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 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. These factors strongly limit the ability to use the current optical approaches for practical simulations on a large scale, and so it is of interest to investigate schemes that may be more easily scalable.

Here we present a novel quantum linear-optical strategy [1-3] whose resource requirements grow much slower than all previous optical approaches. It is currently practical to carry out a table-top version of our new procedure, and in the near future it should be plausible to implement it on much larger scales by integrating all of the required optical elements onto optical chips that can be fabricated in large numbers and arranged into the desired configurations with high stability. In contrast to the quadratic growth in conventional optical implementations of quantum walks, the resources required in our new approach scale only linearly with number of steps. Furthermore, this scheme has the advantage that the parameters of the underlying system on which the walk occurs can be readily varied to produce a variety of simulated behaviors.

Professor Alexander Sergienko holds joint appointments in the Department of Electrical and Computer Engineering, in the Photonics center, and in the Department of Physics at Boston University. His research interests include quantum information processing including quantum cryptography and communications, quantum simulation, quantum networking, quantum imaging, the development of novel ultra-precise optical-measurement and characterization techniques (quantum metrology) that are based on the use of non-classical states of light. He pioneered the experimental development of practical quantum-measurement techniques using entangled-photon states. Professor Sergienko has published more than 400 research and conference papers and holds 6 patents in the fields of experimental quantum optics and entanglement. He is the editor of "Quantum Communications and Cryptography" (CRC/Taylor & Francis, 2006) and a co-author of “Quantum Metrology, Imaging, and Communication" (Springer, 2017). He is a Fellow of the Optical Society of America, a member of the APS and IEEE.

Department of Physics and Astronomy

1. D. S. Simon, C. A. Fitzpatrick, and A. V. Sergienko, ''Group Transformations and Entangled-State Quantum Gates with Directionally-Unbiased Linear-Optical Multiports,'', Phys. Rev. A 93, 043845 (2016).
2. D. S. Simon, C. A. Fitzpatrick, S. Osawa and A. V. Sergienko, ''Quantum Simulation of Discrete-Time Hamiltonians Using Directionally-UnbiasedLinear Optical Multiports,'' Phys. Rev. A 95, 042109 (2017).
3. D. S. Simon, C. A. Fitzpatrick, S. Osawa, and A. V. Sergienko, ''Quantum Simulation of Topologically Protected States Using Directionally Unbiased Linear-Optical Multiports'', Physical Review A 96, 013858 (2017).

Researchers should cite this work as follows:

• Alexander V. Sergienko (2017), "Quantum Optical Simulation of Complex Physical Hamiltonians," https://nanohub.org/resources/27459.

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