29,872 research outputs found
A Study on the Noise Threshold of Fault-tolerant Quantum Error Correction
Quantum circuits implementing fault-tolerant quantum error correction (QEC)
for the three qubit bit-flip code and five-qubit code are studied. To describe
the effect of noise, we apply a model based on a generalized effective
Hamiltonian where the system-environment interactions are taken into account by
including stochastic fluctuating terms in the system Hamiltonian. This noise
model enables us to investigate the effect of noise in quantum circuits under
realistic device conditions and avoid strong assumptions such as maximal
parallelism and weak storage errors. Noise thresholds of the QEC codes are
calculated. In addition, the effects of imprecision in projective measurements,
collective bath, fault-tolerant repetition protocols, and level of parallelism
in circuit constructions on the threshold values are also studied with emphasis
on determining the optimal design for the fault-tolerant QEC circuit. These
results provide insights into the fault-tolerant QEC process as well as useful
information for designing the optimal fault-tolerant QEC circuit for particular
physical implementation of quantum computer.Comment: 9 pages, 9 figures; to be submitted to Phys. Rev.
Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
Decoherence-free subspaces (DFSs) shield quantum information from errors
induced by the interaction with an uncontrollable environment. Here we study a
model of correlated errors forming an Abelian subgroup (stabilizer) of the
Pauli group (the group of tensor products of Pauli matrices). Unlike previous
studies of DFSs, this type of errors does not involve any spatial symmetry
assumptions on the system-environment interaction. We solve the problem of
universal, fault-tolerant quantum computation on the associated class of DFSs.Comment: 22 pages, 4 figures. Sequel to quant-ph/990806
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
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
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