  Quantum algorithms theoretically outperform classical algorithms in solving
problems of increasing size, but computational errors must be kept to a minimum
to realize this potential. Despite the development of increasingly capable
quantum computers (QCs), an experimental demonstration of a provable
algorithmic quantum speedup employing today's non-fault-tolerant, noisy
intermediate-scale quantum (NISQ) devices has remained elusive. Here, we
unequivocally demonstrate such a speedup, quantified in terms of the scaling
with the problem size of the time-to-solution metric. We implement the
single-shot Bernstein-Vazirani algorithm, which solves the problem of
identifying a hidden bitstring that changes after every oracle query, utilizing
two different 27-qubit IBM Quantum (IBMQ) superconducting processors. The
speedup is observed on only one of the two QCs (ibmq_montreal) when the quantum
computation is protected by dynamical decoupling (DD) -- a carefully designed
sequence of pulses applied to the QC that suppresses its interaction with the
environment, but not without DD. In contrast to recent quantum supremacy
demonstrations, the quantum speedup reported here does not rely on any
additional assumptions or complexity-theoretic conjectures and solves a bona
fide computational problem, in the setting of a game with an oracle and a
verifier.
