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Journal articleChevalier H, Kwon H, Khosla KE, et al., 2022,
Many-body probes for quantum features of spacetime
, AVS Quantum Science, Vol: 4, Pages: 021402-021402<jats:p> Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work, we inspect the capacity for correlated many-body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a nonstandard phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators. </jats:p>
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Journal articleThekkadath G, Sempere-Llagostera S, Bell B, et al., 2022,
Experimental demonstration of Gaussian boson sampling with displacement
, PRX Quantum, ISSN: 2691-3399 -
Journal articleAlexander R, Gvirtz-Chen S, Jennings D, 2022,
Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
, New Journal of Physics, ISSN: 1367-2630Symmetry principles are fundamental in physics, and while they are well understood within Lagrangian mechanics, their impact on quantum channels has a range of open questions. The theory of asymmetry grew out of information-theoretic work on entanglement and quantum reference frames, and allows us to quantify the degree to which a quantum system encodes coordinates of a symmetry group. Recently, a complete set of entropic conditions was found for asymmetry in terms of correlations relative to infinitely many quantum reference frames. However, these conditions are difficult to use in practice and their physical implications unclear. In the present theoretical work, we show that this set of conditions has extensive redundancy, and one can restrict to reference frames forming any closed surface in the state space that has the maximally mixed state in its interior. This in turn implies that asymmetry can be reduced to just a single entropic condition evaluated at the maximally mixed state. Contrary to intuition, this shows that we do not need macroscopic, classical reference frames to determine the asymmetry properties of a quantum system, but instead infinitesimally small frames suffice. Building on this analysis, we provide simple, closed conditions to estimate the minimal depolarization needed to make a given quantum state accessible under channels covariant with any given symmetry group.
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Journal articleGirling M, Cirstoiu C, Jennings D, 2022,
Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
, Physical Review Research, Vol: 4, ISSN: 2643-1564The ability to transfer quantum information between systems is a fundamental component of quantum technologies and leads to correlations within the global quantum process. However, correlation structures in quantum channels are less studied than those in quantum states. Motivated by recent techniques in randomized benchmarking, we develop a range of results for efficient estimation of correlations within a bipartite quantum channel. We introduce subunitarity measures that are invariant under local changes of basis, generalize the unitarity of a channel, and allow for the analysis of quantum information exchange within channels. Using these, we show that unitarity is monogamous, and we provide an information-disturbance relation. We then define a notion of correlated unitarity that quantifies the correlations within a given channel. Crucially, we show that this measure is strictly bounded on the set of separable channels and therefore provides a witness of nonseparability. Finally, we describe how such measures for effective noise channels can be efficiently estimated within different randomized benchmarking protocols. We find that the correlated unitarity can be estimated in a SPAM-robust manner for any separable quantum channel, and we show that a benchmarking/tomography protocol with mid-circuit resets can reliably witness nonseparability for sufficiently small reset errors. The tools we develop provide information beyond that obtained via simultaneous randomized benchmarking and so could find application in the analysis of cross-talk errors in quantum devices.
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Journal articleSong W, Lim Y, Jeong K, et al., 2022,
Quantum solvability of noisy linear problems by divide-and-conquer strategy
, Quantum Science and Technology, Vol: 7, ISSN: 2058-9565Noisy linear problems have been studied in various science and engineering disciplines. A class of 'hard' noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector b constructed using a finite set of samples, a hidden vector or structure involved in b is obtained by solving a noise-corrupted linear equation $\hat{A}\mathbf{x}\approx \mathbf{b}+\boldsymbol{\eta }$, where η is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems.
