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Nonlinear interferometers that replace beamsplitters in Mach-Zehnder interferometers with nonlinear amplifiers for quantum-enhanced phase measurements have drawn increasing interest in recent years, but practical quantum sensors based on nonlinear interferometry remain an outstanding challenge. Here, we demonstrate the first practical application of nonlinear interferometry by measuring the displacement of an atomic force microscope microcantilever with quantum noise reduction of up to 3~dB below the standard quantum limit, corresponding to a quantum-enhanced measurement of beam displacement of $\mathrm{1.7~fm/\sqrt{Hz}}$. Further, we show how to minimize photon backaction noise while taking advantage of quantum noise reduction by transducing the cantilever displacement signal with a weak squeezed state while using dual homodyne detection with a higher power local oscillator. This approach offers a path toward quantum-enhanced broadband, high-speed scanning probe microscopy.

We present error mitigation (EM) techniques for noisy intermediate-scale quantum computers (QC) based on density matrix purification and perturbative corrections to the target energy. We incorporate this scheme into the variational quantum eigensolver (VQE) and demonstrate chemically-accurate ground state energy calculations of various alkali metal hydrides using IBM quantum computers. Both the density matrix purification improvements and the perturbative corrections require only meager classical computational resources, and are conducted exclusively as post-processing of the measured density matrix. The improved density matrix leads to better simulation accuracy at each step of the variational optimization, resulting in a better input into the next optimization step without additional measurements. Adding perturbative corrections to the resulting energies further increases the accuracy, and decreases variation between consecutive measurements. These EM schemes allow for previously unavailable levels of accuracy over remote QC resources.

Distilling precise estimates from noisy intermediate scale quantum (NISQ) data has recently attracted considerable attention. In order to augment digital qubit metrics, such as gate fidelity, we discuss analog error mitigability, i.e. the ability to accurately distill precise observable estimates, as a hybrid quantum-classical computing benchmarking task. Specifically, we characterize single qubit error rates on IBM's Poughkeepsie superconducting quantum hardware, incorporate control-mediated noise dependence into a generalized rescaling protocol, and analyze how noise characteristics influence Richardson extrapolation-based error mitigation. Our results identify regions in the space of Hamiltonian control fields and circuit-depth which are most amenable to reliable noise extrapolation, as well as shedding light on how low-level hardware characterization can be used as a predictive tool for uncertainty quantification in error mitigated NISQ computations., Comment: 5 pages, 3 figures, comments welcome

We report demonstrations of both quadrature squeezed vacuum and photon number difference squeezing generated in an integrated nanophotonic device. Squeezed light is generated via strongly driven spontaneous four-wave mixing below threshold in silicon nitride microring resonators. The generated light is characterized with both homodyne detection and direct measurements of photon statistics using photon number-resolving transition edge sensors. We measure $1.0(1)$~dB of broadband quadrature squeezing (${\sim}4$~dB inferred on-chip) and $1.5(3)$~dB of photon number difference squeezing (${\sim}7$~dB inferred on-chip). Nearly-single temporal mode operation is achieved, with measured raw unheralded second-order correlations $g^{(2)}$ as high as $1.95(1)$. Multi-photon events of over 10 photons are directly detected with rates exceeding any previous quantum optical demonstration using integrated nanophotonics. These results will have an enabling impact on scaling continuous variable quantum technology., Comment: Minor revisions, and Fig. 5 corrected; Now published in Science Advances

We present a stochastic analog spatial light modulator designed for compressive imaging applications. We rely on the unpredictable nature of multi-particle collisions to provide randomization for the particle location. We demonstrate this concept in an optical imaging system using a single-pixel camera. This design can be applied to imaging or spectroscopic systems in which no analog to optical spatial light modulators currently exist or in non-optical lensless imaging systems., Comment: 4 pages, 8 figures

