Alexander Lvovsky

Abstract:

A prerequisite to the successful development of quantum computers and simulators is precise understanding of the physical processes occurring therein, which can be achieved by measuring the quantum states that they produce. However, the resources required for traditional quantum state estimation scale exponentially with the system size, highlighting the need for alternative approaches. Here, we demonstrate an efficient method for reconstruction of significantly entangled multiqubit quantum states. Using a variational version of the matrix-product-state ansatz, we perform the tomography (in the pure-state approximation) of quantum states produced in a 20-qubit trapped-ion Ising-type quantum simulator, using the data acquired in only 27 bases, with 1000 measurements in each basis. We observe superior state-reconstruction quality and faster convergence compared to the methods based on neural-network quantum state representations: restricted Boltzmann machines and feed-forward neural networks with autoregressive architecture. Our results pave the way toward efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems.

Abstract:

Quantum state tomography is an essential component of modern quantum technology. In application to continuous-variable harmonic-oscillator systems, such as the electromagnetic field, existing tomography methods typically reconstruct the state in discrete bases, and are hence limited to states with relatively low amplitudes and energies. Here, we overcome this limitation by utilizing a feed-forward neural network to obtain the density matrix directly in the continuous position basis. An important benefit of our approach is the ability to choose specific regions in the phase space for detailed reconstruction. This results in a relatively slow scaling of the amount of resources required for the reconstruction with the state amplitude, and hence allows us to dramatically increase the range of amplitudes accessible with our method.

Abstract:

The need to observe objects that are smaller than the diffraction limit has led to the development of various superresolution techniques. However, most such techniques require active interaction with the sample, which may not be possible in multiple practical scenarios. The recently developed technique of Hermite–Gaussian imaging (HGI) achieves superresolution by passively observing the light coming from an object. This approach involves decomposing the incoming field into the Hermite–Gaussian basis of spatial modes and measuring the amplitude or intensity of each component. From these measurements, the original object can be reconstructed. However, implementing HGI experimentally has proven to be challenging, and previous achievements have focused on coherent imaging or parameter estimation of simple objects. In this paper, we implement interferometric HGI in the incoherent regime and demonstrate a three-fold improvement in the resolution compared to direct imaging. We evaluate the performance of our method under different noise levels. Our results constitute a step towards powerful passive superresolution imaging techniques in fluorescent microscopy and astronomy.