Resource quantification for programming low-depth quantum circuits

Quantum 10, 2166 (2026).

https://doi.org/10.22331/q-2026-07-20-2166

Noisy intermediate-scale quantum (NISQ) devices pave the way for implementing quantum algorithms that offer quantum advantages over their classical counterparts. Due to the intrinsic noise and decoherence in the physical system, NISQ machines are naturally modeled as large-scale, low-depth quantum circuits. In practice, executing such circuits requires sending program states that encode the relevant instructions to a programmable quantum computer, typically through a cloud service. Existing programming approaches designed for generic unitary transformations are computationally inefficient in the low-depth setting, and therefore remain unsatisfactory. As such, to realize NISQ algorithms, it is crucial to find an efficient way to program low-depth circuits as the number of qubits $N$ increases. Here, we investigate the circuit complexity and the size of quantum memory, known as the program cost, required to program low-depth brickwork circuits. We establish a tight worst-case program cost of $Theta(N mathrm{polylog} N)$ for universally programming low-depth brickwork circuits in the large-$N$ regime. Moreover, we analyze the trade-off between the cost of describing the layout of local gates and the cost of programming them to implement the target unitaries via the light-cone argument. Our findings suggest that faithful gate-wise programming is essentially optimal in the low-depth regime.