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We characterize in-situ grown parallel nanowires bridged by a superconducting island. The magnetic-field and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends are consistent with a sub-gap state extended over the hybrid parallel-nanowire island. Being gate-tunable, accessible by multiple terminals and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms., Comment: 9 pages, 5 figures

Superconducting devices subject to strong charging energy interactions and Coulomb blockade are one of the key elements for the development of nanoelectronics and constitute common building blocks of quantum computation platforms and topological superconducting setups. The study of their transport properties is non-trivial and some of their non-perturbative aspects are hard to capture with the most ordinary techniques. Here we present a matrix product state approach to simulate the real-time dynamics of these systems. We propose a study of their transport based on the analysis of the currents after quantum quenches connecting such devices with external leads. Our method is based on the combination of a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers. In particular, we employ a quasiparticle energy eigenbasis which greatly reduces their entanglement growth and we introduce an auxiliary degree of freedom to encode the device total charge. This approach allows us to treat non-perturbatively both their charging energy and coupling with external electrodes. We show that our construction is able to describe the Coulomb diamond structure of a superconducting dot with subgap states, including its sequential tunneling and cotunneling features. We also study the conductance zero-bias peaks caused by Majorana modes in a blockaded Kitaev chain, and compare our results with common Breit-Wigner predictions., Comment: 21 pages, 10 figures

We show that the quantum approximate optimization algorithm (QAOA) can construct, with polynomially scaling resources, the ground state of the fully connected $p$-spin Ising ferromagnet, a problem that notoriously poses severe difficulties to a vanilla quantum annealing (QA) approach due to the exponentially small gaps encountered at first-order phase transition for $p\ensuremath{\ge}3$. For a target ground state at arbitrary transverse field, we find that an appropriate QAOA parameter initialization is necessary to achieve good performance of the algorithm when the number of variational parameters $2P$ is much smaller than the system size $N$ because of the large number of suboptimal local minima. Instead, when $P$ exceeds a critical value ${P}_{N}^{*}\ensuremath{\propto}N$, the structure of the parameter space simplifies, as all minima become degenerate. This allows achieving the ground state with perfect fidelity with a number of parameters scaling extensively with $N$ and with resources scaling polynomially with $N$.

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quan-tum approximate optimization algorithm (QAOA). QAOA requires a variational minimization for states constructed by applying a sequence of unitary operators, depending on parameters living ina highly dimensional space. We reformulate such a minimum search as a learning task, where a RL agent chooses the control parameters for the unitaries, given partial information on the system. We show that our RL scheme finds a policy converging to the optimal adiabatic solution for QAOA found by Mbeng et al. arXiv:1906.08948 for the translationally invariant quantum Ising chain. In presence of disorder, we show that our RL scheme allows the training part to be performed on small samples, and transferred successfully on larger systems., 4 pages, 3 figures

We address the second-harmonic generation process in a quantum frame. Starting with a perturbative approach, we show that it is possible to achieve a number of analytic results, ranging from the up-conversion probability to the statistical properties of the generated light. In particular, the moments and the correlations of the photon-number distribution of the second-harmonic light generated by any initial state are retrieved. When possible, a comparison with the results achieved with the classical regime is successfully provided. The nonclassicality of some benchmark states is investigated by inspecting the corresponding autocorrelation function.

We study the robustness of the quantization of the Hall conductivity in the Harper-Hofstadter model towards the details of the protocol with which a longitudinal uniform driving force $F_x(t)$ is turned on. In the vector potential gauge, through Peierls substitution, this involves the switching-on of complex time-dependent hopping amplitudes $\mathrm{e}^{-\frac{i}{\hbar}\mathcal{A}_x(t)}$ in the $\hat{\mathbf{x}}$-direction such that $\partial_t \mathcal{A}_x(t)=F_x(t)$. The switching-on can be sudden, $F_x(t)=\theta(t) F$, where $F$ is the steady driving force, or more generally smooth $F_x(t)=f(t/t_{0}) F$, where $f(t/t_{0})$ is such that $f(0)=0$ and $f(1)=1$. We investigate how the time-averaged (steady-state) particle current density $j_y$ in the $\hat{\mathbf{y}}$-direction deviates from the quantized value $j_y \, h/F = n$ due to the finite value of $F$ and the details of the switching-on protocol. Exploiting the time-periodicity of the Hamiltonian $\hat{H}(t)$, we use Floquet techniques to study this problem. In this picture the (Kubo) linear response $F\to 0$ regime corresponds to the adiabatic limit for $\hat{H}(t)$. In the case of a sudden quench $j_y \, h/F$ shows $F^2$ corrections to the perfectly quantized limit. When the switching-on is smooth, the result depends on the switch-on time $t_{0}$: for a fixed $t_{0}$ we observe a crossover force $F^*$ between a quadratic regime for $FF^*$. The crossover $F^*$ decreases as $t_{0}$ increases, eventually recovering the topological robustness. These effects are in principle amenable to experimental tests in optical lattice cold atomic systems with synthetic gauge fields., Comment: 13 pages, 11 figures

We compare the performance of quantum annealing (QA, through Schr\"odinger dynamics) and simulated annealing (SA, through a classical master equation) on the $p$-spin infinite range ferromagnetic Ising model, by slowly driving the system across its equilibrium, quantum or classical, phase transition. When the phase transition is second-order ($p=2$, the familiar two-spin Ising interaction) SA shows a remarkable exponential speed-up over QA. For a first-order phase transition ($p \ge 3$, i.e., with multi-spin Ising interactions), in contrast, the classical annealing dynamics appears to remain stuck in the disordered phase, while we have clear evidence that QA shows a residual energy which decreases towards $0$ when the total annealing time $\tau$ increases, albeit in a rather slow (logarithmic) fashion. This is one of the rare examples where a limited quantum speedup, a speedup by QA over SA, has been shown to exist by direct solutions of the Schr\"odinger and master equations in combination with a non-equilibrium Landau-Zener analysis. We also analyse the imaginary-time QA dynamics of the model, finding a $1/\tau^2$ behaviour for all finite values of $p$, as predicted by the adiabatic theorem of quantum mechanics. The Grover-search limit $p({\rm odd})=\infty$ is also discussed., Comment: Submitted to PRA

We propose an implementation of a two-dimensional Z2 lattice gauge theory model on a shallow quan-tum circuit, involving a number of single-and two-qubit gates comparable to what can be achieved with present-day and near-future technologies. The ground-state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.