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  • Journal article
    Sun J, Vilchez-Estevez L, Vedral V, Boothroyd AT, Kim MSet al., 2025,

    Probing spectral features of quantum many-body systems with quantum simulators.

    , Nat Commun, Vol: 16

    The efficient probing of spectral features is important for characterising and understanding the structure and dynamics of quantum materials. In this work, we establish a framework for probing the excitation spectrum of quantum many-body systems with quantum simulators. Our approach effectively realises a spectral detector by processing the dynamics of observables with time intervals drawn from a defined probability distribution, which only requires native time evolution governed by the Hamiltonian without ancilla. The critical element of our method is the engineered emergence of frequency resonance such that the excitation spectrum can be probed. We show that the time complexity for transition energy estimation has a logarithmic dependence on simulation accuracy and how such observation can be guaranteed in certain many-body systems. We discuss the noise robustness of our spectroscopic method and show that the total running time maintains polynomial dependence on accuracy in the presence of device noise. We further numerically test the error dependence and the scalability of our method for lattice models. We present simulation results for the spectral features of typical quantum systems, either gapped or gapless, including quantum spins, fermions and bosons. We demonstrate how excitation spectra of spin-lattice models can be probed experimentally with IBM quantum devices.

  • Journal article
    Wang P, Kwon H, Luan C-Y, Chen W, Qiao M, Zhou Z, Wang K, Kim MS, Kim Ket al., 2025,

    Author Correction: Snapshotting quantum dynamics at multiple time points.

    , Nat Commun, Vol: 16
  • Journal article
    Wang J, Driver T, Franz PL, Kolorenč P, Thierstein E, Robles RR, Isele E, Guo Z, Cesar D, Alexander O, Beauvarlet S, Borne K, Cheng X, Dimauro LF, Duris J, Glownia JM, Graßl M, Hockett P, Hoffman M, Kamalov A, Larsen KA, Li S, Li X, Lin MF, Obaid R, Rosenberger P, Walter P, Wolf TJA, Marangos JP, Kling MF, Bucksbaum PH, Marinelli A, Cryan JPet al., 2025,

    Probing Electronic Coherence between Core-Level Vacancies at Different Atomic Sites

    , Physical Review X, Vol: 15

    The detailed understanding of electronic coherence in quantum systems requires measurements on the attosecond timescale. Attosecond x-ray pulses enable the study of electronic coherence in core-excited molecular systems. Here we report on the coherent motion of electrons in the 1,1-difluoroethylene ion following ionization of the K shell of the two nonequivalent carbon sites with a subfemtosecond x-ray pulse. Using the angular streaking technique to track the Auger-Meitner decay, we observe temporal modulations of the emission, indicating the electronic coherence of the core-excited ionic states, and extract a 6.5±0.8 fs average lifetime of the core-level vacancies. A quantum-mechanical model is employed to interpret the measurement, and we find the observed temporal modulations are independent of charge density oscillations. This work opens a new regime of coherent electronic motion, beyond charge migration, where electronic coherence manifests in the nonlocal quantum correlation between atomic sites while charge density oscillation is absent. Our results broaden the landscape of electronic coherence in molecular systems.

  • Journal article
    Gerry CC, Birrittella RJ, Alsing PM, Mimih J, Knight PLet al., 2024,

    Non-classicality and the effect of one photon.

    , Philos Trans A Math Phys Eng Sci, Vol: 382

    The quantum interference effects of mixing the most non-classical states of light, number states, with the most classical-like of pure field states, the coherent state, are investigated. We demonstrate how the non-classicality of a single photon when mixed with a coherent field can transform the statistical properties of the output and further demonstrate that the entanglement of the output is independent of the coherent state amplitude.This article is part of the theme issue 'The quantum theory of light'.

  • Journal article
    White A, Popa S, Mellado Munoz J, Fitch N, Sauer B, Lim J, Tarbutt Met al., 2024,

    Slow molecular beams from a cryogenic buffer gas source

    , Physical Review Research, Vol: 6, ISSN: 2643-1564

    We study the properties of a cryogenic buffer gas source that uses a low temperature two-stage buffer gas cell to produce very slow beams of ytterbium monofluoride molecules. The molecules are produced by laser ablation inside the cell and extracted into a beam by a flow of cold helium. We measure the flux and velocity distribution of the beam as a function of ablation energy, helium flow rate, cell temperature, and the size of the gap between the first and second stages of the cell. We also compare the velocity distributions from one-stage and two-stage cells. The one-stage cell emits a beam with a speed of about 82 m s¯¹ and a translational temperature of 0.63 K. The slowest beams are obtained using the two-stage cell at the lowest achievable cell temperature of 1.8 K. This beam has a peak velocity of 56 m s¯¹ and a flux of 9×10⁹ ground state molecules per steradian per pulse, with a substantial fraction at speeds below 40 m s¯¹. These slow molecules can be decelerated further by radiation pressure slowing and then captured in a magneto-optical trap.

