Resource frugal optimizer for quantum machine learning

Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.Comment: 22 pages, 6 figures - extra quantum autoencoder results adde

Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Error mitigation is an essential component of achieving practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a common feature: they are data-driven, employing classical data obtained from runs of different quantum circuits. For example, Zero-noise extrapolation (ZNE) uses variable noise data and Clifford-data regression (CDR) uses data from near-Clifford circuits. We show that Virtual Distillation (VD) can be viewed in a similar manner by considering classical data produced from different numbers of state preparations. Observing this fact allows us to unify these three methods under a general data-driven error mitigation framework that we call UNIfied Technique for Error mitigation with Data (UNITED). In certain situations, we find that our UNITED method can outperform the individual methods (i.e., the whole is better than the individual parts). Specifically, we employ a realistic noise model obtained from a trapped ion quantum computer to benchmark UNITED, as well as state-of-the-art methods, for problems with various numbers of qubits, circuit depths and total numbers of shots. We find that different techniques are optimal for different shot budgets. Namely, ZNE is the best performer for small shot budgets ($10^5$), while Clifford-based approaches are optimal for larger shot budgets ($10^6 - 10^8$), and for our largest considered shot budget ($10^{10}$), UNITED gives the most accurate correction. Hence, our work represents a benchmarking of current error mitigation methods, and provides a guide for the regimes when certain methods are most useful.Comment: 13 pages, 4 figure

Cadherin-26 (CDH26) regulates airway epithelial cell cytoskeletal structure and polarity.

Polarization of the airway epithelial cells (AECs) in the airway lumen is critical to the proper function of the mucociliary escalator and maintenance of lung health, but the cellular requirements for polarization of AECs are poorly understood. Using human AECs and cell lines, we demonstrate that cadherin-26 (CDH26) is abundantly expressed in differentiated AECs, localizes to the cell apices near ciliary membranes, and has functional cadherin domains with homotypic binding. We find a unique and non-redundant role for CDH26, previously uncharacterized in AECs, in regulation of cell-cell contact and cell integrity through maintaining cytoskeletal structures. Overexpression of CDH26 in cells with a fibroblastoid phenotype increases contact inhibition and promotes monolayer formation and cortical actin structures. CDH26 expression is also important for localization of planar cell polarity proteins. Knockdown of CDH26 in AECs results in loss of cortical actin and disruption of CRB3 and other proteins associated with apical polarity. Together, our findings uncover previously unrecognized functions for CDH26 in the maintenance of actin cytoskeleton and apicobasal polarity of AECs

The battle of clean and dirty qubits in the era of partial error correction

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.Comment: 27 pages, 15 figures, (v2) minor change

Inference-Based Quantum Sensing

In a standard Quantum Sensing (QS) task one aims at estimating an unknown parameter $\theta$, encoded into an $n$-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response $\mathcal{R}(\theta)$ (i.e., changes in the measurement outcomes). For simple cases the form of $\mathcal{R}(\theta)$ is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this work we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, $\mathcal{R}(\theta)$ can be fully characterized by only measuring the system response at $2n+1$ parameters. In turn, this allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the sensing scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than $\delta$, if one measures the system response with a number of shots that scales only as $\Omega(\log^3(n)/\delta^2)$. Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.Comment: 5+10 pages, 3+5 figure

Free energy barrier for melittin reorientation from a membrane-bound state to a transmembrane state

An important step in a phospholipid membrane pore formation by melittin antimicrobial peptide is a reorientation of the peptide from a surface into a transmembrane conformation. In this work we perform umbrella sampling simulations to calculate the potential of mean force (PMF) for the reorientation of melittin from a surface-bound state to a transmembrane state and provide a molecular level insight into understanding peptide and lipid properties that influence the existence of the free energy barrier. The PMFs were calculated for a peptide to lipid (P/L) ratio of 1/128 and 4/128. We observe that the free energy barrier is reduced when the P/L ratio increased. In addition, we study the cooperative effect; specifically we investigate if the barrier is smaller for a second melittin reorientation, given that another neighboring melittin was already in the transmembrane state. We observe that indeed the barrier of the PMF curve is reduced in this case, thus confirming the presence of a cooperative effect

In the dedicated pursuit of dedicated capital: restoring an indigenous investment ethic to British capitalism

Tony Blair’s landslide electoral victory on May 1 (New Labour Day?) presents the party in power with a rare, perhaps even unprecedented, opportunity to revitalise and modernise Britain’s ailing and antiquated manufacturing economy.* If it is to do so, it must remain true to its long-standing (indeed, historic) commitment to restore an indigenous investment ethic to British capitalism. In this paper we argue that this in turn requires that the party reject the very neo-liberal orthodoxies which it offered to the electorate as evidence of its competence, moderation and ‘modernisation’, which is has internalised, and which it apparently now views as circumscribing the parameters of the politically and economically possible

Mitiq : a software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators

What does inflation really predict?

If the inflaton potential has multiple minima, as may be expected in, e.g., the string theory "landscape", inflation predicts a probability distribution for the cosmological parameters describing spatial curvature (Omega_tot), dark energy (rho_Lambda, w, etc.), the primordial density fluctuations (Omega_tot, dark energy (rho_Lambda, w, etc.). We compute this multivariate probability distribution for various classes of single-field slow-roll models, exploring its dependence on the characteristic inflationary energy scales, the shape of the potential V and and the choice of measure underlying the calculation. We find that unless the characteristic scale Delta-phi on which V varies happens to be near the Planck scale, the only aspect of V that matters observationally is the statistical distribution of its peaks and troughs. For all energy scales and plausible measures considered, we obtain the predictions Omega_tot ~ 1+-0.00001, w=-1 and rho_Lambda in the observed ballpark but uncomfortably high. The high energy limit predicts n_s ~ 0.96, dn_s/dlnk ~ -0.0006, r ~ 0.15 and n_t ~ -0.02, consistent with observational data and indistinguishable from eternal phi^2-inflation. The low-energy limit predicts 5 parameters but prefers larger Q and redder n_s than observed. We discuss the coolness problem, the smoothness problem and the pothole paradox, which severely limit the viable class of models and measures. Our findings bode well for detecting an inflationary gravitational wave signature with future CMB polarization experiments, with the arguably best-motivated single-field models favoring the detectable level r ~ 0.03. (Abridged)Comment: Replaced to match accepted JCAP version. Improved discussion, references. 42 pages, 17 fig

Sloan Digital Sky Survey Imaging of Low Galactic Latitude Fields: Technical Summary and Data Release

The Sloan Digital Sky Survey (SDSS) mosaic camera and telescope have obtained five-band optical-wavelength imaging near the Galactic plane outside of the nominal survey boundaries. These additional data were obtained during commissioning and subsequent testing of the SDSS observing system, and they provide unique wide-area imaging data in regions of high obscuration and star formation, including numerous young stellar objects, Herbig-Haro objects and young star clusters. Because these data are outside the Survey regions in the Galactic caps, they are not part of the standard SDSS data releases. This paper presents imaging data for 832 square degrees of sky (including repeats), in the star-forming regions of Orion, Taurus, and Cygnus. About 470 square degrees are now released to the public, with the remainder to follow at the time of SDSS Data Release 4. The public data in Orion include the star-forming region NGC 2068/NGC 2071/HH24 and a large part of Barnard's loop.Comment: 31 pages, 9 figures (3 missing to save space), accepted by AJ, in press, see http://photo.astro.princeton.edu/oriondatarelease for data and paper with all figure