Detecting quantum complexity using transformer based neural network (I)*

The minimum depth required for a quantum circuit to perform a given computation is the quantum complexity of the circuit. This quantity is relevant for establishing a regime of quantum supremacy for the task. We want to address whether it can be identified from the sampled output of a quantum circuit. The quantum circuit is simulated classically using google's Cirq software, and the output wavefunction is sampled to generate a set of measured bit-strings. The circuit we choose is a pseudo-random quantum circuit consisting of random one-qubit and local two-qubit gates implemented on 20 qubits, following the reference [1]. Noise is then introduced in the circuit using a depolarizing channel, similar to the noise model for the Sycamore processor. Using the simulated data for noisy circuits, it will also be possible to address the effect of increasing noise levels on the signal for quantum complexity. We use the simulated data to train a transformer-based neural network model. 

[1] Arute, F., Arya, K., Babbush, R. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019)