Floquet quantum simulation with superconducting qubits

We propose a quantum algorithm for simulating spin models based on periodic modulation of transmon qubits. Using Floquet theory we derive an effective time-averaged Hamiltonian, which is of the general XYZ class, different from the isotropic XY Hamiltonian typically realised by the physical setup. As an example, we provide a simple recipe to construct a transverse Ising Hamiltonian in the Floquet basis. For a 1D system we demonstrate numerically the dynamical simulation of the transverse Ising Hamiltonian and quantum annealing to its ground state. We benchmark the Floquet approach with a digital simulation procedure, and demonstrate that it is advantageous for limited resources and finite anharmonicity of the transmons. The described protocol can serve as a simple yet reliable path towards configurable quantum simulators with currently existing superconducting chips.Comment: 6+12 pages, 4+5 figure

Unsupervised quantum machine learning for fraud detection

We develop quantum protocols for anomaly detection and apply them to the task of credit card fraud detection (FD). First, we establish classical benchmarks based on supervised and unsupervised machine learning methods, where average precision is chosen as a robust metric for detecting anomalous data. We focus on kernel-based approaches for ease of direct comparison, basing our unsupervised modelling on one-class support vector machines (OC-SVM). Next, we employ quantum kernels of different type for performing anomaly detection, and observe that quantum FD can challenge equivalent classical protocols at increasing number of features (equal to the number of qubits for data embedding). Performing simulations with registers up to 20 qubits, we find that quantum kernels with re-uploading demonstrate better average precision, with the advantage increasing with system size. Specifically, at 20 qubits we reach the quantum-classical separation of average precision being equal to 15%. We discuss the prospects of fraud detection with near- and mid-term quantum hardware, and describe possible future improvements.Comment: 7 pages, 4 figure

Quantum nondemolition measurement of mechanical motion quanta

The fields of opto- and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to preclude the detection of the mechanical mode occupation, unless strong single photon optomechanical coupling is achieved. Here, we propose and analyse an electromechanical setup, which allows to overcome this limitation and resolve the energy levels of a mechanical oscillator. We find that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups.Comment: 8 pages, 5 figures plus 24 pages, 11 figures supplemental materia

Intersubband polaritonics revisited

We revisited the intersubband polaritonics - the branch of mesoscopic physics having a huge potential for optoelectronic applications in the infrared and terahertz domains - and found that, contrary to the general opinion, the Coulomb interactions play crucial role in the processes of light-matter coupling in the considered systems. Electron-electron and electron-hole interactions radically change the nature of the elementary excitations in these systems. We show that intersubband polaritons represent the result of the coupling of a photonic mode with collective excitations, and not non-interacting electron-hole pairs as it was supposed in the previous works on the subject

Quantum topological data analysis via the estimation of the density of states

We develop a quantum topological data analysis (QTDA) protocol based on the estimation of the density of states (DOS) of the combinatorial Laplacian. Computing topological features of graphs and simplicial complexes is crucial for analyzing datasets and building explainable AI solutions. This task becomes computationally hard for simplicial complexes with over sixty vertices and high-degree topological features due to a combinatorial scaling. We propose to approach the task by embedding underlying hypergraphs as effective quantum Hamiltonians and evaluating their density of states from the time evolution. Specifically, we compose propagators as quantum circuits using the Cartan decomposition of effective Hamiltonians and sample overlaps of time-evolved states using multi-fidelity protocols. Next, we develop various post-processing routines and implement a Fourier-like transform to recover the rank (and kernel) of Hamiltonians. This enables us to estimate the Betti numbers, revealing the topological features of simplicial complexes. We test our protocol on noiseless and noisy quantum simulators and run examples on IBM quantum processors. We observe the resilience of the proposed QTDA approach to real-hardware noise even in the absence of error mitigation, showing the promise to near-term device implementations and highlighting the utility of global DOS-based estimators.Comment: 15 pages, 8 figure

Continuous wave single photon switch based on a Rydberg atom ensemble

We propose an optical single-photon switch based on Rydberg atoms that interact through van der Waals interactions. A weak coherent field probes the atomic cloud continuously, and when a single photon excites a Rydberg state, it breaks the conditions for electromagnetically induced transparency, altering the reflection/transmission. Two versions of the device are proposed, one in a single-sided cavity and the other in free space. The proposed device extends the toolkit for quantum light manipulation and photon readout, and represents a continuous wave version of previously demonstrated single-photon transistors

Continuous wave quantum light control via engineered Rydberg induced dephasing

We analyze several variations of a single-photon optical switch operating in the continuous wave regime, as presented in the accompanying paper [Tsiamis et al., Continuous wave single photon switch based on a Rydberg atom ensemble]. The devices are based on ensembles of Rydberg atoms that interact through van der Waals interaction. Continuously probing the atomic cloud with a weak coherent probe field, under the conditions of electromagnetically induced transparency (EIT) leads to total reflection/transmission of the probe in the absence of control photons. Exciting a Rydberg state with a single control photon breaks the EIT conditions, drastically altering the probe's reflectance/transmittance. We examine how the collective Rydberg interaction in an atomic ensemble enclosed in an optical cavity or in free space induces two probe-induced dephasing processes. These processes localize the control photons and modify the probe's reflectance/transmittance, enhancing the lifetime of control excitations and increasing the devices' efficiency. The devices are characterized by the probability to absorb a control photon and the associated gain as described by the change in the probe's reflectance/transmittance. The results are confirmed through numerical calculations of realistic one- and three-dimensional atomic ensembles in a cavity and an one-dimensional atomic ensemble in free space. The proposed continuous wave devices complement previously realized single photon transistors and expand the possible quantum light manipulation circuitry