11,100 research outputs found
Is Fault-Tolerant Quantum Computation Really Possible?
The so-called "threshold" theorem says that, once the error rate per qubit
per gate is below a certain value, indefinitely long quantum computation
becomes feasible, even if all of the qubits involved are subject to relaxation
processes, and all the manipulations with qubits are not exact. The purpose of
this article, intended for physicists, is to outline the ideas of quantum error
correction and to take a look at the proposed technical instruction for
fault-tolerant quantum computation. It seems that the mathematics behind the
threshold theorem is somewhat detached from the physical reality, and that some
ideal elements are always present in the construction. This raises serious
doubts about the possibility of large scale quantum computations, even as a
matter of principle.Comment: Based on a talk given at the Future Trends in Microelectronics
workshop, Crete, June 2006. 8 pages, 1 figur
Universal blind quantum computation
We present a protocol which allows a client to have a server carry out a
quantum computation for her such that the client's inputs, outputs and
computation remain perfectly private, and where she does not require any
quantum computational power or memory. The client only needs to be able to
prepare single qubits randomly chosen from a finite set and send them to the
server, who has the balance of the required quantum computational resources.
Our protocol is interactive: after the initial preparation of quantum states,
the client and server use two-way classical communication which enables the
client to drive the computation, giving single-qubit measurement instructions
to the server, depending on previous measurement outcomes. Our protocol works
for inputs and outputs that are either classical or quantum. We give an
authentication protocol that allows the client to detect an interfering server;
our scheme can also be made fault-tolerant.
We also generalize our result to the setting of a purely classical client who
communicates classically with two non-communicating entangled servers, in order
to perform a blind quantum computation. By incorporating the authentication
protocol, we show that any problem in BQP has an entangled two-prover
interactive proof with a purely classical verifier.
Our protocol is the first universal scheme which detects a cheating server,
as well as the first protocol which does not require any quantum computation
whatsoever on the client's side. The novelty of our approach is in using the
unique features of measurement-based quantum computing which allows us to
clearly distinguish between the quantum and classical aspects of a quantum
computation.Comment: 20 pages, 7 figures. This version contains detailed proofs of
authentication and fault tolerance. It also contains protocols for quantum
inputs and outputs and appendices not available in the published versio
Postselection threshold against biased noise
The highest current estimates for the amount of noise a quantum computer can
tolerate are based on fault-tolerance schemes relying heavily on postselecting
on no detected errors. However, there has been no proof that these schemes give
even a positive tolerable noise threshold. A technique to prove a positive
threshold, for probabilistic noise models, is presented. The main idea is to
maintain strong control over the distribution of errors in the quantum state at
all times. This distribution has correlations which conceivably could grow out
of control with postselection. But in fact, the error distribution can be
written as a mixture of nearby distributions each satisfying strong
independence properties, so there are no correlations for postselection to
amplify.Comment: 13 pages, FOCS 2006; conference versio
Efficient fault-tolerant quantum computing
Fault tolerant quantum computing methods which work with efficient quantum
error correcting codes are discussed. Several new techniques are introduced to
restrict accumulation of errors before or during the recovery. Classes of
eligible quantum codes are obtained, and good candidates exhibited. This
permits a new analysis of the permissible error rates and minimum overheads for
robust quantum computing. It is found that, under the standard noise model of
ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an
order of magnitude larger than the logical machine contained within it in order
to be reliable. For example, a scale-up by a factor of 22, with gate error rate
of order , is sufficient to permit large quantum algorithms such as
factorization of thousand-digit numbers.Comment: 21 pages plus 5 figures. Replaced with figures in new format to avoid
problem
Sufficient condition on noise correlations for scalable quantum computing
I study the effectiveness of fault-tolerant quantum computation against
correlated Hamiltonian noise, and derive a sufficient condition for
scalability. Arbitrarily long quantum computations can be executed reliably
provided that noise terms acting collectively on k system qubits are
sufficiently weak, and decay sufficiently rapidly with increasing k and with
increasing spatial separation of the qubits.Comment: 13 pages, 1 figure. (v2) Minor corrections and clarification
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