Fast Classical Simulation of Linear Quantum Optics Applied to Topics in Quantum Communication and Computation

E. Knill, Raymond Laflamme, Gerard J Milburn

Lucas Andrade Alonso

In this work, we discuss the classical theory of computation, focusing specifically on the so-called computational complexity theory. We develop a theoretical background on this subject which is very useful for discussions on quantum computational supremacy, the main topic of this work, and which is currently researched very actively. It is expected that linear optics without post-selection is not universal for quantum computation, and thus is an insteresting system to try to simulate classically or to search for evidence of quantum supremacy. To set up this discussion, however, we must first, define what is linear optics, how it can be used for quantum information processing, and how this information can be encoded into photons. It is more usual to address these topics using the circuit model of computation, although the Turing model will also be briefly introduced here. Finally, by the end of this work, all tools introduced can be combined in the study of quantum computational supremacy using other restricted quantum systems.

Jeremy L. O’Brien, Geoff J. Pryde, TB Bell +3 more

Ronald E. Meyers, Keith S. Deacon, David L. Rosen

A new quantum optics tool for simulating quantum probability density functions resulting from the linear and nonlinear interaction of photons with atoms and with other photons is developed and presented. It can be used to design and simulate quantum optics experiments used in quantum communications, quantum computing, and quantum imaging. Examples of a photon interacting with linears systems of mirrors and beamsplitters are simulated. Nonlinear simulations of the interaction of three photons resulting in photon momentum entanglement is presented. The wavefunction is expanded in Fock states. Fock states cannot be represented by classical modeling and therefore, the results of our modeling can in general represent phenomena in both the linear and nonlinear cases which cannot be modeled by classical linear optics. The modeling presented here is more general than the classical linear optics. Models of atmospheric turbulence and their simulations are presented and demonstrate the potential for first principles physics quantum optics simulations through turbulence in realistic environments.

Burhan Gülbahar

Multi-plane diffraction (MPD) systems with classical sources and conventional intensity detection are recently proposed for scalable quantum computing (QC) and communications (QComm) with time domain entanglement resources and by exploiting the energy efficient interference of exponentially increasing number of propagation paths. MPD provides unique advantages for the challenges of scalability of qubits and complex set-ups including single photon generation and detection mechanisms in state-of-the-art linear optics implementations. However, MPD based QC architectures denoted by quantum path computing (QPC) are theoretically modeled for only electron based system set-up with Gaussian sources while proposed classical communication architectures are defined for free space propagation without modeling for arbitrary Fourier optical set-ups being mathematically equivalent to linear canonical transforms (LCTs). In this article, MPD architectures are defined, theoretically modeled and numerically analyzed for Fourier optics with arbitrary LCTs between diffraction planes while utilizing both Gaussian and Hermite-Gaussian laser modes. Photonic MPD proposes QC and QComm based on the mature science of Fourier optics significantly developed since the last century with globally available resources for fast and wide spread development of the proposed design. It promises the simplest linear optical system with important QC applications while promising novel resources for classical and quantum communications.

Christoph Adami, Nicolas J. Cerf