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Journal articleZhang C, Zhang C, Cheng L, et al., 2022,
Inner-shell excitation in the YbF molecule and its impact on laser cooling
, Journal of Molecular Spectroscopy, Vol: 386, ISSN: 0022-2852The YbF molecule is a sensitive system for measuring the electron's electric dipole moment. The precision of this measurement can be improved by direct laser cooling of the molecules to ultracold temperature. However, low-lying electronic states arising from excitation of a 4f electron may hinder laser cooling. One set of these “4f hole” states lies below the A2Π1/2 excited state used for laser cooling, and radiative decay to these intermediate levels, even with branching ratios as small as 10−5, can be a hindrance. Other 4f hole states lie very close to the A2Π1/2 state, and a perturbation results in states of mixed character that are involved in the laser cooling cycle. This perturbation may enhance the loss of molecules to states outside of the laser cooling cycle. We model the perturbation of the A2Π1/2 state to determine the strength of the coupling between the states, the de-perturbed potential energy curves, and the radiative branching ratios to various vibrational levels of the ground state, X2Σ+. We use electronic structure calculations to characterize the 4f hole states and the strengths of transitions between these states and the A2Π1/2 and X2Σ+ states. We identify a leak out of the cooling cycle with a branching ratio of roughly 5×10−4, dominated by the contribution of the ground state configuration in a 4f hole state. Finally, we assess the impact of these results for laser cooling of YbF and molecules with similar structure.
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Working paperKoukoulekidis N, Jennings D, 2022,
Constraints on magic state protocols from the statistical mechanics of Wigner negativity
, Publisher: Nature ResearchMagic states are key ingredients in schemes to realize universalfault-tolerant quantum computation. Theories of magic states attempt toquantify this computational element via monotones and determine how thesestates may be efficiently transformed into useful forms. Here, we develop astatistical mechanical framework based on majorization to describe Wignernegative magic states for qudits of odd prime dimension processed underClifford circuits. We show that majorization allows us to both quantifydisorder in the Wigner representation and derive upper bounds for magicdistillation. These bounds are shown to be tighter than other bounds, such asfrom mana and thauma, and can be used to incorporate hardware physics, such astemperature dependence and system Hamiltonians. We also show that a subset ofsingle-shot R\'{e}nyi entropies remain well-defined on quasi-distributions, arefully meaningful in terms of data processing and can acquire negative valuesthat signal magic. We find that the mana of a magic state is the measure ofdivergence of these R\'{e}nyi entropies as one approaches the Shannon entropyfor Wigner distributions, and discuss how distillation lower bounds could beobtained in this setting. This use of majorization for quasi-distributionscould find application in other studies of non-classicality, and raises novelquestions in the context of classical statistical mechanics.
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Journal articleAyuso Molinero D, Ordonez AF, Decleva P, et al., 2022,
Strong chiral response in non-collinear high harmonic generation driven by purely electric-dipole interactions
, Optics Express, Vol: 30, ISSN: 1094-4087High harmonic generation (HHG) records the ultrafast electronic response of matter to light, encoding key properties of the interrogated quantum system, such as chirality. The first implementation of chiral HHG [Cireasa et al, Nat. Phys. 11, 654 (2015) [CrossRef] ] relied on the weak electronic response of a medium of randomly oriented chiral molecules to the magnetic component of an elliptically polarized wave, yielding relatively weak chiro-optical signals. Here we apply state-of-the-art semi-analytical modelling to show that elliptically polarized light can drive a strong chiral response in chiral molecules via purely electric-dipole interactions – the magnetic component of the wave does not participate at all. This strong chiro-optical response, which remains hidden in standard HHG experiments, can be mapped into the macroscopic far-field signal using a non-collinear configuration, creating new opportunities for imaging chiral matter and chiral dynamics on ultrafast time scales.
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Journal articleTang H, Banchi L, Wang T-Y, et al., 2022,
Generating Haar-uniform randomness using stochastic quantum walks on a photonic chip
, Physical Review Letters, Vol: 128, ISSN: 0031-9007As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide applications, such as boson sampling. Recently, a theoretical protocol was proposed to combine quantum control theory and driven stochastic quantum walks to generate Haar-uniform random operations. This opens up a promising route to converting classical randomness to quantum randomness. Here, we implement a two-dimensional stochastic quantum walk on the integrated photonic chip and demonstrate that the average of all distribution profiles converges to the even distribution when the evolution length increases, suggesting the 1-pad Haar-uniform randomness. We further show that our two-dimensional array outperforms the one-dimensional array of the same number of waveguide for the speed of convergence. Our Letter demonstrates a scalable and robust way to generate Haar-uniform randomness that can provide useful building blocks to boost future quantum information techniques.
