Limitations in Quantum Computing from Resource Constraints

Abstract

Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily accurate, provided that errors per physical component are smaller than a certain threshold and independent of the computer size. However, in current experiments, physical-resource limitations such as energy, volume, or available bandwidth induce error rates that typically grow as the computer grows. We analyse how error correction performs under such constraints and show that the amount of error correction can be optimized, leading to a maximum attainable computational accuracy. We find this maximum for generic situations where noise is scale dependent. By inverting the logic, we provide experimenters with a tool for finding the minimum resources required to run an algorithm with a given computational accuracy. When combined with a full-stack quantum computing model, this provides the basis for energetic estimates of future large-scale quantum computers.