Preparing projected entangled pair states on a quantum computer

Abstract

We present a quantum algorithm to prepare injective PEPS on a quantum computer, a class of open tensor networks representing quantum states. The run-time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS' parent Hamiltonian.

5 pages, 1 figure. To be published in Physical Review Letters. Removed heuristics, refined run-time bound

References in corpus (5)

• Quantum algorithm for solving linear systems of equations
• Matrix product states represent ground states faithfully
• Criticality, the area law, and the computational power of PEPS
• Valence Bond Solids for Quantum Computation
• Quantum rejection sampling

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