Lian-Ao Wu

Continuous-variable (CV) systems are attracting increasing attention in the realization of universal quantum computation. Several recent experiments have shown the feasibility of using CV systems to, e.g., encode a qubit into a trapped-ion mechanical oscillator and perform logic gates [Nature 566, 513-517 (2019)]. The essential next step is to protect the encoded qubit from quantum decoherence, e.g., the motional decoherence due to the interaction between a mechanical oscillator and its environment. Here we propose a scheme to suppress quantum decoherence of a single-mode harmonic oscillator used to encode qubits by introducing a nonperturbative leakage elimination operator (LEO) specifically designed for this purpose. Remarkably, our nonperturbative LEO can be used to analytically derive exact equations of motion without approximations. It also allows us to prove that the effectiveness of these LEOs only depends on the integral of the pulse sequence in the time domain, while details of the pulse shape does not make a significant difference when the time period is chosen appropriately. This control method can be applied to a system at an arbitrary temperature and arbitrary system-bath coupling strength which makes it extremely useful for general open quantum systems.

We propose an analog quantum simulator that uses ion traps to realize the many-body electron-electron Coulomb interaction of an electron gas. This proposal maps a system that is difficult to solve and control to an experimentally-feasible setup that can be realized with current technologies. Using a dilatation transform, we show that ion traps can efficiently simulate electronic Coulomb interactions. No complexity overhead is added if only the energy spectrum is desired, and only a simple unitary transform is needed on the initial state otherwise. The runtime of the simulation is found to be much shorter than the timescale of the corresponding electronic system, minimizing susceptibility of the proposed quantum simulator to external noise and decoherence. This proposal works in any number of dimensions, and could be used to simulate different topological phases of electrons in graphene-like structures, by using ions trapped in honeycomb lattices.

Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest. While AQC has distinct advantages, recent researches have shown that quantumness such as quantum coherence in adiabatic processes may be lost entirely due to the system-bath interaction when the evolution time is long, and consequently the expected quantum speedup dose not show up. Here we propose a fast-signal assisted adiabatic quantum algorithm. We find that by applying a sequence of fast random or regular signals during the evolution process, the runtime can be reduced greatly, yet advantages of the adiabatic algorithm remain intact. Significantly, we present a \emph{randomized} Trotter formula and show that the driving Hamiltonian and the sequence of fast signals can be implemented simultaneously. We apply the algorithm for solving the $3$-bit exact cover problem~(EC$3$) and put forward an approach for implementing the problem with trapped ions.