Undecidability in Tensor Network States

The theory of quantized directions

R. Penrose · 1967

Earlier work this paper cites.

Closed systems of functions and predicates

D. Geiger · 1968

Earlier work this paper cites.

Galois theory for post algebras. i

VG Bodnarchuk, LA Kaluzhnin, VN Kotov, and BA Romov · 1969

Earlier work this paper cites.

Unsolvability in 3 × \times 3 matrices

M. Paterson · 1970

Earlier work this paper cites.

Word problems solvable in logspace

R.J. Lipton and Y. Zalcstein · 1977

Earlier work this paper cites.

Tensor rank is np-complete

J. Hastad · 1990

Earlier work this paper cites.

Quantum mechanics near closed timelike lines

D. Deutsch · 1991

Earlier work this paper cites.

Examples of undecidable problems for 2-generator matrix semigroups

J. Cassaigne and J. Karhumäki · 1998

Cited alongside, same era.

Decidable and undecidable problems about quantum automata

V.D. Blondel, E. Jeandel, P. Koiran, and N. Portier · 2005

Cited alongside, same era.

Implementability among predicates

M. Cook and J. Bruck · 2005

Cited alongside, same era.

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

F. Verstraete, V. Murg, and J. I. Cirac · 2008

Cited alongside, same era.

Structure identification of boolean relations and plain bases for co-clones

N. Creignou, P. Kolaitis, and B. Zanuttini · 2008

Cited alongside, same era.

Renormalization and tensor product states in spin chains and lattices

J. I. Cirac and F. Verstraete · 2009

Quantum measurement occurrence is undecidable

Original

J. Eisert, MP Mueller, and C. Gogolin · 2011

Later among the works it cites.

Are problems in quantum information theory (un) decidable?

Original

M.M. Wolf, T.S. Cubitt, and D. Perez-Garcia · 2011

Later among the works it cites.

Closed timelike curves via postselection: theory and experimental test of consistency

S. Lloyd, L. Maccone, R. Garcia-Patron, V. Giovannetti, Y. Shikano, S. Pirandola, L.A. Rozema, A. Darabi, Y. Soudagar, L.K. Shalm, and A. Steinberg · 2011

Later among the works it cites.

Categorical quantum circuits

V. Bergholm and J.D. Biamonte · 2011

Later among the works it cites.

Categorical tensor network states

J.D. Biamonte, S.R. Clark, and D. Jaksch · 2011

Later among the works it cites.