Implementation of a Toffoli Gate with Superconducting Circuits

The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubit, the number of elementary gates needed for the implementation of the Toffoli gate, as well as the total gate time can be reduced significantly in comparison to theoretical proposals using two-level systems only. We characterize the performance of the gate by full process tomography and Monte Carlo process certification. The gate fidelity is found to be $68.5\pm0.5$%.Comment: 4 pages, 5figure

Computing prime factors with a Josephson phase qubit quantum processor

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5], however this has yet to be shown using solid state quantum bits (qubits). Two advantages of superconducting qubit architectures are the use of conventional microfabrication techniques, which allow straightforward scaling to large numbers of qubits, and a toolkit of circuit elements that can be used to engineer a variety of qubit types and interactions[6, 7]. Using a number of recent qubit control and hardware advances [7-13], here we demonstrate a nine-quantum-element solid-state QuP and show three experiments to highlight its capabilities. We begin by characterizing the device with spectroscopy. Next, we produces coherent interactions between five qubits and verify bi- and tripartite entanglement via quantum state tomography (QST) [8, 12, 14, 15]. In the final experiment, we run a three-qubit compiled version of Shor's algorithm to factor the number 15, and successfully find the prime factors 48% of the time. Improvements in the superconducting qubit coherence times and more complex circuits should provide the resources necessary to factor larger composite numbers and run more intricate quantum algorithms.Comment: 5 pages, 3 figure

Trapped electron coupled to superconducting devices

We propose to couple a trapped single electron to superconducting structures located at a variable distance from the electron. The electron is captured in a cryogenic Penning trap using electric fields and a static magnetic field in the Tesla range. Measurements on the electron will allow investigating the properties of the superconductor such as vortex structure, damping and decoherence. We propose to couple a superconducting microwave resonator to the electron in order to realize a circuit QED-like experiment, as well as to couple superconducting Josephson junctions or superconducting quantum interferometers (SQUIDs) to the electron. The electron may also be coupled to a vortex which is situated in a double well potential, realized by nearby pinning centers in the superconductor, acting as a quantum mechanical two level system that can be controlled by a transport current tilting the double well potential. When the vortex is trapped in the interferometer arms of a SQUID, this would allow its detection both by the SQUID and by the electron.Comment: 13 pages, 5 figure

OpenFermion: The Electronic Structure Package for Quantum Computers

Quantum simulation of chemistry and materials is predicted to be an important application for both near-term and fault-tolerant quantum devices. However, at present, developing and studying algorithms for these problems can be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. To help bridge this gap and open the field to more researchers, we have developed the OpenFermion software package (www.openfermion.org). OpenFermion is an open-source software library written largely in Python under an Apache 2.0 license, aimed at enabling the simulation of fermionic models and quantum chemistry problems on quantum hardware. Beginning with an interface to common electronic structure packages, it simplifies the translation between a molecular specification and a quantum circuit for solving or studying the electronic structure problem on a quantum computer, minimizing the amount of domain expertise required to enter the field. The package is designed to be extensible and robust, maintaining high software standards in documentation and testing. This release paper outlines the key motivations behind design choices in OpenFermion and discusses some basic OpenFermion functionality which we believe will aid the community in the development of better quantum algorithms and tools for this exciting area of research.Comment: 22 page

On the distance of the globular cluster M4 (NGC 6121) using RR Lyrae stars: I. optical and near-infrared Period-Luminosity and Period-Wesenheit relations

We present new distance determinations to the nearby globular M4 (NGC~6121) based on accurate optical and Near Infrared (NIR) mean magnitudes for fundamental (FU) and first overtone (FO) RR Lyrae variables (RRLs), and new empirical optical and NIR Period-Luminosity (PL) and Period-Wesenheit (PW) relations. We have found that optical-NIR and NIR PL and PW relations are affected by smaller standard deviations than optical relations. The difference is the consequence of a steady decrease in the intrinsic spread of cluster RRL apparent magnitudes at fixed period as longer wavelengths are considered. The weighted mean visual apparent magnitude of 44 cluster RRLs is \left=13.329\pm0.001 (standard error of the mean) $\pm$0.177 (weighted standard deviation) mag. Distances were estimated using RR Lyr itself to fix the zero-point of the empirical PL and PW relations. Using the entire sample (FU$+$FO) we found weighted mean true distance moduli of 11.35$\pm$0.03$\pm$0.05 mag and 11.32$\pm$0.02$\pm$0.07 mag. Distances were also evaluated using predicted metallicity dependent PLZ and PWZ relations. We found weighted mean true distance moduli of 11.283$\pm$0.010$\pm$0.018 mag (NIR PLZ) and 11.272$\pm$0.005$\pm$0.019 mag (optical--NIR and NIR PWZ). The above weighted mean true distance moduli agree within 1$\sigma$. The same result is found from distances based on PWZ relations in which the color index is independent of the adopted magnitude (11.272$\pm$0.004$\pm$0.013 mag). These distances agree quite well with the geometric distance provided by \citep{kaluzny2013} based on three eclipsing binaries. The available evidence indicates that this approach can provide distances to globulars hosting RRLs with a precision better than 2--3\%.Comment: Accepted for publication on Ap

