High-precision quantum phase estimation on a trapped-ion quantum computer

Quantum computers keep getting bigger and bigger, with dramatically increasing physical qubit counts. In the world of applications, it is generally expected that the simulation of quantum chemistry will be of major interest; however, experiments in this area are highly constrained by circuit depth and shot count. Combined, these two facts lead to the question: before fault tolerance, how can we actually use all of the qubits?

In this talk, we first discuss difficulties presented by near-term variational algorithms within quantum-quantum chemistry. By discarding scalability with regard to system register size, we demonstrate that simulating exceptionally small chemical examples -- combined with general purpose compilation techniques -- can result in quantum phase estimation circuits that grow quadratically in depth with the number of readout qubits used, rather than exponentially. This allows us to obtain exponentially precise estimates of the ground state energy with limited resource use. We present results using this method on a 56-qubit trapped-ion quantum computer, obtaining approximately 50 bit precision on the ground state energy of the hydrogen molecule in 200 shots. Finally, we argue that despite the restriction to exceptionally small chemical systems, the approach presents a useful benchmark task for near-term devices.