  While quantum speed-up in solving certain decision problems by a
fault-tolerant universal quantum computer has been promised, a timely research
interest includes how far one can reduce the resource requirement to
demonstrate a provable advantage in quantum devices without demanding quantum
error correction, which is crucial for prolonging the coherence time of qubits.
We propose a model device made of locally-interacting multiple qubits, designed
such that simultaneous single-qubit measurements on it can output probability
distributions whose average-case sampling is classically intractable, under
similar assumptions as the sampling of non-interacting bosons and instantaneous
quantum circuits. Notably, in contrast to these previous unitary-based
realizations, our measurement-based implementation has two distinctive
features. (i) Our implementation involves no adaptation of measurement bases,
leading output probability distributions to be generated in constant time,
independent of the system size. Thus, it could be implemented in principle
without quantum error correction. (ii) Verifying the classical intractability
of our sampling is done by changing the Pauli measurement bases only at certain
output qubits. Our usage of random commuting quantum circuits in place of
computationally universal circuits allows a unique unification of sampling and
verification, so that they require the same physical resource requirements in
contrast to the more demanding verification protocols seen elsewhere in the
literature.
