Abstract
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.
Highlights
Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems
The key to achieving a quantum memory advantage is maintaining coherence of the quantum memory during the simulation process, enabling the encoding of relevant past information into nonorthogonal quantum states. This memory reduction comprises a new application of quantum processing, complementary to computational speedup[3], cryptography[4], sensing[5,6] and phase estimation[7]. This advantage was first illustrated for simulating a particular stochastic process, where past information was encoded within non-orthogonal polarisation states of a single photon[8]
The scheme, maintained quantum coherence over only a single simulation cycle. This limitation meant that the resulting simulator exhibited a memory advantage only when simulating a single time step
Summary
Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. The key to achieving a quantum memory advantage is maintaining coherence of the quantum memory during the simulation process, enabling the encoding of relevant past information into nonorthogonal quantum states. This memory reduction comprises a new application of quantum processing, complementary to computational speedup[3], cryptography[4], sensing[5,6] and phase estimation[7]. As an important additional benefit, our device enables us to create a quantum superposition over all potential future outcomes of a process We illustrate that such an output lets us estimate the distinguishability in the statistical futures of two stochastic systems via quantum interference. These are interfered, allowing estimation of how well the corresponding statistical futures coincide
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
