YQI Colloquium - Murphy Yuezhen Niu, Massachusetts Institute of Technology, “Three-wave-mixing Hamiltonian based quantum algorithm, quantum computation and error correcting code”

Three-wave-mixing Hamiltonians describe the lowest order nonlinear optical interactions that we know. Due to the weak photon-photon interaction strength, it is commonly used in the lab with one of the three bosonic modes set in a non-depleted coherent state for producing squeezed light. The full quantum dynamics of three-wave-mixing process and its consequence in quantum information processing is only known in the single-photon regime. Over the past decade, exciting new technologies have been expanding the platforms and increasing the efficiency of three-wave-mixing interactions. Novel systems, including solid state circuit, Josephson parametric amplifier, superconducting resonator arrays, in addition to non-depleted four-wave-mixing-induced three-wave mixing in photonic micro-structured fibers, ring resonators, and frequency-degenerate double-lambda systems, to name a few, are bringing the full quantum treatment of three-wave mixing process closer to reality.
We study the quantum dynamics of the three-wave-mixing Hamiltonians in many-photon regime, and use it to design an amplitude amplification algorithm to realize coherent photon conversion with unity-efficiency by adding nonlinear sign gates as quantum oracles. This inspires us to prove the universality of three-wave-mixing Hamiltonians in any qudit Fock-basis supported in its irreducible subspace through Lie group theoretic analysis and construction of universal gate set. Finally, we propose a new class of hardware-efficient quantum error correction for this new computing scheme, to correct any m-photon loss, m-photon gain and dephasing errors, for m<=N, using a total of O(N) photons. It is the first bosonic quantum error correcting code that has a linear scaling with N. I will give a brief overview of our previous work, and talk about some of the unpublished results in the three-wave-mixing universality and the corresponding error correcting code.