16,714 research outputs found
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
Quantum states are very delicate, so it is likely some sort of quantum error
correction will be necessary to build reliable quantum computers. The theory of
quantum error-correcting codes has some close ties to and some striking
differences from the theory of classical error-correcting codes. Many quantum
codes can be described in terms of the stabilizer of the codewords. The
stabilizer is a finite Abelian group, and allows a straightforward
characterization of the error-correcting properties of the code. The stabilizer
formalism for quantum codes also illustrates the relationships to classical
coding theory, particularly classical codes over GF(4), the finite field with
four elements. To build a quantum computer which behaves correctly in the
presence of errors, we also need a theory of fault-tolerant quantum
computation, instructing us how to perform quantum gates on qubits which are
encoded in a quantum error-correcting code. The threshold theorem states that
it is possible to create a quantum computer to perform an arbitrary quantum
computation provided the error rate per physical gate or time step is below
some constant threshold value.Comment: 46 pages, with large margins. Includes quant-ph/0004072 plus 30 pages
of new material, mostly on fault-toleranc
Resilient Quantum Computation: Error Models and Thresholds
Recent research has demonstrated that quantum computers can solve certain
types of problems substantially faster than the known classical algorithms.
These problems include factoring integers and certain physics simulations.
Practical quantum computation requires overcoming the problems of environmental
noise and operational errors, problems which appear to be much more severe than
in classical computation due to the inherent fragility of quantum
superpositions involving many degrees of freedom. Here we show that arbitrarily
accurate quantum computations are possible provided that the error per
operation is below a threshold value. The result is obtained by combining
quantum error-correction, fault tolerant state recovery, fault tolerant
encoding of operations and concatenation. It holds under physically realistic
assumptions on the errors.Comment: 19 pages in RevTex, many figures, the paper is also avalaible at
http://qso.lanl.gov/qc
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
Teleportation-Based Quantum Computation, Extended Temperley-Lieb Diagrammatical Approach and Yang--Baxter Equation
This paper focuses on the study of topological features in
teleportation-based quantum computation as well as aims at presenting a
detailed review on teleportaiton-based quantum computation (Gottesman and
Chuang, Nature 402, 390, 1999). In the extended Temperley-Lieb diagrammatical
approach, we clearly show that such topological features bring about the
fault-tolerant construction of both universal quantum gates and four-partite
entangled states more intuitive and simpler. Furthermore, we describe the
Yang--Baxter gate by its extended Temperley-Lieb configuration, and then study
teleportation-based quantum circuit models using the Yang--Baxter gate.
Moreover, we discuss the relationship between the extended Temperley-Lieb
diagrammatical approach and the Yang-Baxter gate approach. With these research
results, we propose a worthwhile subject, the extended Temperley-Lieb
diagrammatical approach, for physicists in quantum information and quantum
computation.Comment: Latex, 47 pages, many figure
- …