  Virtual distillation is an error-mitigation technique that reduces
quantum-computation errors without assuming the noise type. In scenarios where
the user of a quantum circuit is required to additionally employ peripherals,
such as delay lines, that introduce excess noise, we find that the
error-mitigation performance can be improved if the peripheral, whenever
possible, is split across the entire circuit; that is, when the noise channel
is uniformly distributed in layers within the circuit. We show that under the
multiqubit loss and Pauli noise channels respectively, for a given overall
error rate, the average mitigation performance improves monotonically as the
noisy peripheral is split~(diluted) into more layers, with each layer
sandwiched between subcircuits that are sufficiently deep to behave as
two-designs. For both channels, analytical and numerical evidence show that
second-order distillation is generally sufficient for (near-)optimal
mitigation. We propose an application of these findings in designing a
quantum-computing cluster that houses realistic noisy intermediate-scale
quantum circuits that may be shallow in depth, where measurement detectors are
limited and delay lines are necessary to queue output qubits from multiple
circuits.
