Zhaokai Li

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10−5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers

Quantum chemistry simulation on quantum computers: theories and experiments

It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.

Experimental realization of a quantum support vector machine.

Zhaokai Li, 2 Xiaomei Liu, Nanyang Xu, 2, ∗ and Jiangfeng Du 2, † Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230036, People’s Republic of China CAS Center for Excellence and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Repubilic of China

Experimental realization of quantum algorithm for solving linear systems of equations

National Key Basic Research Program of China [2013CB921800, 2014CB848700]; National Natural Science Foundation of China [11227901, 91021005, 11375167, 11004181, 11161160553]; Strategic Priority Research Program (B) of the CAS [XDB01030400]; NSF Center for Quantum Information and Computation for Chemistry [CHE-1037992]

Direct Measurement of Topological Numbers with Spins in Diamond

Topological numbers can characterize the transition between different topological phases, which are not described by Landaus paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.

Experimental observation of topological transitions in interacting multispin systems

Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct measurement of topological properties, however, is still a challenge especially in interacting quantum system. Here we realize one-dimensional Heisenberg spin chains using nuclear magnetic resonance simulators and observe the interaction-induced topological transitions, where Berry curvature in the parameter space of Hamiltonian is probed by means of dynamical response and then the first Chern number is extracted by integrating the curvature over the closed surface. The utilized experimental method provides a powerful means to explore topological phenomena in quantum systems with many-body interactions.

Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenbergs original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.

The adsorption of h-BN monolayer on the Ni(111) surface studied by density functional theory calculations with a semiempirical long-range dispersion correction

The geometric and spin-resolved electronic structure of a h-BN adsorbed Ni(111) surface has been investigated by density functional theory calculations. Two energy minima (physisorption and chemisorption) are obtained when the dispersive van der Waals correction is included. The geometry of N atom on top site and B atom on fcc site is the most energetically favorable. Strong hybridization with the ferromagnetic Ni substrate induces considerable gap states in the h-BN monolayer. The induced π* states are spin-polarized.

Experimentally probing topological order and its breakdown through modular matrices

Fundamental fingerprints of topological orders may be characterized uniquely and purely by experimental means. Here the authors provide a proof of principle demonstration using interferometric measurement in a two-dimensional lattice system.

Experimental study of quantum simulation for quantum chemistry with a nuclear magnetic resonance simulator

Quantum computers have been proved to be able to mimic quantum systems efficiently in polynomial time. Quantum chemistry problems, such as static molecular energy calculations and dynamical chemical reaction simulations, become very intractable on classical computers with scaling up of the system. Therefore, quantum simulation is a feasible and effective approach to tackle quantum chemistry problems. Proof-of-principle experiments have been implemented on the calculation of the hydrogen molecular energies and one-dimensional chemical isomerization reaction dynamics using nuclear magnetic resonance systems. We conclude that quantum simulation will surpass classical computers for quantum chemistry in the near future.