Walter V. Pogosov

We develop a theoretical description of quantum wave mixing (QWM) in a cascaded waveguide-QED system of two superconducting qubits, where the probe is driven by an external coherent tone and by the resonance fluorescence of a strongly driven source qubit. Starting from the field correlation functions of the source emission, we derive an effective master-equation treatment for the probe and identify the regime in which the incident fluorescence is characterized by anomalous correlations. When the coherent Rayleigh component of the source spectrum is suppressed, the probe equations of motion become equivalent to those for a qubit driven by a coherent tone and broadband squeezed light, although the light emitted by the source is non-Gaussian and antibunched. This equivalence implies a selection rule for the peaks of the QWM spectrum, with a strong suppression of sidebands associated with processes involving an odd number of photons taken from the source field. Numerical simulations of the full cascaded two-qubit model for different ratios of radiative decay rates unambiguously confirm the participation of correlated photon pairs in QWM processes. The current research illustrates that the analysis of peak amplitudes can be used to probe photon statistics in the incident nonclassical field.

Deep neural networks (DNN) can be applied at the post-processing stage for the improvement of the results of quantum computations on noisy intermediate-scale quantum (NISQ) processors. Here, we propose a method based on this idea, which is most suitable for digital quantum simulation characterized by the periodic structure of quantum circuits consisting of Trotter steps. A key ingredient of our approach is that it does not require any data from a classical simulator at the training stage. The network is trained to transform data obtained from quantum hardware with artificially increased Trotter steps number (noise level) towards the data obtained without such an increase. The additional Trotter steps are fictitious, i.e., they contain negligibly small rotations and, in the absence of hardware imperfections, reduce essentially to the identity gates. This preserves, at the training stage, information about relevant quantum circuit features. Two particular examples are considered that are the dynamics of the transverse-field Ising chain and XY spin chain, which were implemented on two real five-qubit IBM Q processors. A significant error reduction is demonstrated as a result of the DNN application that allows us to effectively increase quantum circuit depth in terms of Trotter steps.

We consider a hybrid digital–analog quantum computing approach, which allows implementing any quantum algorithm without standard two-qubit gates. This approach is based on the always-on interaction between qubits, which can provide an alternative to such gates. We show how digital–analog approach can be applied to simulate the dynamics of fermionic systems, in particular, the Fermi–Hubbard model, using fermionic SWAP network and refocusing technique. We concentrate on the effects of connectivity topology, the spread of interaction constants as well as on errors of entangling operations. We find that an optimal connectivity topology of qubits for the digital–analog simulation of fermionic systems of arbitrary dimensionality is a chain for spinless fermions and a ladder for spin 1/2 particles. Such a simple connectivity topology makes digital–analog approach attractive for the simulation of quantum materials and molecules.