Quantum computational webs

H.-J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86

2001

Earlier work this paper cites.

R. Raussendorf and H.-J. Briegel, Phys. Rev. Lett. 86

2002

Earlier work this paper cites.

M. B. Ruskai, S. Szarek, and E. Werner, Lin. Alg. Appl. 347

2002

Earlier work this paper cites.

O. Mandel et al., Nature 425

2003

Earlier work this paper cites.

P. Aliferis and D. W. Leung, Phys. Rev. A 70

2004

Earlier work this paper cites.

F. Verstraete and J. I. Cirac, Phys. Rev. A 70

2004

Earlier work this paper cites.

M. Hein, J. Eisert, and H.-J. Briegel, Phys. Rev. A 69

2005

Cited alongside, same era.

M. Borhai and D. Loss, Phys. Rev. A 71

2005

Cited alongside, same era.

Y. Miroshnychenko et al., Nature 442

2006

Cited alongside, same era.

D. Gross and J. Eisert, Phys. Rev. Lett. 98

2007

Cited alongside, same era.

R. Hanson et al., Rev. Mod. Phys. 79

2007

Cited alongside, same era.

M. Fannes, B. Nachtergaele, and R. F. Werner, Commun. Math. Phys. 144

2007

Cited alongside, same era.

M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, and H.-J. Briegel, quant-ph/0602096

Cited in the paper.

Note that for the definition of a qubit wire as such, we do not require being able to compensate randomness of outcomes by exploiting a finite group structure of the by-product operators

Cited in the paper.

Note that our definition differs from the conventional one by the action of a local Hadamard gate on every site

Cited in the paper.

Away from (and independently of) the boundaries, an MPS is completely specified by the matrices Eq. ( 3

Cited in the paper.

We can now prove the earlier claim that in the normal form Eq. ( 3

Cited in the paper.

More generally, the method sketched above may be implemented as soon as there is some basis { | 0 θ ⟩ , | 1 θ ⟩ } \{\mbox{$|0_{\theta}\rangle$},\mbox{$|1_{\theta}\rangle$}\} s.t. A ⁡ [ 0 θ ] , A ⁡ [ 1 θ ] A[0_{\theta}],A[1_{\theta}] generate a finite group (up to scalars). It can be shown that whenever one such basis exists, there is a one-parameter set of bases with the same property upcoming . This gives rise to continuous families of wires in which randomness can be compensated by the same method

Cited in the paper.

D. Gross, J. Eisert, N. Schuch, and D. Perez-Garcia, Phys. Rev. A 76

2008

Closest in time.

B. Vaucher, A. Nunnenkamp, and D. Jaksch, New J. Phys. 10

2008

Closest in time.

G. K. Brennen and A. Miyake, Phys. Rev. Lett. 101

2008

Closest in time.

P. Barmettler at al., Phys. Rev. A 78

2008

Closest in time.

H. J. Kimble, Nature 453

2008

Closest in time.

D. Gross, S. T. Flammia, and J. Eisert, Phys. Rev. Lett. 102

2009

Closest in time.