Papers for

quantum computer architects

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Limited shared entanglement does not increase power of quantum proofs

QMA(2) with Limited Shared Entanglement

Abstract: A $\mathsf{QMA}(2)$ protocol involves two provers submitting unentangled witnesses to a polynomial-time quantum verifier. In The Power of Unentanglement (ToC, 2009), Aaronson et al. proposed $\mathsf{QMA}(2;h)$, a variant of $\mathsf{QMA}(2)$ in which the two provers may share $h$ EPR pairs. Our main result shows that the power of $\mathsf{QMA}(2)$ remains unchanged for up to logarithmically many shared EPR pairs: $\mathsf{QMA}(2;h)=\mathsf{QMA}(2)$ for $h=O(\log n)$, where $n$ is the input length. The result follows from a simulation using four unentangled witnesses, combined with the Harrow-Montanaro equality $\mathsf{QMA}(4)=\mathsf{QMA}(2)$ (FOCS, 2010). We also prove monotonicity in the EPR budget: $\mathsf{QMA}(2;h)\subseteq\mathsf{QMA}(2;H)$ for $h\le H$, preserving completeness and soundness. Combined with input padding, this shows that establishing $\mathsf{QMA}(2;n^\varepsilon)=\mathsf{QMA}(2)$ for any fixed $\varepsilon>0$ would imply equality for every polynomially bounded budget, resolving the open problem raised by Aaronson et al. Finally, we extend these results to a variant of the model in which the provers may use local operations and classical communication (LOCC) during witness preparation. For logarithmic-size witnesses and inverse-polynomial gaps, both models remain equivalent to their unentangled counterpart when $h=O(\log n)$. We show that extending this equivalence to any superlogarithmic EPR budget in the LOCC model would imply $\mathsf{NP}\subseteq\mathsf{BQP}$.

Wed 30 SeptComputational Complexity
The gist
Quantum Merlin-Arthur protocols involve two helpers sending quantum proofs to a verifier, usually without sharing special quantum links called entanglement. This paper shows that even if the helpers share a small, logarithmic amount of entanglement, it doesn't make the verification system any more powerful. They also explore what happens if the helpers can communicate classically while preparing proofs and find similar limits. Extending these results to larger entanglement budgets would imply surprising breakthroughs in classical vs quantum computing.
Open → 2609.39668v1