  This paper presents a novel quantum walk approach to simulating parton
showers on a quantum computer. We demonstrate that the quantum walk paradigm
offers a natural and more efficient approach to simulating parton showers on
quantum devices, with the emission probabilities implemented as the coin flip
for the walker, and the particle emissions to either gluons or quark pairs
corresponding to the movement of the walker in two dimensions. A quantum
algorithm is proposed for a simplified, toy model of a 31-step, collinear
parton shower, hence significantly increasing the number of steps of the parton
shower that can be simulated compared to previous quantum algorithms.
Furthermore, it scales efficiently: the number of possible shower steps
increases exponentially with the number of qubits, and the circuit depth grows
linearly with the number of steps. Reframing the parton shower in the context
of a quantum walk therefore brings dramatic improvements, and is a step towards
extending the current quantum algorithms to simulate more realistic parton
showers.