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Journal articleLi S, Driver T, Rosenberger P, et al., 2022,
Attosecond coherent electron motion in Auger-Meitner decay
, SCIENCE, Vol: 375, Pages: 285-+, ISSN: 0036-8075 -
Journal articleMoroney N, Del Bino L, Zhang S, et al., 2022,
A Kerr polarization controller
, NATURE COMMUNICATIONS, Vol: 13- Author Web Link
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- Citations: 1
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Journal articleAlsing PM, Birrittella RJ, Gerry CC, et al., 2022,
Extending the Hong-Ou-Mandel effect: the power of nonclassicality
, Physical Review A: Atomic, Molecular and Optical Physics, Vol: 105, ISSN: 1050-2947We show that the parity (evenness or oddness) of a nonclassical state of light has a dominant influence on the interference effects at a balanced beam splitter, irrespective of the state initially occupying the other input mode. Specifically, the parity of the nonclassical state gives rise to destructive interference effects that result in deep valleys in the output joint number distribution of which the Hong-Ou-Mandel (HOM) effect is a limiting case. The counterintuitive influence of even a single photon to control the output of a beam splitter illuminated by any field, be it a coherent or even a noisy thermal field, demonstrates the extraordinary power of nonclassicality. The canonical example of total destructive interference of quantum amplitudes leading to the absence of coincidence counts from a 50:50 beam splitter (BS) is the celebrated HOM effect, characterized by the vanishing of the joint probability of detecting singe photons in each of the output beams. We show that this is a limiting case of more general input states upon which a 50:50 BS can create total, or near total, destructive interference of quantum amplitudes. For the case of an odd photon-number input Fock state of arbitrary value n>0 we show that the joint photon-number probabilities vanish when detecting identical photon numbers in each output beams. We specifically examine the mixing of photon-number states of n=1, 2, and 3 with a continuous-variable state, such as a coherent state of arbitrary amplitude, and a thermal state. These vanishing joint probabilities form what we call a central nodal line: A contiguous set of zeros representing complete destructive interference of quantum amplitudes. We further show that with odd or even photon-number Fock states n, with n>1, there will be additional off-diagonal curves along which the joint photon-number probabilities are either zero, or near zero, which we call pseudonodal curves, which constitute a near, but not complete, destructive inte
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Journal articleKwon H, Mukherjee R, Kim MS, 2022,
Reversing Lindblad dynamics via continuous Petz recovery map
, Physical Review Letters, Vol: 128, Pages: 1-7, ISSN: 0031-9007An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the Lindblad master equation. The reverse dynamics can be obtained by constructing the Petz recovery map in continuous time. By providing the exact form of the Hamiltonian and jump operators for the reverse dynamics, we explore the potential of utilizing the near-optimal recovery of the Petz map in controlling noisy quantum dynamics. While time-dependent dissipation engineering enables us to fully recover a single quantum trajectory, we also design a time-independent recovery protocol to protect encoded quantum information against decoherence. Our protocol can efficiently suppress only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.
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Journal articleThekkadath GS, Bell BA, Patel RB, et al., 2022,
Measuring the joint spectral mode of photon pairs using intensity interferometry
, Physical Review Letters, Vol: 128, Pages: 1-6, ISSN: 0031-9007The ability to manipulate and measure the time-frequency structure of quantum light is useful for information processing and metrology. Measuring this structure is also important when developing quantum light sources with high modal purity that can interfere with other independent sources. Here, we present and experimentally demonstrate a scheme based on intensity interferometry to measure the joint spectral mode of photon pairs produced by spontaneous parametric down-conversion. We observe correlations in the spectral phase of the photons due to chirp in the pump. We show that our scheme can be combined with stimulated emission tomography to quickly measure their mode using bright classical light. Our scheme does not require phase stability, nonlinearities, or spectral shaping and thus is an experimentally simple way of measuring the modal structure of quantum light.
