Quantum algorithms for fermionic simulations

The problem reduces to the quantum simulation of the effective Hamiltonian, which can be done in polynomial time using the procedure outlined by Ortiz et al.

“The problem then reduces to the quantum simulation of this effective Hamiltonian, , which can be done in polynomial time using the procedure outlined by Ortiz et al.23”

A quantum device can efficiently evaluate the expectation value of a tensor product of an arbitrary number of simple Pauli operators.

“A quantum device can efficiently evaluate the expectation value of a tensor product of an arbitrary number of simple Pauli operators23.”

A diverse set of experimental groups worldwide have already implemented various variational quantum algorithms on their physical systems.

“A diverse set of experimental groups worldwide have already implemented various variational quantum algorithms on their physical systems 52-59 .”

The algorithms described in Section 4 are typically beyond the limit of current error-prone quantum computers, so only proof-of-principle demonstrations for simple problems have been executed thus far.

“The algorithms described in this section are typically beyond this limit. Thus, only proof-of-principle demonstrations for simple problems have been executed thus far 55,234-236 .”

UCCSD has been demonstrated experimentally for H2 on a superconducting quantum computer.

“Finally, UCCSD has been demonstrated experimentally for HeH + using a single trapped ion 53 , for H 2 on a superconducting quantum computer 55 ,”

The first experimental demonstration of VQE was performed in 2014; the first scalable demonstration of both IPEA and VQE employed three superconducting qubits for simulating H2 in a minimal basis, and VQE with a hardware-based ansatz for H2, LiH and BeH2 was demonstrated in a six-qubit system.

“The first experimental demonstration of VQE was performed in 2014 52 .”

The variational quantum eigensolver has become the focus of state-of-the-art quantum experiments.

“This algorithm, known as the variational quantum eigensolver, as described in Section 5.1 has become the focus of the state-of-the-art quantum experiments 55,56 .”