Interfering trajectories in experimental quantum-enhanced stochastic simulation.

Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices that execute a simulation using less memory than possible by classical means. To realise this advantage it is essential that the memory register remains coherent, and coherently interacts with the processor, allowing the simulator to operate over many time steps. Here we report a multi-time-step experimental simulation of a stochastic process using less memory than the classical limit. A key feature of the photonic quantum information processor is that it creates a quantum superposition of all possible future trajectories that the system can evolve into. This superposition allows us to introduce, and demonstrate, the idea of comparing statistical futures of two classical processes via quantum interference. We demonstrate interference of two 16-dimensional quantum states, representing statistical futures of our process, with a visibility of 0.96 ± 0.02.

Experimental realization of a delayed-choice quantum walk.

Many paradoxes of quantum mechanics come from the fact that quantum systems can possess different features simultaneously, such as in wave-particle duality or quantum superposition. In recent delayed-choice experiments, a quantum system can be observed to manifest one feature such as the wave or particle nature, depending on the measurement setup, which is chosen after the system itself has already entered the measuring device; hence its behaviour is not predetermined. Here we adapt this paradigmatic scheme to multi-dimensional quantum walks. In our experiment, the way in which a photon interferes with itself in a strongly non-trivial pattern depends on its polarization, which is determined after the photon has already been detected. This is the first experiment realizing a multi-dimensional quantum walk with a single photon source and we present also the first experimental simulation of the Grover walk, a model that can be used to implement the Grover quantum search algorithm.

A no-go result on the purification of quantum states.

The information encoded in a quantum system is generally spoiled by the influences of its environment, leading to a transition from pure to mixed states. Reducing the mixedness of a state is a fundamental step in the quest for a feasible implementation of quantum technologies. Here we show that it is impossible to "transfer" part of such mixedness to a "trash" system without losing some of the initial information. Such loss is lower-bounded by a value determined by the properties of the initial state to purify. We discuss this interesting phenomenon and its consequences for general quantum information theory, linking it to the information theoretical primitive embodied by the quantum state-merging protocol and to the behaviour of general quantum correlations.