Challenges in Open-air Microwave Quantum Communication and Sensing

Quantum communication is a holy grail to achieve secure communication among a set of partners, since it is provably unbreakable by physical laws. Quantum sensing employs quantum entanglement as an extra resource to determine parameters by either using less resources or attaining a precision unachievable in classical protocols. A paradigmatic example is the quantum radar, which allows one to detect an object without being detected oneself, by making use of the additional asset provided by quantum entanglement to reduce the intensity of the signal. In the optical regime, impressive technological advances have been reached in the last years, such as the first quantum communication between ground and satellites, as well as the first proof-of-principle experiments in quantum sensing. The development of microwave quantum technologies turned out, nonetheless, to be more challenging. Here, we will discuss the challenges regarding the use of microwaves for quantum communication and sensing. Based on this analysis, we propose a roadmap to achieve real-life applications in these fields.Comment: Long version of the article published in the Proceeding

Digital-Analog Quantum Simulations with Superconducting Circuits

Quantum simulations consist in the intentional reproduction of physical or unphysical models into another more controllable quantum system. Beyond establishing communication vessels between unconnected fields, they promise to solve complex problems which may be considered as intractable for classical computers. From a historic perspective, two independent approaches have been pursued, namely, digital and analog quantum simulations. The former usually provide universality and flexibility, while the latter allows for better scalability. Here, we review recent literature merging both paradigms in the context of superconducting circuits, yielding: digital-analog quantum simulations. In this manner, we aim at getting the best of both approaches in the most advanced quantum platform involving superconducting qubits and microwave transmission lines. The discussed merge of quantum simulation concepts, digital and analog, may open the possibility in the near future for outperforming classical computers in relevant problems, enabling the reach of a quantum advantage.Comment: Review article, 26 pages, 4 figure

Modelling and designing a Paul ion trap

A Paul trap or quadrupole ion trap is a device designed to confine ions or charged particles in a given space. It consists of four electrodes that produce electric fields varying in time. The voltage applied to these electrodes varies harmonically with low frequency (quasi-static regime), which simplifies the model. The goal of this project is to numerically simulate in matlab a Paul trap and the motion of the ions trapped in it by discretizing the Poisson equation and applying the method of moments (MoM), first in 2D and then generalized to 3D2019/202

Coplanar Antenna Design for Microwave Entangled Signals Propagating in Open Air

Open-air microwave quantum communication and metrology protocols must be able to transfer quantum resources from a fridge, where they are created, into an environment dominated by thermal noise. Indeed, the states that carry such quantum resources are generated in a cryostat at $T_\text{in} \simeq 10^{-2}$~K and with $Z_\text{in} = 50 \, \Omega$ intrinsic impedance, and require an antenna-like device to transfer them into the open air, characterized by an intrinsic impedance of $Z_\text{out} = 377 \, \Omega$ and a temperature of $T_\text{out} \simeq 300$ K, with minimal losses. This device accomplishes a smooth impedance matching between the cryostat and the open air. Here, we study the transmission of two-mode squeezed thermal states, developing a technique to design the optimal shape of a coplanar antenna to preserve the entanglement. Based on a numerical optimization procedure we find the optimal shape of the impedance is exponential, and we adjust this shape to an analytical function. Additionally, this study reveals that losses are very sensitive to this shape, and small changes dramatically affect the outcoming entanglement, which could have been a limitation in previous experiments employing commercial antennae. This work will impact the fields of quantum sensing and quantum metrology, as well as any open-air microwave quantum communication protocol, with special application to the development of the quantum radar

Digital-analog co-design of the Harrow-Hassidim-Lloyd algorithm

The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core of various applications. However, there is not an explicit quantum circuit for the subroutine which maps the inverse of the problem matrix $A$ into an ancillary qubit. This makes challenging the implementation in current quantum devices, forcing us to use hybrid approaches. Here, we propose a systematic manner to implement this subroutine, which can be adapted to other functions $f(A)$ of the matrix $A$, we present a co-designed quantum processor which reduces the depth of the algorithm, and we introduce its digital-analog implementation. The depth of our proposal scales with the precision $\epsilon$ as $\mathcal{O}(\epsilon^{-1})$, which is bounded by the number of samples allowed for a certain experiment. The co-design of the Harrow-Hassidim-Lloyd algorithm leads to a "kite-like" architecture, which allows us to reduce the number of required SWAP gates. Finally, merging a co-design quantum processor architecture with a digital-analog implementation contributes to the reduction of noise sources during the experimental realization of the algorithm.Comment: 7 pages, 3 figure

Bi-frequency illumination: a quantum-enhanced protocol

We propose a quantum-enhanced sensing protocol to measure the response of a target object to the frequency of a probe in a noisy and lossy scenario. In our protocol, a bi-frequency state illuminates a target embedded in a thermal bath, whose reflectivity $\eta(\omega)$ is frequency-dependent. After a lossy interaction with the object, we estimate the parameter $\lambda = \eta(\omega_2)-\eta(\omega_1)$ in the reflected beam, which captures information about the response of the object to different electromagnetic frequencies. Computing the quantum Fisher information $H$ relative to the parameter $\lambda$ in an assumed neighborhood of $\lambda \sim 0$ for a two-mode squeezed state ($H_Q$), and a coherent state ($H_C$), we show that a quantum enhancement in the estimation of $\lambda$ is obtained when $H_Q / H_C >1$. This quantum advantage grows with the mean reflectivity of the probed object, and is noise-resilient. We derive explicit formulas for the optimal observables, and propose a general experimental scheme based on elementary quantum optical transformations. Furthermore, our work opens the way to applications in both radar and medical imaging, in particular in the microwave domain

Quantum Genetic Algorithm with Individuals in Multiple Registers

Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution, which are characterized by successfully finding robust solutions for optimization problems. Here, we propose a subroutine-based quantum genetic algorithm with individuals codified in independent registers. This distinctive codification allows our proposal to depict all the fundamental elements characterizing genetic algorithms, i.e. population-based search with selection of many individuals, crossover, and mutation. Our subroutine-based construction permits us to consider several variants of the algorithm. For instance, we firstly analyze the performance of two different quantum cloning machines, a key component of the crossover subroutine. Indeed, we study two paradigmatic examples, namely, the biomimetic cloning of quantum observables and the Bu\v zek-Hillery universal quantum cloning machine, observing a faster average convergence of the former, but better final populations of the latter. Additionally, we analyzed the effect of introducing a mutation subroutine, concluding a minor impact on the average performance. Furthermore, we introduce a quantum channel analysis to prove the exponential convergence of our algorithm and even predict its convergence-ratio. This tool could be extended to formally prove results on the convergence of general non-unitary iteration-based algorithms

Entanglement, fractional magnetization and long-range interactions

Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the state of a quantum spin chain.Comment: 11 pages, 1 figur