Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation

Consistency testing for robust phase estimation

“…where σ x is the Pauli X matrix, and θ is the parameter we would like to learn. a single-qubit gate, noting that generalization to multiqubit unitaries is relatively straightforward [17].…”

“…Robust phase estimation (RPE) is one such protocol that was originally conceived as a method for characterizing single-qubit gates [14]. Recently, RPE implementations have been experimentally demonstrated on trapped-ion qubits [15,16] and used to simulate the ground state and low-lying electronic excitations of a hydrogen molecule on a superconducting cloud-based quantum computer [17]. RPE has Heisenberg scaling, so it is optimally fast up to constant factors.…”

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

“…Note that quantum algorithms for the direct estimation of the energy gap by combining Ramsey-type measurement and Rabi oscillation experiments or quantum annealing were proposed recently. 52,53…”

Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer

“…Such algorithms include the Lie-Trotter-Suzuki decomposition [4,37,38], truncated Taylor series [39,40], linear combinations of Lie-Trotter-Suzuki products [41,42] and random compiler [43]. Based on the simulation of unitary time evolution, one can also simulate open-system dynamics [44][45][46][47][48], solve equilibrium-state problems [49][50][51][52][53] and find the ground state for certain Hamiltonians [54][55][56][57][58][59][60][61]. However, implementing these algorithms at a meaningful scale usually requires a fault-tolerant quantum computer [62][63][64], on which the logical error rate can be reduced to any level at a polynomial cost in quantum error correction [65].…”

“…In this paper, we focus on the non-variational simulation of real time evolution. With the real time simulation, we can construct quantum phase estimation circuits [56][57][58] and eigenenergy filtering operators [59,60] to solve eigenstate and finite-temperature problems. The QCMC algorithm also provides a flexible tool for promoting variational quantum algorithms.…”