Ansatz

A quantum circuit consisting of parameterized gates RX(theta), RY(theta) and RZ(theta), represents a unitary transformation \(U(\theta)\) that transforms the initial quantum state into an Ansatz state \(|\psi(\theta)\rangle\).

Hardware Efficient Ansatz

Qibochem provides a hardware efficient ansatz that simply consists of a layer of single qubit rotation gates followed by a layer of two-qubit gates that entangle the qubits. For the H₂ case discussed in previous sections, a possible hardware efficient ansatz can be constructed as such:

Example

Placeholder for hardware-efficient ansatz example

Unitary Coupled Cluster Ansatz

The Unitary Coupled Cluster ansatz [1] [2] is a variant of the popular gold standard Coupled Cluster ansatz [3] of quantum chemistry. The unitary coupled cluster wave function is a parameterized unitary transformation of a reference wave function, of which a common choice is the Hartree-Fock wave function.

\[|\psi_{\mathrm{UCC}}\rangle = U(\theta)|\psi_{\mathrm{ref}}\rangle\]

Example

Placeholder for UCCD example

References

[1]

Whitfield, J. D. et al., ‘Simulation of electronic structure Hamiltonians using quantum computers’, Mol. Phys. 109 (2011) 735.

[2]

Anand. A. et al., ‘A quantum computing view on unitary coupled cluster theory’, Chem. Soc. Rev. 51 (2022) 1659.

[3]

Crawford, T. D. et al., ‘An Introduction to Coupled Cluster Theory for Computational Chemists’, in Reviews in Computational Chemistry 14 (2007) 33.