Shi-Liang Zhu

Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous-variable for simulating quantum systems at finite temperatures. Our algorithm has a time complexity scaling polynomially with the inverse temperature and the desired accuracy. We demonstrate the quantum algorithm by simulating finite temperature phase diagram of the Kitaev model. It is found that the important crossover phase diagram of the Kitaev ring can be accurately simulated by a quantum computer with only a few qubits and thus the algorithm may be readily implemented on current quantum processors. We further propose a protocol implementable with superconducting or trapped ion quantum computers.

Nonparametric learning is able to make reliable predictions by extracting information from similarities between a new set of input data and all samples. Here we point out a quantum paradigm of nonparametric learning which offers an exponential speedup over the sample size. By encoding data into quantum feature space, similarity between the data is defined as an inner product of quantum states. A quantum training state is introduced to superpose all data of samples, encoding relevant information for learning in its bipartite entanglement spectrum. We demonstrate that a trained state for prediction can be obtained by entanglement spectrum transformation, using quantum matrix toolbox. We further work out a feasible protocol to implement the quantum nonparametric learning with trapped ions, and demonstrate the power of quantum superposition for machine learning.

We propose an experimental scheme to simulate and observe the Klein tunneling of relativistic Maxwell particles with trapped ions. We explore the scattering dynamics of the pseudospin-one Maxwell particles and demonstrate that the scattered state should be a superposition of a reflection state, a localization state, and a transmission state. The probabilities of these states can be analytically obtained by the approach of Landau-Zener transition. We further show that the Maxwell Hamiltonian and the associated scattering dynamics can be mimicked with two trapped ions. The Maxwell spinors are encoded by three internal states of the first ion, the position and momentum are described by those of the motional modes, and the desired linear potential barrier is built by the second ion.

In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear regression, which utilizes both discrete and continuous quantum variables, in contrast to existing wisdoms based solely upon discrete qubits. In our framework, data information is encoded in a qubit system, while information processing is tackled using auxiliary continuous qumodes via qubit-qumode interactions. Moreover, it is also elaborated that finite squeezing is quite helpful for efficiently running the quantum algorithms in realistic setup. Comparing with an all-qubit approach, the present hybrid approach is more efficient and feasible for implementing quantum algorithms, still retaining exponential quantum speed-up.

We propose a scheme to implement high-fidelity conditional phase gates on pair of trapped ions immersed in a two-dimensional Coulomb crystal, using interaction mediated by all axial modes without side-band addressing. We show through numerical calculations that only local modes can be excited to achieve entangling gates through shaping the laser beams, so that the complexity of the quantum gate does not increase with the size of the system. These results suggest a promising approach for realization of large scale fault-tolerant quantum computation in two dimensional traps architecture.

We propose a scenario to physically implement a kind of topologically decoherence-protected qubit using superconducting devices coupled to a micro-wave cavity mode with unconventional geometric operations. It is shown that the two needed interactions for selective devices, which are required for implementing such protected qubits, as well as single-qubit gates, can be achieved by using the external magnetic flux. The easy combination of individual addressing with the many-device setup proposed in the system presents a distinct merit in comparison with the implementation of topologically protected qubits in a trapped-ion system.

We propose for the first time an experimentally feasible scheme to disclose the noncommutative effects induced by a light-induced non-Abelian gauge structure with trapped ions. Under an appropriate configuration, a true non-Abelian gauge potential naturally arises in connection with the geometric phase associated with two degenerated dark states in a four-state atomic system interacting with three pulsed laser fields. We show that the population in atomic state at the end of a composed path formed by two closed loops $C_1$ and $C_2$ in the parameter space can be significantly different from the composed counter-ordered path. This population difference is directly induced by the noncommutative feature of non-Abelian geometric phases and can be detected unambiguously with current technology.

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.

We propose a scheme to implement arbitrary-speed quantum entangling gates on two trapped ions immersed in a large linear crystal of ions, with minimal control of laser beams. For gate speeds slower than the oscillation frequencies in the trap, a single appropriately-detuned laser pulse is sufficient for high-fidelity gates. For gate speeds comparable to or faster than the local ion oscillation frequency, we discover a five-pulse protocol that exploits only the local phonon modes. This points to a method for efficiently scaling the ion trap quantum computer without shuttling ions.