distance-2 code, we perform error detection after every logical gate, and every time we detect an error we flag the corresponding logical gate as being a possibly faulty. Further, imagine we repeat this encoding in a self-similar way several times so that eventually computation is encoded in a concatenated distance-2 code. This is Knill's Fibonacci scheme which I will discuss in this talk.

Michael Ben-Or

Limitations  of Noisy Reversible Computations II

Together with Dorit Aharonov, Noam Nisan and Russel Impagliazzo [quant-ph/9611028] we studied the limitations of noisy reversible computation when no fresh ancillary bits/qubits are available, and each bit/qubit is subjected to an independent depolarizing channel.Answering a question of Robert Alicki we study the same problem when we replace the depolarizing channel by a general 1-qubit noise model. Our results divide the possible single qubit noise models to three distinct groups: Log-Group: Extending the result on the depolarizing channel we show that for any unital channel that maps the entire Bloch sphere into the interior of the sphere one cannot compute for more than logarithmic time, and if the noise is weak enough logarithmic time quantum computation is possible. Exp-Group: For any non-unital (weak enough) noise an exponentially long computation is possible (and this is tight of course). 

Poly-Group: For unital channels such as the phase damping channel (i.e. the map of the Bloch sphere intersects the boundary at exactly two antipodal points) arbitrary long classical computation is possible, but general quantum computation is limited to polynomial time (and this is indeed possible if the noise is weak enough).

Andrew Cross (work with David DiVincenzo and Barbara Terhal)
Fault-tolerant quantum architecture: a comparative code analysis 
For the foreseeable future, large scale quantum computer architectures capable of executing Shor's factoring algorithm will require fault-tolerant logic gates constructed using a hierarchy of concatenated quantum codes. It is highly desirable that such code architecture has a (1) high noise threshold which is largely determined by the quantum code used at the inner, physical, level, and (2) minimizes the code overhead. We have carried out a comparative code analysis of quantum codes that can be used at the inner, physical, level. In particular we have numerically studied the noise rates of controlled-NOT extended rectangles for CSS codes such as quadratic residue codes, polynomial codes, Bacon-Shor codes, and surface codes under depolarizing noise. Our numerical results suggest that thresholds of O(1e-3) are possible with modest overhead. We outline how our inner code analysis fits in the larger code hierarchy.

Austin Fowler
Scalable quantum computer architecture for superconducting flux qubits
For a quantum computer architecture to be called scalable, it should in principle be possible to construct an arbitrarily large number of qubits, including all necessary classical control circuitry and devices, and the number of simultaneous measurements and gates should grow linearly with the number of qubits.  Furthermore, where heat dissipation is an issue, the cooling power of the computer should also grow linearly with the number of qubits.  Lastly, and most importantly, the physics of each individual measurement or gate should not depend on the total number of qubits.  In this talk, we present a quantum computer architecture for superconducting flux qubits that satisfies the above definition of scalability.  We also show that despite optimising the design to permit simple and efficient error correction, the threshold two-qubit gate error rate of the architecture is $6.25\times 10^{-6}$ due to the lack of arbitrarily long-range interactions and the limited dimensionality of the qubit layout -- both general features of real quantum computer architectures.

Michael Garrett and David L. Feder
Perfect Cluster States from Imperfect Entanglement in Optical Lattices 

The cluster state, the highly entangled multipartite initial state for one-way quantum computing, can be generated from a gas of ultracold atoms confined in a 2D optical lattice. In practice, a systematic phase error is expected in the entangling process, resulting in imperfect cluster states. We present a technique for generating perfect cluster states from such imperfect entanglement, employing a stochastic measurement protocol and multiple applications of the entangling operation. The technique also allows the construction of more exotic graph states, and is applicable to any implementation in which the cluster state is generated by a global Hamiltonian with imperfect timings.

Daniel Lidar
Low-level fault tolerance via Concatenated Dynamical Decoupling

Chris Monroe
Errors in the Trapped Ion Quantum Computer 

While ion traps are arguably one of the most attractive candidates for large-scale quantum computing, there remain several sources of errors that currently limit gate fidelities.  These experimental imperfections will be outlined, in the context of several approaches for scaling the trapped ion quantum computer.

Robert Raussendorf 
Fault-tolerant quantum computation with high threshold in two dimensions 
Together with J. Harrington and K. Goyal, we present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is  0.75\% for each source in an error model with preparation, gate, storage and measurement errors.

Ben Reichardt

Symmetrised tomography for efficient characterisation of noisy quantum channels

A complete description of a noise process E acting on a quantum state of n qubits requires O(2^(4n)) parameters, and the measurement of such parameters requires an exponential number of experimental configurations.

This task is infeasible in practice already for the systems of qubits that can be coherently controlled with current technology.  To address this problem, we propose an efficient symmetrisation process for estimating coarse-grained parameters describing E.  These coarse grained parameters are of practical interest as they can be used to test a necessary condition for independence of fault locations, as well as to test for some non-Markovian effects. Moreover, these parameters can be used to evaluate the fidelity of a noise process with respect to the identity map as well as probabilities for low-weight multi-qubit errors.  We demonstrate the application of this protocol to characterise control sequeces in solid state NMR.

Federico Spedalieri 
Latency in fault-tolerant quantum computing with local, two-dimensional architecture 
Authors: Federico Spedalieri and Vwani Roychowdhury, Department of Electrical Engineering, UCLA 

We analyze the latency of fault-tolerant quantum computing with a two-dimensional architecture, using the 9-qubit Bacon-Shor code, and exploiting its remarkable fault-tolerant features pointed out by Aliferis and Cross (q-ph/0610063) .Using only local operations (CNOT, SWAP, preparation and measurement) we show how to implement the encoded operations necessary for fault-tolerant error correction. This scheme improves the latency for error correction with respect to the similar work done by Svore, DiVincenzo and Terhal (q-ph/0604090), by a factor of (0.4)^k, for k levels of concatenation, using essentially the same number of physical qubits. Furthemore, this reduction in latency implies a smaller number of locations in the CNOT extended rectangle, and hence may provide a higher error threshold.

Jake Taylor
Small scale gadgets for large scale processing 
Efforts for improving fault-tolerant thresholds generally rely on critical assumptions about the scale and complexity of the underlying physical architecture.  To date, experimental efforts have been limited to small scale quantum systems which have naturally occurring complexity issues as system size grows.  Accordingly, I would like to consider fault tolerant operation when there exists a limiting natural scale above which operations (such as measurement and entanglement generation) are extremely faulty.  The conditions under which fault tolerance can emerge in such a scenario will be considered for some specific error correction and detection protocols.