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Journal articleMa Y, Guff T, Morley GW, et al., 2022,
Limits on inference of gravitational entanglement
, Physical Review Research, Vol: 4, Pages: 1-7, ISSN: 2643-1564Combining gravity with quantum mechanics remains one of the biggest challenges of physics. In the past years, experiments with opto-mechanical systems have been proposed that may give indirect clues about the quantum nature of gravity. In a recent variation of such tests [D. Carney et al., Phys.Rev.X Quantum 2, 030330 (2021)], the authors ropose to gravitationally entangle an atom interferometer with a mesoscopic oscillator. The interaction results in periodic drops and revivals of the interferometeric visibility, which under specific assumptions indicate the gravitational generation of entanglement. Here we study semi-classical models of the atom interferometer that can reproduce the same effect. We show that the core signature – periodic collapses and revivals of the visibility – can appear if the atom is subject to a random unitary channel, including the casewhere the oscillator is fully classical and situations even without explicit modelling of the oscillator. We also show that the non-classicality of the oscillator vanishes unless the system is very close to its ground state, and even when the system is in the ground state, the non-classicality is limitedby the coupling strength. Our results thus indicate that deducing ntanglement from the proposed experiment is very challenging, since fulfilling and verifying the non-classicality assumptions is a significant challenge on its own right.
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Journal articleCorfield O, Lishman J, Lee C, et al., 2021,
Certifying Multilevel Coherence in the Motional State of a Trapped Ion
, PRX QUANTUM, Vol: 2 -
Working paperBarontini G, Blackburn L, Boyer V, et al., 2021,
Measuring the stability of fundamental constants with a network of clocks
, Publisher: arXivThe detection of variations of fundamental constants of the Standard Modelwould provide us with compelling evidence of new physics, and could lift theveil on the nature of dark matter and dark energy. In this work, we discuss howa network of atomic and molecular clocks can be used to look for suchvariations with unprecedented sensitivity over a wide range of time scales.This is precisely the goal of the recently launched QSNET project: A network ofclocks for measuring the stability of fundamental constants. QSNET will includestate-of-the-art atomic clocks, but will also develop next-generation molecularand highly charged ion clocks with enhanced sensitivity to variations offundamental constants. We describe the technological and scientific aims ofQSNET and evaluate its expected performance. We show that in the range ofparameters probed by QSNET, either we will discover new physics, or we willimpose new constraints on violations of fundamental symmetries and a range oftheories beyond the Standard Model, including dark matter and dark energymodels.
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Journal articleEnzian G, Freisem L, Price JJ, et al., 2021,
Non-Gaussian Mechanical Motion via Single and Multiphonon Subtraction from a Thermal State
, PHYSICAL REVIEW LETTERS, Vol: 127, ISSN: 0031-9007- Author Web Link
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- Citations: 2
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Journal articleKanari-Naish LA, Clarke J, Vanner MR, et al., 2021,
Can the displacemon device test objective collapse models?
