Applying quantum approximate optimization to the heterogeneous vehicle routing problem.

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the heterogeneous vehicle routing problem (HVRP): the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the HVRP using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the HVRP to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We show that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the HVRP, finding a trade-off between optimizer performance and runtime.

Gradient-Descent Quantum Process Tomography by Learning Kraus Operators.

We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive. To make the process trace preserving, we use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. Our ansatz uses a few Kraus operators to avoid direct estimation of large process matrices, e.g., the Choi matrix, for low-rank quantum processes. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes, but shines by combining the best features of these two methods. Similar to CS (but unlike PLS), GD-QPT can reconstruct a process from just a small number of random measurements, and similar to PLS (but unlike CS) it also works for larger system sizes, up to at least five qubits. We envisage that the data-driven approach of GD-QPT can become a practical tool that greatly reduces the cost and computational effort for QPT in intermediate-scale quantum systems.

Giant Atoms in a Synthetic Frequency Dimension.

Giant atoms that interact with real-space waveguides at multiple spatial points have attracted extensive attention due to their unique interference effects. Here we propose a feasible scheme for constructing giant atoms in a synthetic frequency dimension with, e.g., a dynamically modulated superconducting resonator and a tailored three-level artificial atom. Both analytical and numerical calculations show good agreement between our scheme and real-space two-level giant atoms. In particular, the symmetry of the model in momentum space can be broken by tuning the phase of the external field applied on the atom, enabling chiral interactions between the atom and the frequency lattice. We further demonstrate the possibility of simulating cascaded interaction and directional excitation transfer in the frequency dimension by directly extending our model to involve more such effective giant atoms.

Quantum State Tomography with Conditional Generative Adversarial Networks.

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.

Tunable Chiral Bound States with Giant Atoms.

We propose tunable chiral bound states in a system composed of superconducting giant atoms and a Josephson photonic-crystal waveguide (PCW), with no analog in other quantum setups. The chiral bound states arise due to interference in the nonlocal coupling of a giant atom to multiple points of the waveguide. The chirality can be tuned by changing either the atom-waveguide coupling or the external bias of the PCW. Furthermore, the chiral bound states can induce directional dipole-dipole interactions between multiple giant atoms coupling to the same waveguide. Our proposal is ready to be implemented in experiments with superconducting circuits, where it can be used as a tunable toolbox to realize topological phase transitions and quantum simulations.

Interaction of Mechanical Oscillators Mediated by the Exchange of Virtual Photon Pairs.

Two close parallel mirrors attract due to a small force (Casimir effect) originating from the quantum vacuum fluctuations of the electromagnetic field. These vacuum fluctuations can also induce motional forces exerted upon one mirror when the other one moves. Here, we consider an optomechanical system consisting of two vibrating mirrors constituting an optical resonator. We find that motional forces can determine noticeable coupling rates between the two spatially separated vibrating mirrors. We show that, by tuning the two mechanical oscillators into resonance, energy is exchanged between them at the quantum level. This coherent motional coupling is enabled by the exchange of virtual photon pairs, originating from the dynamical Casimir effect. The process proposed here shows that the electromagnetic quantum vacuum is able to transfer mechanical energy somewhat like an ordinary fluid. We show that this system can also operate as a mechanical parametric down-converter even at very weak excitations. These results demonstrate that vacuum-induced motional forces open up new possibilities for the development of optomechanical quantum technologies.

Photodetection probability in quantum systems with arbitrarily strong light-matter interaction.

Cavity-QED systems have recently reached a regime where the light-matter interaction strength amounts to a non-negligible fraction of the resonance frequencies of the bare subsystems. In this regime, it is known that the usual normal-order correlation functions for the cavity-photon operators fail to describe both the rate and the statistics of emitted photons. Following Glauber's original approach, we derive a simple and general quantum theory of photodetection, valid for arbitrary light-matter interaction strengths. Our derivation uses Fermi's golden rule, together with an expansion of system operators in the eigenbasis of the interacting light-matter system, to arrive at the correct photodetection probabilities. We consider both narrow- and wide-band photodetectors. Our description is also valid for point-like detectors placed inside the optical cavity. As an application, we propose a gedanken experiment confirming the virtual nature of the bare excitations that enrich the ground state of the quantum Rabi model.

Decoherence-Free Interaction between Giant Atoms in Waveguide Quantum Electrodynamics.

In quantum-optics experiments with both natural and artificial atoms, the atoms are usually small enough that they can be approximated as pointlike compared to the wavelength of the electromagnetic radiation with which they interact. However, superconducting qubits coupled to a meandering transmission line, or to surface acoustic waves, can realize "giant artificial atoms" that couple to a bosonic field at several points which are wavelengths apart. Here, we study setups with multiple giant atoms coupled at multiple points to a one-dimensional (1D) waveguide. We show that the giant atoms can be protected from decohering through the waveguide, but still have exchange interactions mediated by the waveguide. Unlike in decoherence-free subspaces, here the entire multiatom Hilbert space (2^{N} states for N atoms) is protected from decoherence. This is not possible with "small" atoms. We further show how this decoherence-free interaction can be designed in setups with multiple atoms to implement, e.g., a 1D chain of atoms with nearest-neighbor couplings or a collection of atoms with all-to-all connectivity. This may have important applications in quantum simulation and quantum computing.

Frequency conversion in ultrastrong cavity QED.

We propose a new method for frequency conversion of photons which is both versatile and deterministic. We show that a system with two resonators ultrastrongly coupled to a single qubit can be used to realise both single- and multiphoton frequency-conversion processes. The conversion can be exquisitely controlled by tuning the qubit frequency to bring the desired frequency-conversion transitions on or off resonance. Considering recent experimental advances in ultrastrong coupling for circuit QED and other systems, we believe that our scheme can be implemented using available technology.

Propagating phonons coupled to an artificial atom.

Quantum information can be stored in micromechanical resonators, encoded as quanta of vibration known as phonons. The vibrational motion is then restricted to the stationary eigenmodes of the resonator, which thus serves as local storage for phonons. In contrast, we couple propagating phonons to an artificial atom in the quantum regime and reproduce findings from quantum optics, with sound taking over the role of light. Our results highlight the similarities between phonons and photons but also point to new opportunities arising from the characteristic features of quantum mechanical sound. The low propagation speed of phonons should enable new dynamic schemes for processing quantum information, and the short wavelength allows regimes of atomic physics to be explored that cannot be reached in photonic systems.