On the moments of random quantum circuits and robust quantum complexity

We prove new lower bounds on the growth of robust quantum circuit complexity -- the minimal number of gates $C_{\delta}(U)$ to approximate a unitary $U$ up to an error of $\delta$ in operator norm distance. More precisely we show two bounds for random quantum circuits with local gates drawn from a subgroup of $SU(4)$. First, for $\delta=\Theta(2^{-n})$, we prove a linear growth rate: $C_{\delta}\geq d/\mathrm{poly}(n)$ for random quantum circuits on $n$ qubits with $d\leq 2^{n/2}$ gates. Second, for $\delta=\Omega(1)$, we prove a square-root growth of complexity: $C_{\delta}\geq \sqrt{d}/\mathrm{poly}(n)$ for all $d\leq 2^{n/2}$. Finally, we provide a simple conjecture regarding the Fourier support of randomly drawn Boolean functions that would imply linear growth for constant $\delta$. While these results follow from bounds on the moments of random quantum circuits, we do not make use of existing results on the generation of unitary $t$-designs. Instead, we bound the moments of an auxiliary random walk on the diagonal unitaries acting on phase states. In particular, our proof is comparably short and self-contained.Comment: 13 pages, 1 figure, v2: modified main theorem due to a gap in v

A Radio-fingerprinting-based Vehicle Classification System for Intelligent Traffic Control in Smart Cities

The measurement and provision of precise and upto-date traffic-related key performance indicators is a key element and crucial factor for intelligent traffic controls systems in upcoming smart cities. The street network is considered as a highly-dynamic Cyber Physical System (CPS) where measured information forms the foundation for dynamic control methods aiming to optimize the overall system state. Apart from global system parameters like traffic flow and density, specific data such as velocity of individual vehicles as well as vehicle type information can be leveraged for highly sophisticated traffic control methods like dynamic type-specific lane assignments. Consequently, solutions for acquiring these kinds of information are required and have to comply with strict requirements ranging from accuracy over cost-efficiency to privacy preservation. In this paper, we present a system for classifying vehicles based on their radio-fingerprint. In contrast to other approaches, the proposed system is able to provide real-time capable and precise vehicle classification as well as cost-efficient installation and maintenance, privacy preservation and weather independence. The system performance in terms of accuracy and resource-efficiency is evaluated in the field using comprehensive measurements. Using a machine learning based approach, the resulting success ratio for classifying cars and trucks is above 99%

Evaluation of Anticipatory Decision-Making in Ride-Sharing Services

In recent years, innovative ride-sharing services have gained significant attention. Such services require dynamic decisions on the acceptance of arriving trip requests and vehicle routing to ensure the fulfillment of requests. Decision support for acceptance and routing must be made under uncertainty of future requests. In this paper, we highlight that state-of-the-art approaches focus on anticipatory decision-making for either acceptance or routing decisions. Our aim is to evaluate the potential of different levels of anticipation in ride-sharing services. Up to now, it is unclear how the value of information differs between none, partial, or fully anticipatory decision-making processes. To this end, we define and solve variants of the underlying dial-a-ride problem, which differ in the information available about future requests. Using a large neighborhood search, our experimental results demonstrate that ride-sharing services can highly benefit from anticipatory decision-making, while the favorable level of anticipation depends on particular characteristics of the service, esp. the demand-to-service ratio