aiqbench takeQuantum Computing

This paper claims that process matrices, which allow quantum operations without a fixed causal order, could solve NP problems and unique-sink orientation in polynomial time, and possibly exceed BQP. Any claim of polynomial-time solutions for all of NP would be a major result, so it needs independent verification and a clear account of whether the model is physically realisable. The BQP-exceeding claim is also conditional on unproven complexity assumptions, so readers should treat it as a theoretical proposal, not a demonstrated advantage.

Source coveringQuantum Zeitgeist

Process Matrices Solve NP Problems with Indefinite Causal Order

Quantum ZeitgeistOctober 30, 20264 min read

Can computation bypass established limits by abandoning strict ordering of operations? This work demonstrates algorithms solving every problem in NP and unique-sink orientation, a notoriously difficult optimisation challenge, in polynomial time using indefinite causal structures. If unique-sink orientation truly resists efficient quantum solutions, this suggests a path to computations exceeding the capabilities of standard quantum computers.

Computation can benefit from abandoning usual rules governing cause and effect using process matrices, a framework allowing connections between quantum operations without enforcing a fixed sequence. By utilising these structures, algorithms solve every problem in NP, a broad class where no fast solution has yet been discovered. Algorithms developed with this framework solve problems belonging to NP, a group considered exceptionally difficult to resolve efficiently. The work relies on ‘purifiable’ processes which adhere to…

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