On the Use of Field RR Lyrae as Galactic Probes. V. Optical and radial velocity curve templates

We collected the largest spectroscopic catalog of RR Lyrae (RRLs) including $\approx$20,000 high-, medium- and low-resolution spectra for $\approx$10,000 RRLs. We provide the analytical forms of radial velocity curve (RVC) templates. These were built using 36 RRLs (31 fundamental -- split into three period bins -- and 5 first overtone pulsators) with well-sampled RVCs based on three groups of metallic lines (Fe, Mg, Na) and four Balmer lines (H$_\alpha$, H$_\beta$, H$_\gamma$, H$_\delta$). We tackled the long-standing problem of the reference epoch to anchor light curve and RVC templates. For the $V$-band, we found that the residuals of the templates anchored to the phase of the mean magnitude along the rising branch are $\sim$35\% to $\sim$45\% smaller than those anchored to the phase of maximum light. For the RVC, we used two independent reference epochs for metallic and Balmer lines and we verified that the residuals of the RVC templates anchored to the phase of mean RV are from 30\% (metallic lines) up to 45\% (Balmer lines) smaller than those anchored to the phase of minimum RV. We validated our RVC templates by using both the single- and the three-phase points approach. We found that barycentric velocities based on our RVC templates are two-three times more accurate than those available in the literature. We applied the current RVC templates to Balmer lines RVs of RRLs in the globular NGC~3201 collected with MUSE at VLT. We found the cluster barycentric RV of $V_{\gamma}$=496.89$\pm$8.37(error)$\pm$3.43 (standard deviation) km/s, which agrees well with literature estimates

Mister Mary Somerville: Husband and Secretary

Mary Somerville’s life as a mathematician and savant in nineteenth-century Great Britain was heavily influenced by her gender; as a woman, her access to the ideas and resources developed and circulated in universities and scientific societies was highly restricted. However, her engagement with learned institutions was by no means nonexistent, and although she was 90 before being elected a full member of any society (Società Geografica Italiana, 1870), Somerville (Figure 1) nevertheless benefited from the resources and social networks cultivated by such institutions from as early as 1812. A key intermediary between Somerville and these societies was her husband, Dr. William Somerville, whose mediation was vital to her access to knowledge and her subsequent career as a scientific author. In this paper we will consider how spousal cooperation enabled the overcoming of gendered barriers to scientific institutions in the nineteenth century

Phytoplankton composition from sPACE: Requirements, opportunities, and challenges

Ocean color satellites have provided a synoptic view of global phytoplankton for over 25 years through near surface measurements of the concentration of chlorophyll a. While remote sensing of ocean color has revolutionized our understanding of phytoplankton and their role in the oceanic and freshwater ecosystems, it is important to consider both total phytoplankton biomass and changes in phytoplankton community composition in order to fully understand the dynamics of the aquatic ecosystems. With the upcoming launch of NASA\u27s Plankton, Aerosol, Clouds, ocean Ecosystem (PACE) mission, we will be entering into a new era of global hyperspectral data, and with it, increased capabilities to monitor phytoplankton diversity from space. In this paper, we analyze the needs of the user community, review existing approaches for detecting phytoplankton community composition in situ and from space, and highlight the benefits that the PACE mission will bring. Using this three-pronged approach, we highlight the challenges and gaps to be addressed by the community going forward, while offering a vision of what global phytoplankton community composition will look like through the “eyes” of PACE

Removing leakage-induced correlated errors in superconducting quantum error correction

Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing