We discuss the resource requirements for simulating quantum chemistry on a fault-tolerant, photonic quantum computer, reviewing and detailing modern algorithmic and compilation approaches for performing Hamiltonian simulation. In particular, we discuss the cost in terms of logical qubit and T gate count for estimating ground state energies of chemical systems using Quantum Phase Estimation (QPE) and a Hamiltonian input query model called qubitization. Certain fault-tolerant operations require the use of single-qubit “magic states” prepared by dedicated “magic state factories” (MSFs). Producing and consuming magic states in parallel is typically a prohibitively expensive task, resulting in the serial application of fault-tolerant gates. However, for larger chemical systems, the MSF constitutes a negligible fraction of the total footprint of the quantum computer, allowing for the use of multiple MSFs to produce magic states in parallel. We suggest architectural and algorithmic techniques that can accommodate such a capability. We propose a method to consume multiple magic states simultaneously, which can potentially lead to an order of magnitude reduction in the computational runtime without additional expense in the footprint. We also compile these hardware-agnostic fault-tolerant instructions into the native hardware primitives of a photonics-based approach.

Compiling quantum chemistry algorithms on photonic fault-tolerant quantum computers

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ACS Fall 2022

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