Journal
PHYSICAL REVIEW RESEARCH
Volume 2, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevResearch.2.032060
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Funding
- National Science Foundation [NSF PHY-1125915]
- Simons Foundation
- Heising-Simons Foundation
- Perimeter Institute for Theoretical Physics
- NSERC
- CRC program
- Government of Canada through the Department of Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Economic Development, Job Creation and Trade
- Canada CIFAR AI chair program
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We introduce a procedure to systematically search for a local unitary transformation that maps a wave function with a nontrivial sign structure into a positive-real form. The transformation is parametrized as a quantum circuit compiled into a set of one- and two-qubit gates. We design a cost function that maximizes the average sign of the output state and removes its complex phases. The optimization of the gates is performed through automatic differentiation algorithms, widely used in the machine learning community. We provide numerical evidence for significant improvements in the average sign for a two-leg triangular Heisenberg ladder with next-to-nearest-neighbor and ring-exchange interactions. This model exhibits phases where the sign structure can be removed by simple local one-qubit unitaries, but also an exotic Bose-metal phase whose sign structure induces Bose surfaces with a fermionic character and a higher entanglement that requires deeper circuits.
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