Tensor networks and graphical calculus for open quantum systems

Christopher J. Wood, Jacob Biamonte, David G. Cory

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks. In particular we demonstrate the construction of tensor networks to pictographically represent the Liouville-superoperator, Choi-matrix, process-matrix, Kraus, and system-environment representations for the evolution of quantum states, review how these representations interrelate, and illustrate how graphical manipulations of the tensor networks may be used to concisely transform between them. To further demonstrate the utility of the presented graphical calculus we include several examples where we provide arguably simpler graphical proofs of several useful quantities in quantum information theory including the composition and contraction of multipartite channels, a condition for whether an arbitrary bipartite state may be used for ancilla assisted process tomography, and the derivation of expressions for the average gate delity and entanglement delity of a channel in terms of each of the dierent representations of the channel.

Original languageEnglish (US)
Pages (from-to)759-811
Number of pages53
JournalQuantum Information and Computation
Volume15
Issue number9-10
StatePublished - Jan 1 2015

Fingerprint

Open Quantum Systems
calculus
Tensors
Calculus
Tensor
information theory
Information theory
tensors
Quantum Information Theory
matrices
Completely Positive Maps
contraction
Tomography
manipulators
derivation
Quantum State
tomography
Entanglement
Demonstrate
Manipulation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Computational Theory and Mathematics

Cite this

Wood, C. J., Biamonte, J., & Cory, D. G. (2015). Tensor networks and graphical calculus for open quantum systems. Quantum Information and Computation, 15(9-10), 759-811.
Wood, Christopher J. ; Biamonte, Jacob ; Cory, David G. / Tensor networks and graphical calculus for open quantum systems. In: Quantum Information and Computation. 2015 ; Vol. 15, No. 9-10. pp. 759-811.
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Wood, CJ, Biamonte, J & Cory, DG 2015, 'Tensor networks and graphical calculus for open quantum systems', Quantum Information and Computation, vol. 15, no. 9-10, pp. 759-811.

Tensor networks and graphical calculus for open quantum systems. / Wood, Christopher J.; Biamonte, Jacob; Cory, David G.

In: Quantum Information and Computation, Vol. 15, No. 9-10, 01.01.2015, p. 759-811.

Research output: Contribution to journalArticle

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