Resource Estimate for Quantum Many-Body Ground State Preparation on a Quantum Computer*

Quantum devices promise efficient simulation of quantum many-body systems. Of particular interest are properties at low temperature where, to a good approximation, the system is in its ground state. Thus, a quantum simulation requires a quantum circuit that maps a fiducial state to the ground state of interest. This problem is generally QMA-complete, so the existence of a general-purpose efficient procedure is believed to be impossible. Nonetheless, heuristic methods could be sufficiently fast for intermediate-size problems.

We present an estimate of the resources required to prepare the ground state of a quantum many-body system on a quantum computer. This estimate is made possible using a combination of tensor network methods and analytic upper bounds. Our procedure can also be used to optimize certain design parameters for specific instances. Lastly, we propose and benchmark an improved quantum state preparation algorithm. We find that it reduces the circuit T-depth by a factor as large as 10⁷ for intermediate-size lattices, an impressive gain for fault-tolerant quantum computers.

Based on arXiv:2006.04650.