905 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 versus Gaussian noise
We study the robustness of a fault-tolerant quantum computer subject to
Gaussian non-Markovian quantum noise, and we show that scalable quantum
computation is possible if the noise power spectrum satisfies an appropriate
"threshold condition." Our condition is less sensitive to very-high-frequency
noise than previously derived threshold conditions for non-Markovian noise.Comment: 30 pages, 6 figure
The Non-Equilibrium Reliability of Quantum Memories
The ability to store quantum information without recourse to constant
feedback processes would yield a significant advantage for future
implementations of quantum information processing. In this paper, limitations
of the prototypical model, the Toric code in two dimensions, are elucidated
along with a sufficient condition for overcoming these limitations.
Specifically, the interplay between Hamiltonian perturbations and dynamically
occurring noise is considered as a system in its ground state is brought into
contact with a thermal reservoir. This proves that when utilizing the Toric
code on N^2 qubits in a 2D lattice as a quantum memory, the information cannot
be stored for a time O(N). In contrast, the 2D Ising model protects classical
information against the described noise model for exponentially long times. The
results also have implications for the robustness of braiding operations in
topological quantum computation.Comment: 4 pages. v3: published versio
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 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
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