Colloquium: Dr. Alexander V. Sergienko, Boston University

ABSTRACT:

The rapidly expanding research activity on quantum computing is ultimately an outgrowth of the profound Feynman’s observation that only quantum systems are capable to efficiently simulate other quantum systems. The goal of quantum simulation is therefore to find simple quantum systems that can accurately and efficiently simulate specific properties of interest in more complex quantum physical entities. The approaches used up to now for quantum simulations of nontrivial physical systems have substantial limitations. For example, working with cold atoms or superconducting qubits requires extremely low temperatures in order to avoid decoherence. This adds numerous complications to the experiments and makes this approach unlikely to be useful outside of research laboratories. On the other hand, analogous simulations done with traditional room-temperature optical quantum walks have their own complications. In particular, they require a set of optical resources (beam splitters, mirrors, etc.) that grows rapidly with the number of steps in the walk. 

Recently, a novel linear-optical multiport executing 3x3 and 4x4 coherent scattering matrix was proposed and demonstrated which allows photons to reverse direction, thus transcending feed-forward linear optics by providing a linear-optical scattering vertex for quantum walks on arbitrary graph structures. A quantum walk using arrays of such multiports allows simulating a broad range of discrete-time Hamiltonian systems including cases where physical systems with both spatial and internal degrees of freedom as well as execution of special topological states that are highly noise resistant. Because input ports also double as output ports, there is substantial savings of resources compared to traditional feed-forward quantum walk networks carrying out similar functions. The simulation is implemented using only linear optics. The implementation of directionally unbiased multiport executing special 4x4 Grover matrix enables access to higher-dimensional quantum optical effects and offers new approach to reconfigurable distribution of entanglement in multi-user quantum networks.