Adiabatic feedback control of Hamiltonian systems

Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators

The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site $\mathcal{PT}$-symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realise this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classi…

Addressing hard classical problems with Adiabatically Assisted Variational Quantum Eigensolvers

We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for this new algorithm is to circumvent the problem of facing very small gradients in the classical optimization piece of a VQE, while being able to run in current hardware efficient devices. A discrete concatenation of VQEs adapted to interpolating Hamiltonians provides a method to keep the quantum state always close to a path faithfully directed to find the final…

Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation

Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate the Berry phase and use it to classify the topological order of both single-particle and interacting models, highlighting the differences between the two. This algorithm is immediately extensible to any interacting topological system. Our results evidence the potential of near-term quantum hardware for the topological classification of quantum matter.

绝热量子算法的下界：基于量子速度极限

Lower bounds for adiabatic quantum algorithms by quantum speed limits

提出基于量子速度极限的框架，通过计算最终哈密顿量方差来估计绝热量子算法运行时间下界，并应用于k-团问题，证明与谱隙方法等价。

Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a multi-dimensional (usually two-dimensional) parameter space in which paths can be defined for adiabatic changes in the Hamiltonian, i.e., without closing the gap. Here, we extend the concept of Thouless pumps of band insulators by considering a larger, three-dimensional parameter space. We show that the connectivity of this parameter space is crucial for def…