Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation

Abstract

Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in an experiment a quantum simulation of the two-dimensional non-Hermitian quantum anomalous Hall (QAH) model using the nuclear magnetic resonance processor. Unlike the usual experiments using auxiliary qubits, we develop a stochastic average approach based on the stochastic Schrödinger equation to realize the non-Hermitian dissipative quantum dynamics, which has advantages in saving the quantum simulation sources and simplifying the implementation of quantum gates. We demonstrate the stability of dynamical topology against weak noise and observe two types of dynamical topological transitions driven by strong noise. Moreover, a region where the emergent topology is always robust regardless of the noise strength is observed. Our work shows a feasible quantum simulation approach for dissipative quantum dynamics with stochastic Schrödinger equation and opens a route to investigate non-Hermitian dynamical topological physics.

Noisy intermediate-scale quantum computers

“…NMR has also found applications in various chemistry problems by directly simulating molecules or chemical reactions, such as computing the ground-state energy of a hydrogen molecule [735], finding the energy spectrum of a water molecule [736], and exploring the prototype laser-driven isomerization chemical reaction dynamics [737]. Besides, the NMR quantum simulator can also be used to investigate topological orders by simulating the ground state of a topological Hamiltonian [738][739][740][741].…”

Experimental quantum simulation of a topologically protected Hadamard gate via braiding Fibonacci anyons

“… 22 The and spins serve as two physical qubits, each being controlled by a radio-frequency (rf) field. 23 , 24 The total Hamiltonian is 25 where is the coupling strength between the qubits, and are the tunable amplitude and phase of the -th rf fields, and are the Pauli matrices acting on qubit . All experiments are conducted on a Bruker AVANCE 600 MHz spectrometer at 295 K.…”

Non-Hermitian non-equipartition theory for trapped particles

“…In recent years, interest in non-Hermitian physics 33 , 34 has grown. This interest was initially sparked by studies in quantum mechanics 35 – 39 and then spread to a wide range of areas of physical science, including classical mechanics 40 , 41 , optics 42 – 44 , acoustics 45 , 46 , metamaterials 47 , 48 , electrical circuits 49 – 52 , nuclear magnetic resonance 53 , topological photonics 54 – 56 , and optical manipulation 31 , 57 – 62 . We note that many of these topics are associated with classical physics.…”