Measurement-based quantum computation with the toric code states
Open accessAbstract
We study measurement-based quantum computation (MQC) using as a quantum resource the planar code state on a two-dimensional square lattice (planar analog of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer if at each step of MQC the sets of measured and unmeasured qubits correspond to connected subsets of the lattice. The simulation scheme is built upon Barahona's algorithm for computing the partition function of the Ising model on a planar graph. Our results provide a simulation method for MQC centered around planarity of graphs.
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Toric code states and ground states of several 1D spin systems are examples of simulatable states.
“Further interesting examples of simulatable states include the toric code states 92 and the ground states of several 1D spin systems 93 .”
From Measurement-based quantum computation (2009) · cites this paper as [92]
The solvability of the 2D Ising model without magnetic fields implies that MQC on the toric code state can be efficiently simulated.
“For example, the solvability of the 2D Ising model without magnetic fields implies that MQC on the toric code state 74 can be efficiently simulated 92 .”
From Measurement-based quantum computation (2009) · cites this paper as [92]
The partition function Z_L is identified with a quantum mechanical amplitude obtained as an overlap between two quantum states.
“This expression states that the partition function Z L is identified with a quantum mechanical amplitude which is obtained as an overlap between two quantum states 92,95,96 (see also 99 ).”
From Measurement-based quantum computation (2009) · cites this paper as [92]
These connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting.
“For one, these connections enable one to phrase statistical physics problems naturally in a quantum mechanical setting 87,92,95,96,99-102 .”
From Measurement-based quantum computation (2009) · cites this paper as [92]
The Ising model on an arbitrary lattice L can be mapped to an MQC model in which the entangled resource is determined by the geometry of L.
“The connection between MQC and the Ising model is given by a mapping of the Ising model on an arbitrary lattice L to an MQC model where the entangled resource is determined by the geometry of L ,”
From Measurement-based quantum computation (2009) · cites this paper as [92]
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- Authors
- Bravyi, S., & Raussendorf, R.
- Affiliations
- IBM Research - Thomas J. Watson Research Center (US)
- Perimeter Institute (CA)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-08-06
- Volume
- 76
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1986240479
- Cited by
- 69
- References
- 28
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 3 · 2023: 2 · 2022: 3 · 2021: 5 · 2019: 3 · 2018: 4 · 2017: 1 · 2016: 1 · 2015: 2 · 2014: 6 · 2013: 4 · 2012: 4
- FWCI
- 9.06
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- measurement-based quantum computation, toric code, classical simulation of quantum computation, planar graphs, square lattice
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