Modeling Quantum Algorithm Performance on Early Fault-Tolerant Quantum Computers

Will quantum computing become useful in the early fault-tolerant era (EFTQC)?

To answer this question, we must have accurate models of such quantum computers and of algorithm performance. In the EFTQC regime, qubits will be noisy, and quantum error correction will be expensive. Hence, it is also important to analyze the cost of quantum error correction needed to achieve a certain level of performance on the quantum computer.

Toward these goals, we develop a modularized framework to model the circuit-level noise, the algorithmic noise, the algorithm success probability, and the links between them. Specifically, we apply our framework to study the performance of a phase estimation algorithm. We analyze the error correction cost for this algorithm as a function of the target error rate, physical error rate, and error-correcting code properties. Our work lays the foundation for assessing the interplay between hardware and algorithmic performances in the early fault-tolerant era and beyond.