, AVS Quantum Science, Vol: 3Testing the limits of the applicability of quantum mechanics will deepen our understanding of the universe and may shed light on the interplay between quantum mechanics and gravity. At present there is a wide range of approaches for such macroscopic tests spanning from matter-wave interferometry of large molecules to precision measurements of heating rates in the motion of micro-scale cantilevers. The "displacemon"is a proposed electromechanical device consisting of a mechanical resonator flux-coupled to a superconducting qubit enabling generation and readout of mechanical quantum states. In the original proposal, the mechanical resonator was a carbon nanotube, containing 106 nucleons. Here, in order to probe quantum mechanics at a more macroscopic scale, we propose using an aluminum mechanical resonator on two larger mass scales, one inspired by the Marshall-Simon-Penrose-Bouwmeester moving-mirror proposal, and one set by the Planck mass. For such a device, we examine the experimental requirements needed to perform a more macroscopic quantum test and thus feasibly detect the decoherence effects predicted by two objective collapse models: Diósi-Penrose and continuous spontaneous localization. Our protocol for testing these two theories takes advantage of the displacemon architecture to create non-Gaussian mechanical states out of equilibrium with their environment and then analyzes the measurement statistics of a superconducting qubit. We find that with improvements to the fabrication and vibration sensitivities of these electromechanical devices, the displacemon device provides a new route to feasibly test decoherence mechanisms beyond standard quantum theory.
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Journal articleSmith AWR, Khosla KE, Self CN, et al., 2021,
Qubit readout error mitigation with bit-flip averaging
, Science Advances, Vol: 7, Pages: 1-10, ISSN: 2375-2548Quantum computers are becoming increasingly accessible, and may soonoutperform classical computers for useful tasks. However, qubit readout errorsremain a significant hurdle to running quantum algorithms on current devices.We present a scheme to more efficiently mitigate these errors on quantumhardware and numerically show that our method consistently gives advantage overprevious mitigation schemes. Our scheme removes biases in the readout errorsallowing a general error model to be built with far fewer calibrationmeasurements. Specifically, for reading out $n$-qubits we show a factor of$2^n$ reduction in the number of calibration measurements without sacrificingthe ability to compensate for correlated errors. Our approach can be combinedwith, and simplify, other mitigation methods allowing tractable mitigation evenfor large numbers of qubits.
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Journal articleEnzian G, Freisem L, Price J, et al., 2021,
Non-Gaussian mechanical motion via single and multi-phonon subtraction from a thermal state
, Physical Review Letters, ISSN: 0031-9007Quantum optical measurement techniques offer a rich avenue for quantum control of mechanical oscillators via cavity optomechanics. In particular, a powerful yet little explored combination utilizes optical measurements to perform heralded non-Gaussian mechanical state preparation followed by tomography to determine the mechanical phase-space distribution. Here, we experimentally perform heralded single- and multi-phonon subtraction via photon counting to a laser-cooled mechanical thermal state with a Brillouin optomechanical system at room temperature, and use optical heterodyne detection to measure the s-parameterized Wigner distribution of the non-Gaussian mechanical states generated. The techniques developed here advance the state-of-the-art for optics-based tomography of mechanical states and will be useful for a broad range of applied and fundamental studies that utilize mechanical quantum-state engineering and tomography.
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Journal articleDriver T, Bachhawat N, Pipkorn R, et al., 2021,
Proteomic Database Search Engine for Two-Dimensional Partial Covariance Mass Spectrometry
, ANALYTICAL CHEMISTRY, Vol: 93, Pages: 14946-14954, ISSN: 0003-2700 -
Journal articleMa Y, Kim MS, Stickler BA, 2021,
Torque-free manipulation of nanoparticle rotations via embedded spins
, Physical Review B: Condensed Matter and Materials Physics, Vol: 104, ISSN: 1098-0121Spin angular momentum and mechanical rotation both contribute to the total angular momentum of rigid bodies, leading to spin-rotational coupling via the Einstein–de Haas and Barnett effects. Here, we show that the revolutions of symmetric nanorotors can be strongly affected by a small number of intrinsic spins. The resulting dynamics are observable with freely rotating nanodiamonds with embedded nitrogen-vacancy centers and persist for realistically shaped near-symmetric particles, opening the door to torque-free schemes to control their rotations at the quantum level.
