Abstract
The class QMA plays a fundamental role in quantum complexity theory and it has found surprising connections to condensed matter physics and in particular in the study of the minimum energy of quantum systems. In this paper, we further investigate the class QMA and its related class QCMA by asking what makes quantum witnesses potentially more powerful than classical ones. We provide a definition of a new class, SQMA, where we restrict the possible quantum witnesses to the “simpler” subset states, i.e. a uniform superposition over the elements of a subset of n-bit strings. Surprisingly, we prove that this class is equal to QMA, hence providing a new characterisation of the class QMA. We also describe a new complete problem for QMA and a stronger lower bound for the class \({\text {QMA}}_1\).
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Notes
- 1.
This polynomial needs to have degree at least that of m (see Theorem 3 for a formal statement).
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Acknowledgements
We acknowledge support from a Government of Canada NSERC Postdoctoral Fellowship, ANR RDAM (ANR-12-BS02-005), ERC QCC and FP7 QAlgo. Research at CQT at NUS is partially funded by the Singapore Ministry of Education and the National Research Foundation, also through the Tier 3 Grant “Random numbers from quantum processes,” (MOE2012-T3-1-009).
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Grilo, A.B., Kerenidis, I., Sikora, J. (2015). QMA with Subset State Witnesses. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48054-0_14
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