Hamiltonians, groups, graphs and ans\"atze
- URL: http://arxiv.org/abs/2312.17146v1
- Date: Thu, 28 Dec 2023 17:28:23 GMT
- Title: Hamiltonians, groups, graphs and ans\"atze
- Authors: Abhinav Anand and Kenneth R. Brown
- Abstract summary: We introduce a new circuit design that combines graph-based diagonalization circuits with arbitrary single-qubit rotation gates.
We test the accuracy of the proposed ansatz in estimating ground state energies of various molecules of size up to 12-qubits.
- Score: 2.4094285826152593
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: One promising application of near-term quantum devices is to prepare trial
wavefunctions using short circuits for solving different problems via
variational algorithms. For this purpose, we introduce a new circuit design
that combines graph-based diagonalization circuits with arbitrary single-qubit
rotation gates to get Hamiltonian-based graph states ans\"atze (H-GSA). We test
the accuracy of the proposed ansatz in estimating ground state energies of
various molecules of size up to 12-qubits. Additionally, we compare the gate
count and parameter number complexity of the proposed ansatz against previously
proposed schemes and find an order magnitude reduction in gate count complexity
with slight increase in the number of parameters. Our work represents a
significant step towards constructing compact quantum circuits with good
trainability and convergence properties and applications in solving chemistry
and physics problems.
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