Fault-tolerant quantum computation using graph states
by
Robert Raussendorf
IQI, Caltech
Coauthors: Simon Anders, Hans Briegel (University of Innsbruck, Austria)

Graph states are highly entangled multi-qubit quantum states which can be created from a product state via an Ising-type (i.e. z-z-) interaction. The neighborhood relation, i.e. which qubit interacts with whom, is specified by a graph.

Graph states form algorithmic resources for quantum computation: for every quantum algorithm there exists (at least) one graph state such that this algorithm can be realized by measuring the graph state qubits in one-qubit measurements [1]. There arises the question of whether the graph state picture of quantum computation is useful for fault- tolerance, too. In particular, can graph state constructions improve the error threshold?

As a simple illustrative example, an efficient circuit for fault- tolerant data storage (i.e. a stabilizer tester circuit) using purified bicolorable graph states [2] in a gate teleportation scheme [3] is shown. The more general problem of fault-tolerant universal quantum computation is reduced to fault-tolerantly creating two types of encoded quantum states: - +>:=X - +> and - T>:= (X+Y)/sqrt(2) - T>. Procedures to manufacture these states making use of redundant syndrome information are displayed.

[1] R. Raussendorf, D.E. Browne and H.J. Briegel, PRA 68, 022312 (2003).

[2] W. Dür, H. Aschauer and H.J. Briegel, PRL 91, 107903 (2003).

[3] D. Gottesman and I.L. Chuang, Nature 402, 390 (1999).

Date received: April 30, 2004