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Journal articleHaug T, Bharti K, Kim MS, 2021,
Capacity and quantum geometry of parametrized quantum circuits
, PRX Quantum, Vol: 2, Pages: 1-14, ISSN: 2691-3399To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively implemented on current devices. Here, we evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space via the effective quantum dimension, which reveals the expressive power of circuits in general as well as of particular initialization strategies. We assess the expressive power of various popular circuit types and find striking differences depending on the type of entangling gates used. Particular circuits are characterized by scaling laws in their expressiveness. We identify a transition in the quantum geometry of the parameter space, which leads to a decay of the quantum natural gradient for deep circuits. For shallow circuits, the quantum natural gradient can be orders of magnitude larger in value compared to the regular gradient; however, both of them can suffer from vanishing gradients. By tuning a fixed set of circuit parameters to randomized ones, we find a region where the circuit is expressive but does not suffer from barren plateaus, hinting at a good way to initialize circuits. We show an algorithm that prunes redundant parameters of a circuit without affecting its effective dimension. Our results enhance the understanding of parametrized quantum circuits and can be immediately applied to improve variational quantum algorithms.
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Journal articleWalton A, Ghesquiere A, Brumpton G, et al., 2021,
Thermal state quantum key distribution
, Journal of Physics B: Atomic, Molecular and Optical Physics, Vol: 54, ISSN: 0953-4075We analyse a central broadcast continuous variable quantum key distribution protocol in which a beam produced by a thermal source is used to create a secret key between two parties, Alice and Bob. A beam splitter divides the initial beam into a pair of output beams, which are sent to Alice and Bob, with Eve intercepting Bob's beam. We investigate the protocol in detail, calculating mutual informations through a pair of analytic methods and comparing the results to the outputs of a Monte Carlo simulation of the protocol. In a lossless system, we find that a lower bound on the key rate remains positive in the protocol under a beam splitter attack, provided Bob receives a nonzero proportion of the beam initially sent to him. This suggests that the thermal state protocol could be used experimentally to produce secure keys.
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Journal articleBray AC, Maxwell AS, Kissin Y, et al., 2021,
Polarization in strong-field ionization of excited helium
, JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS, Vol: 54, ISSN: 0953-4075 -
Conference paperBarontini G, Boyer V, Calmet X, et al., 2021,
QSNET, a network of clock for measuring the stability of fundamental constants
, Proceedings Volume 11881, Quantum Technology: Driving Commercialisation of an Enabling Science II, Publisher: SPIE, Pages: 1-4The QSNET consortium is building a UK network of next-generation atomic and molecular clocks that will achieve unprecedented sensitivity in testing variations of the fine structure constant, α, and the electron-to-proton mass ratio, μ. This in turn will provide more stringent constraints on a wide range of fundamental and phenomenological theories beyond the Standard Model and on dark matter models.
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Journal articleZhao H, Smith A, Mintert F, et al., 2021,
Orthogonal Quantum Many-Body Scars
, PHYSICAL REVIEW LETTERS, Vol: 127, ISSN: 0031-9007- Author Web Link
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- Citations: 4
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Journal articleAlauze X, Lim J, Trigatzis MA, et al., 2021,
An ultracold molecular beam for testing fundamental physics
, QUANTUM SCIENCE AND TECHNOLOGY, Vol: 6, ISSN: 2058-9565- Author Web Link
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- Citations: 1
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Journal articleVovrosh J, Khosla KE, Greenaway S, et al., 2021,
Simple mitigation of global depolarizing errors in quantum simulations.
, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 104, Pages: 1-8, ISSN: 1539-3755To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data. We highlight the effectiveness of our mitigation via two examples of recent interest in quantum many-body physics: entanglement measurements and real-time dynamics of confinement in quantum spin chains. Our technique enables us to get quantitative results from the IBM quantum computers showing signatures of confinement, i.e., we are able to extract the meson masses of the confined excitations which were previously out of reach. Additionally, we show the applicability of this mitigation protocol in a wider setting with numerical simulations of more general tasks using a realistic error model. Our protocol is device-independent, simply implementable, and leads to large improvements in results if the global errors are well described by depolarization.
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