In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used ab initio methods, which is critically limited by its nonunitary nature. The unitary modification as an ideal solution to the problem is, however, extremely inefficient in classical conventional computation. Here, we provide experimental evidence that indeed the unitary version of the coupled-cluster ansatz can be reliably performed in a physical quantum system, a trapped-ion system. We perform a simulation on the electronic structure of a molecular ion (${\mathrm{HeH}}^{+}$), where the ground-state energy surface curve is probed, the energies of the excited states are studied, and bond dissociation is simulated nonperturbatively. Our simulation takes advantages from quantum computation to overcome the intrinsic limitations in classical computation, and our experimental results indicate that the method is promising for preparing molecular ground states for quantum simulations.

We show that parity-time ($\mathcal{P}\mathcal{T}$) symmetry can be spontaneously broken in the recently reported energy level attraction of magnons and cavity photons. In the $\mathcal{P}\mathcal{T}$-broken phase, the magnon and photon form a high-fidelity Bell state with maximum entanglement. This entanglement is steady and robust against the perturbation of the environment, which is in contrast to the general wisdom that expects instability of the hybridized state when the symmetry is broken. This anomaly is further understood by the compete of non-Hermitian evolution and particle number conservation of the hybrid system. As a comparison, neither $\mathcal{P}\mathcal{T}$-symmetry breaking nor steady magnon-photon entanglement is observed inside the normal level repulsion case. Our results may open an exciting window to utilize magnon-photon entanglement as a resource for quantum information science.

Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive conditions, reducing the robustness of the resulting geometric gates against control errors. Here we show that nonadiabatic geometric gates can be constructed in an extensible way, called $\mathrm{NHQC}+$, for maintaining both flexibility and robustness against certain types of noises. Consequently, this approach makes it possible to incorporate most of the existing optimal control methods, such as dynamical decoupling, composite pulses, and a shortcut to adiabaticity, into the construction of single-looped geometric gates. Furthermore, this extensible approach of geometric quantum computation can be applied to various physical platforms such as superconducting qubits and nitrogen-vacancy centers. Specifically, we performed numerical simulation to show how the noise robustness in recent experimental implementations [ Phys. Rev. Lett. 119, 140503 (2017); Nat. Photonics 11, 309 (2017)] can be significantly improved by our $\mathrm{NHQC}+$.approach. These results cover a large class of new techniques combing the noise robustness of both geometric phase and optimal control theory.

When a quantum system is driven slowly through a parametric cycle in a degenerate Hilbert space, the state would acquire a non-Abelian geometric phase, which is stable and forms the foundation for holonomic quantum computation (HQC). However, in the adiabatic limit, the environmental decoherence becomes a significant source of errors. Recently, various nonadiabatic holonomic quantum computation (NHQC) schemes have been proposed, but all at the price of increased sensitivity to control errors. Alternatively, there exist theoretical proposals for speeding up HQC by the technique of “shortcut to adiabaticity” (STA), but no experimental demonstration has been reported so far, as these proposals involve a complicated control of four energy levels simultaneously. Here, we propose and experimentally demonstrate that HQC via shortcut to adiabaticity can be constructed with only three energy levels, using a superconducting qubit in a scalable architecture. With this scheme, all holonomic single-qubit operations can be realized nonadiabatically through a single cycle of state evolution. As a result, we are able to experimentally benchmark the stability of $\mathrm{STA}+\mathrm{HQC}$ against NHQC in the same platform. The flexibility and simplicity of our scheme makes it also implementable on other systems, such as nitrogen-vacancy center, quantum dots, and nuclear magnetic resonance. Finally, our scheme can be extended to construct two-qubit holonomic entangling gates, leading to a universal set of STAHQC gates.

Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in “big data.” A crossover between quantum information and machine learning represents a new interdisciplinary area stimulating progress in both fields. Traditionally, a quantum state is characterized by quantum-state tomography, which is a resource-consuming process when scaled up. Here we experimentally demonstrate a machine-learning approach to construct a quantum-state classifier for identifying the separability of quantum states. We show that it is possible to experimentally train an artificial neural network to efficiently learn and classify quantum states, without the need of obtaining the full information of the states. We also show how adding a hidden layer of neurons to the neural network can significantly boost the performance of the state classifier. These results shed new light on how classification of quantum states can be achieved with limited resources, and represent a step towards machine-learning-based applications in quantum information processing.

Magnon-photon coupling inside a cavity has been experimentally realized and has attracted significant attention for its potential docking with quantum information science. Whether this coupling implies the steady entanglement of photons and magnons is crucial for its usage in quantum information but is still an open question. Here we study the entanglement properties among magnons and photons in an antiferromagnet-light system and find that the entanglement between a magnon and a photon is nearly zero, while the magnon-magnon entanglement is very strong and can be even further enhanced through the coupling with the cavity photons. The maximum enhancement occurs when the antiferromagnet is resonant with the light. The essential physics can be well understood within the picture of cavity-induced cooling of the magnon-magnon state near its joint vacuum with stronger entanglement. Our findings can be used to cool magnetic magnons toward their ground state and may also be significant to extend the cavity spintronics to quantum manipulation. Furthermore, the hybrid antiferromagnet-light system provides a natural platform to manipulate the deep strong correlations of continuous modes with a generic stable condition and easy tunability.