Core Concepts
QMA with non-collapsing measurements is equivalent to NEXP, showcasing the power of efficient superposition detection in quantum computing.
Abstract
The content explores the equivalence between QMA and NEXP through the use of non-collapsing measurements for superposition detection. It delves into the complexities of hidden-variable theories and quantum verification, highlighting the power of quantum advice and witness separability. The study introduces a new approach to demonstrate this equivalence by detecting superposition efficiently, providing insights into the limitations and capabilities of different computational models in quantum complexity theory.
Stats
We prove that QMA where the verifier may also make a single non-collapsing measurement [ABFL14] is equal to NEXP.
Recently, [JW23] proposed a new approach to show QMA(2) = NEXP by introducing the class QMA+(2), where the witness is also guaranteed to have non-negative amplitudes in the computational basis.
Very recently, Aaronson asked the following question: What is the power of QMA where the verifier can make non-collapsing measurements?
Consider a variant of QMA where for any constant k and ϵ > 0, there exists some ∆ = Ω(1/poly(n)) such that SupDetectk,ϵ,∆ can be efficiently applied to the quantum witness after a partial measurement in the computational basis.
Quotes
"QMA with non-collapsing measurements equals NEXP." - [AGI+24]
"Efficient superposition detection showcases powerful capabilities in quantum computing." - [BFM23]