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Tensor network method for reversible classical computation

Journal Article · · Physical Review E
 [1];  [2];  [2];  [3];  [2]
  1. Boston Univ., MA (United States). Physics Dept.; DOE/OSTI
  2. Boston Univ., MA (United States). Physics Dept.
  3. Univ. of Central Florida, Orlando, FL (United States). Dept. of Physics
+ Show Author Affiliations
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
Research Organization:
Boston Univ., MA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
FG02-06ER46316
OSTI ID:
1541210
Alternate ID(s):
OSTI ID: 1424821
Journal Information:
Physical Review E, Journal Name: Physical Review E Journal Issue: 3 Vol. 97; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY