New surprises in quantum physics

Solomon Budnik

D A Bradley

I am grateful to Anthony Garrett for his comments in defence of the book The Dancing Wu Li Masters: An Overview of the New Physics ( Physics Bulletin August 1982 p270). It is perhaps not surprising that there should be a ‘champion’ for the book; however, I am surprised that Dr Garrett should believe that ‘any device which can help disseminate the ideas of modern physics to a broader audience is worthwhile …’.

Alex B. Grilo, Iordanis Kerenidis, Jamie Sikora

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 prove the analogous result for QMA(2) and describe a new complete problem for QMA and a stronger lower bound for the class QMA$_1$.

Miguel Ferrero, Alwyn van der Merwe

Alex B. Grilo, Iordanis Kerenidis, Jamie Sikora

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 prove the analogous result for QMA(2) and describe a new complete problem for QMA and a stronger lower bound for the class QMA 1 .