Early Fault-Tolerant Quantum Computing: From Logical Gates to Applications
Recent experiments have demonstrated a universal set of logical gates with logical error rates at or below the dominant physical error rate, suggesting the advent of early fault-tolerant quantum computing. In this talk, I will discuss this development and its implications in three parts. First, I will describe new fault-tolerant constructions that reduce the cost of resource-intensive primitives such as magic state preparation. Second, I will describe compilation techniques that exploit cheaper magic states, including a catalytic approach to rotation synthesis, that realize common subroutines at speeds previously thought impossible. Third, I will describe how physically meaningful quantities, such as topological invariants of a phase of matter, can be extracted from local measurements on states prepared by such a device. Together, these results suggest how early fault-tolerant quantum computers may be used to study strongly interacting quantum many-body systems beyond the reach of classical simulation.
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