We present a quantum-classical algorithm to study the dynamics of the two-spatial-site Schwinger model on IBM's quantum computers. Using rotational symmetries, total charge, and parity, the number of qubits needed to perform computation is reduced by a factor of $\sim 5$, removing exponentially-large unphysical sectors from the Hilbert space. Our work opens an avenue for exploration of other lattice quantum field theories, such as quantum chromodynamics, where classical computation is used to find symmetry sectors in which the quantum computer evaluates the dynamics of quantum fluctuations., Comment: 5 pages, 4 figures, 23 pages supplemental, 8 figures supplemental

We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

The presence of multiple bipartite entangled modes in squeezed states generated by four wave mixing in atomic vapors enables ultra-trace sensing, imaging, and metrology applications that are impossible to achieve with single-spatial-mode squeezed states. For Gaussian seed beams, the spatial distribution of bipartite entangled modes, or coherence areas, across each beam is largely dependent on the spatial modes present in the pump beam, but it has proven difficult to map the distribution of these coherence areas in frequency and space. We demonstrate an accessible method to map the distribution of the coherence areas within these twin beams. We also show that the pump shape can impart different noise properties to each coherence area, and that it is possible to select and detect coherence areas with optimal squeezing with this approach.

We demonstrate compact and accessible squeezed-light magnetometry using four-wave mixing in a single hot rubidium vapor cell. The strong intrinsic coherence of the four wave mixing process results in nonlinear magneto-optical rotation (NMOR) on each mode of a two mode relative-intensity squeezed state. This framework enables 4.7 dB of quantum noise reduction while the opposing polarization rotation signals of the probe and conjugate fields add to increase the total signal to noise ratio.

The displacement of micro-electro-mechanical-systems (MEMS) cantilevers is used to measure a broad variety of phenomena in devices ranging from force microscopes to biochemical sensors to thermal imaging systems. We demonstrate the first direct measurement of a MEMS cantilever displacement with a noise floor at 40% of the shot noise limit (SNL). By combining multi-spatial-mode quantum light sources with a simple differential measurement, we show that sub-SNL MEMS displacement sensitivity is highly accessible compared to previous efforts that measured the displacement of macroscopic mirrors with very distinct spatial structures crafted with multiple optical parametric amplifiers and locking loops. These results support a new class of quantum MEMS sensor with an ultimate signal to noise ratio determined by quantum correlations, enabling ultra-trace sensing, imaging, and microscopy applications in which signals were previously obscured by shot noise., Comment: Journal info added and typo corrected in equations 3 and 7

We present a workbench for the study of real-time quantum imaging by measuring the frame-by-frame quantum noise reduction of multi-spatial-mode twin beams generated by four wave mixing in Rb vapor. Exploiting the multiple spatial modes of this squeezed light source, we utilize spatial light modulators to selectively pass macropixels of quantum correlated modes from each of the twin beams to a high quantum efficiency balanced detector. In low-light-level imaging applications, the ability to measure the quantum correlations between individual spatial modes and macropixels of spatial modes with a single pixel camera will facilitate compressive quantum imaging with sensitivity below the photon shot noise limit.

We demonstrate the coherent transduction of quantum noise reduction, or squeezed light, by Ag localized surface plasmons (LSPs). Squeezed light, generated through four-wave-mixing in Rb vapor, is coupled to a Ag nanohole array designed to exhibit LSP-mediated extraordinary-optical transmission (EOT) spectrally coincident with the squeezed light source at 795 nm. We demonstrate that quantum noise reduction as a function of transmission is found to match closely with linear attenuation models, thus demonstrating that the photon-LSP-photon transduction process is coherent near the LSP resonance.

We present an experimental realization of a low-noise, phase-insensitive optical amplifier using a four-wave mixing interaction in hot Rb vapor. Performance near the quantum limit for a range of amplifier gains, including near unity, can be achieved. Such low-noise amplifiers are essential for so-called quantum cloning machines and are useful in quantum information protocols. We demonstrate that amplification and ``cloning'' of one half of a two-mode squeezed state is possible while preserving entanglement., Comment: To appear in Physical Review Letters July 3rd. 4 pages, 4 figures

This paper has been withdrawn since it was an inadvertant double submission. An updated version of the original submission can be found at quant-ph/0505131, Comment: This paper has been withdrawn since it was an inadvertant double submission. An updated version of the original submission can be found at quant-ph/0505131