  We present an instance of a task of minimum-error discrimination of two
qubit-qubit quantum channels for which a sequential strategy outperforms any
parallel strategy. We then establish two new classes of strategies for channel
discrimination that involve indefinite causal order and show that there exists
a strict hierarchy among the performance of all four strategies. Our proof
technique employs a general method of computer-assisted proofs. We also provide
a systematic method for finding pairs of channels that showcase this
phenomenon, demonstrating that the hierarchy between the strategies is not
exclusive to our main example.
