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Christopher Porter

Publications and source records attributed to Christopher Porter.

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A Framework for Quantum Advantage

As quantum computing approaches the threshold where certain tasks demonstrably outpace their classical machines, the need for a precise, clear, consensus-driven definition of quantum advantage becomes essential. Rapid progress in the field has blurred this term across companies, architectures, and application domains. Here, we aim to articulate an operational definition for quantum advantage that is both platform-agnostic and empirically verifiable. Building on this framework, we highlight the algorithmic families most likely to achieve early advantage. Finally, we outline our vision for the near future, in which quantum computers enhance existing high-performance computing platforms, enabling new frontiers in chemistry, materials discovery, optimization, and beyond.

quant-ph

Effective randomness, strong reductions and Demuth's theorem

We study generalizations of Demuth's Theorem, which states that the image of a Martin-Löf random real under a tt-reduction is either computable or Turing equivalent to a Martin-Löf random real. We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure.

math.LO