Measurement cost of metric-aware variational quantum algorithms

Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits need to be executed for sufficiently reducing shot-noise. We consider metric-aware quantum algorithms: variational algorithms that use a quantum computer to efficiently estimate both a matrix and a vector object. For example, the recently introduced quantum natural gradient approach uses the quantum Fisher information matrix as a metric tensor to correct the gradient vector for the co-dependence of the circuit parameters. We rigorously characterise and upper bound the number of measurements required to determine an iteration step to a fixed precision, and propose a general approach for optimally distributing samples between matrix and vector entries. Finally, we establish that the number of circuit repetitions needed for estimating the quantum Fisher information matrix is asymptotically negligible for an increasing number of iterations and qubits.Comment: 17 pages, 3 figure

The economic pitfalls and barriers of the sustainable tourism concept in the case of national parks

financial management;sustainable development;tourism;national parks

Sustainable tourism and policy

tourism;sustainable development;government policy;rural development

RXTE observations of the dipping low-mass X-ray binary 4U 1624-49

We analyse ~ 360 ks of archival data from the Rossi X-Ray Timing Explorer (RXTE) of the 21 hr orbital period dipping low-mass X-ray binary 4U 1624-49. We find that outside the dips the tracks in the colour-colour and hardness-intensity diagrams (CDs and HIDs) are reminiscent of those of atoll sources in the middle and upper parts of the banana branch. The tracks show secular shifts up to ~ 10%. We study the power spectrum of 4U 1624-49 as a function of the position in the CD. This is the first time power spectra of this source are presented. No quasi-periodic oscillations (QPOs) are found. The power spectra are dominated by very low frequency noise (VLFN), characteristic for atoll sources in the banana state, and band limited noise (BLN) which is not reliably detected but may, uncharacteristically, strengthen and increase in frequency with spectral hardness. The VLFN fits to a power law, which becomes steeper when the source moves to the harder part of the CD. We conclude that 4U 1624-49 is an atoll source which in our observations is in the upper banana branch. Combining this with the high (0.5-0.7 L_Edd) luminosity, the long-term flux stability of the source as seen with the RXTE All-Sky Monitor (ASM), and with the fact that it is an X-ray dip source, we conclude that 4U 1624-49 is most likely a GX atoll source such as GX 3+1 and GX 9+9, but seen edge on.Comment: 8 pages, 5 figures, 2 tables, accepted for publication in A&A. This version: a few typos correcte

The aperiodic timing behaviour of the accretion-driven millisecond pulsar SAX J1808.4-3658

We studied the aperiodic X-ray timing behaviour of the accreting millisecond pulsar SAX J1808.4-3658. The source was recently found to be the first accreting millisecond pulsar that shows the kilohertz quasi-periodic oscillations (kilohertz QPOs) that are found in many other X-ray binaries with accreting neutron stars. The high frequency of these signals reflects the short dynamical time scales in the region near the compact object where they originate. We find that in addition to the kilohertz QPOs SAX J1808.4-3658 shows several low frequency timing features, based on which the source can be classified as a so-called atoll source. The frequencies of the variability components of the atoll sources follow a universal scheme of correlations. The correlations in SAX J1808.4-3658 are similar but show a shift in upper kilohertz QPO frequency. This discrepancy is perhaps related to a stronger or differently configured magnetic field.Comment: 4 pages, 3 figures. To appear in the proceedings of the "The Restless High-Energy Universe" (Amsterdam, The Netherlands), 2003, eds. E.P.J. van den Heuvel, J.J.M. in 't Zand, and R.A.M.J. Wijer

Identification of ‘wasteful commuting’ using search theory

In this paper, we employ search theory as a micro-economic foundation for the wasteful commuting hypothesis. In the empirical analysis, the extent of the ‘wasteful commuting’ is identified by comparing the commute of employees and self-employed individuals who do not work from home. It is argued that the commute of the self-employed is the result of a search process for vacant workplaces, whereas employees search for vacant jobs. Because the arrival rate of workplaces exceeds the arrival rate of jobs, the self-employed have a shorter commute. We find that 35% of the commuting time may be considered ‘wasteful’ and reject alternative hypotheses why the self-employed have a shorter commute.