Preparing Projected Entangled Pair States on a Quantum Computer

2011/04/30 by Martin Schwarz, Kristan Temme, Frank Verstraete · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Hamiltonian (control theory) #Injective function #Inverse #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum many-body systems #Quantum mechanics #Quantum state #cond-mat.stat-mech #cs.CC #quant-ph

paper · pdf · doi:10.1103/physrevlett.108.110502

published as Phys. Rev. Lett. 108, 110502 (2012) · 5 pages, 1 figure. To be published in Physical Review Letters. Removed heuristics, refined run-time bound

arxiv created 2012/02/21 · openalex publication_date 2012/03/13 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a quantum algorithm to prepare injective projected entangled pair states (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's parent Hamiltonian.

Citations

• Criticality, the area law, and the computational power of PEPS
• Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
• Matrix product states represent ground states faithfully
• Valence-bond states for quantum computation

Cited by

• Towards quantum machine learning with tensor networks
• Unsupervised Generative Modeling Using Matrix Product States