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Instantaneous quantum polynomial time (IQP) is a model of (probably)non-universal quantum computation. Since it has been proven that IQP circuitsare unlikely to be simulated classically up to a multiplicative error and anerror in the $l_1$ norm, IQP is considered as one of the promising classes thatdemonstrates quantum supremacy. Although IQP circuits can be realized moreeasily than a universal quantum computer, demonstrating quantum supremacy isstill difficult. It is therefore desired to find subclasses of IQP that areeasy to implement. In this paper, by imposing some restrictions on IQP, wepropose ancilla-driven IQP (ADIQP) as the subclass of commuting quantumcomputation suitable for many experimental settings. We show that even thoughADIQP circuits are strictly weaker than IQP circuits in a sense, they are alsohard to simulate classically up to a multiplicative error and an error in the$l_1$ norm. Moreover, the properties of ADIQP make it easy to investigate theverifiability of ADIQP circuits and the difficulties in realizing ADIQPcircuits.

Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy