Quantum supremacy regime for compressed fermionic models
- URL: http://arxiv.org/abs/2110.09550v2
- Date: Wed, 27 Jul 2022 19:50:06 GMT
- Title: Quantum supremacy regime for compressed fermionic models
- Authors: Guillermo Bl\'azquez-Cruz, Pierre-Luc Dallaire-Demers
- Abstract summary: We identify a class of quadratic fermionic Hamiltonians that can be simulated in compressed space.
In particular, for systems of $n$ orbitals encoded to 2-local qubit models with nearest neighbour interactions, the ground state energy can be evaluated.
We find a regime of quantum supremacy for sampling compressed Gaussian fermionic models.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Compressible models extend the domain of simulable systems in quantum
computers, but little is known about their precise limits of applicability.
Using the theory of compressible matchgate circuits, we identify a class of
quadratic fermionic Hamiltonians that can be simulated in compressed space. In
particular, for systems of $n$ orbitals encoded to 2-local qubit models with
nearest neighbour interactions, the ground state energy can be evaluated with
$O\left(\log n\right)$ sets of measurements, independently of the number of
dimensions in which the $n$ sites are arranged. We also provide an expressible
circuit ansatz in a logarithmic number of qubits for finding the compressed
ground state with a variational quantum eigensolver. From the complexity
analysis of the compressed circuits, we find a regime of quantum supremacy for
sampling compressed Gaussian fermionic models.
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