17 research outputs found
The Fibonacci scheme for fault-tolerant quantum computation
We rigorously analyze Knill's Fibonacci scheme for fault-tolerant quantum
computation, which is based on the recursive preparation of Bell states
protected by a concatenated error-detecting code. We prove lower bounds on the
threshold fault rate of .67\times 10^{-3} for adversarial local stochastic
noise, and 1.25\times 10^{-3} for independent depolarizing noise. In contrast
to other schemes with comparable proved accuracy thresholds, the Fibonacci
scheme has a significantly reduced overhead cost because it uses postselection
far more sparingly.Comment: 24 pages, 10 figures; supersedes arXiv:0709.3603. (v2): Additional
discussion about the overhead cos
Fault-tolerant quantum computation against biased noise
We formulate a scheme for fault-tolerant quantum computation that works effectively against highly biased noise, where dephasing is far stronger than all other types of noise. In our scheme, the fundamental operations performed by the quantum computer are single-qubit preparations, single-qubit measurements, and conditional-phase (CPHASE) gates, where the noise in the CPHASE gates is biased. We show that the accuracy threshold for quantum computation can be improved by exploiting this noise asymmetry; e.g., if dephasing dominates all other types of noise in the CPHASE gates by four orders of magnitude, we find a rigorous lower bound on the accuracy threshold higher by a factor of 5 than for the case of unbiased noise
Effective fault-tolerant quantum computation with slow measurements
How important is fast measurement for fault-tolerant quantum computation?
Using a combination of existing and new ideas, we argue that measurement times
as long as even 1,000 gate times or more have a very minimal effect on the
quantum accuracy threshold. This shows that slow measurement, which appears to
be unavoidable in many implementations of quantum computing, poses no essential
obstacle to scalability.Comment: 9 pages, 11 figures. v2: small changes and reference addition
Simple proof of fault tolerance in the graph-state model
We consider the problem of fault tolerance in the graph-state model of
quantum computation. Using the notion of composable simulations, we provide a
simple proof for the existence of an accuracy threshold for graph-state
computation by invoking the threshold theorem derived for quantum circuit
computation. Lower bounds for the threshold in the graph-state model are then
obtained from known bounds in the circuit model under the same noise process.Comment: 6 pages, 2 figures, REVTeX4. (v4): Minor revisions and new title;
published versio
Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
We present a universal scheme of pulsed operations for the IBM
oscillator-stabilized flux qubit comprising the CPHASE gate, single-qubit
preparations and measurements. Based on numerical simulations, we argue that
the error rates for these operations can be as low as about .5% and that noise
is highly biased, with phase errors being stronger than all other types of
errors by a factor of nearly 10^3. In contrast, the design of a CNOT gate for
this system with an error rate of less than about 1.2% seems extremely
challenging. We propose a special encoding which exploits the noise bias
allowing us to implement a logical CNOT gate where phase errors and all other
types of errors have nearly balanced rates of about .4%. Our results illustrate
how the design of an encoding scheme can be adjusted and optimized according to
the available physical operations and the particular noise characteristics of
experimental devices.Comment: 15 pages, 7 figure