  • Journal article
    Orozco Ruiz M, Le NH, Mintert F, 2024,

    Quantum control without quantum states

    , PRX Quantum, ISSN: 2691-3399

    We show that combining ideas from the fields of quantum invariants and of optimal control can be used to design optimal quantum control solutions without explicit reference to quantum states. We describe how control problems for state preparation and the realization of propagators can be formulated in this approach, and we provide explicit control solutions for a spin chain with an extended Ising Hamiltonian. The states considered for state-preparation protocols include eigenstates of Hamiltonians with more than pairwise interactions, and these Hamiltonians are also used for the definition of target propagators. The cost of describing suitable time-evolving operators grows only quadratically with the system size, allowing us to construct explicit control solutions for up to 50 spins. While sub-exponential scaling is obtained only in special cases, we provide several examples that demonstrate favourable scaling beyond the extended Ising model.

  • Journal article
    Ferte A, Austin D, Johnson AS, McGrath F, Malhado JP, Marangos JP, Vacher Met al., 2024,

    Signature of Attochemical Quantum Interference upon Ionization and Excitation of an Electronic Wave Packet in Fluorobenzene

    , PHYSICAL REVIEW LETTERS, Vol: 133, ISSN: 0031-9007
  • Journal article
    Vylegzhanin A, Nic Chormaic S, Brown DJ, 2024,

    Rydberg electromagnetically induced transparency based laser lock to Zeeman sublevels with 0.6 GHz scanning range.

    , Rev Sci Instrum, Vol: 95

    We propose a technique for frequency locking a laser to the Zeeman sublevel transitions between the 5P3/2 intermediate and 32D5/2 Rydberg states in 87Rb. This method allows for continuous frequency tuning over 0.6 GHz by varying an applied external magnetic field. In the presence of the applied field, the electromagnetically induced transparency (EIT) spectrum of an atomic vapor splits via the Zeeman effect according to the strength of the magnetic field and the polarization of the pump and probe lasers. We show that the 480 nm pump laser, responsible for transitions between the Zeeman sublevels of the intermediate state and the Rydberg state, can be locked to the Zeeman-split EIT peaks. The short-term frequency stability of the laser lock is 0.15 MHz, and the long-term stability is within 0.5 MHz. The linewidth of the laser lock is ∼0.8 and ∼1.8 MHz in the presence and absence of the external magnetic field, respectively. In addition, we show that in the absence of an applied magnetic field and adequate shielding, the frequency shift of the lock point has a peak-to-peak variation of 1.6 MHz depending on the polarization of the pump field, while when locked to Zeeman sublevels, this variation is reduced to 0.6 MHz. The proposed technique is useful for research involving Rydberg atoms, where large continuous tuning of the laser frequency with stable locking is required.

  • Journal article
    Hanif F, Das D, Halliwell J, Home D, Mazumdar A, Ulbricht H, Bose Set al., 2024,

    Testing Whether Gravity Acts as a Quantum Entity When Measured

    , PHYSICAL REVIEW LETTERS, Vol: 133, ISSN: 0031-9007
  • Journal article
    Wang P, Kwon H, Luan C-Y, Chen W, Qiao M, Zhou Z, Wang K, Kim MS, Kim Ket al., 2024,

    Snapshotting quantum dynamics at multiple time points

    , NATURE COMMUNICATIONS, Vol: 15
  • Journal article
    Ruberti M, Averbukh V, Mintert F, Ruberti Met al., 2024,

    Bell test of quantum entanglement in attosecond photoionization

    , Physical Review X, Vol: 14, ISSN: 2160-3308

    Attosecond physics enables the study of ultrafast coherent electron dynamics in matter upon photoexcitation and photoionization, revealing spectacular effects such as hole migration and coherentAuger dynamics in molecules. In the photoionization scenario, there has been a strong focus onprobing the physical manifestations of internal quantum coherence within the individual parent ionand photoelectron systems. However, quantum correlations between these two subsystems emergingfrom attosecond photoionization events have thus far remained much more elusive. In this work, wedesign theoretically and model numerically a direct probe of quantum entanglement in attosecondphotoionization in the form of a Bell test. We simulate from first principles a Bell test protocolfor the case of noble gas atoms photoionized by ultrashort, circularly polarized infrared laser pulsesin the strong-field regime predicting robust violation of the Bell inequality. This theoretical resultpaves the way for the direct observation of entanglement in the context of ultrafast photoionizationof many-electron systems. Our work provides a novel perspective on attosecond physics directedtoward the detection of quantum correlations between systems born during attosecond photoionization and unraveling the signatures of entanglement in ultrafast coherent molecular dynamics,including in the chemical decomposition pathways of molecular ions.

  • Journal article
    Schofield RC, Fu M, Clarke E, Farrer I, Trapalis A, Dhar HS, Mukherjee R, Severs Millard T, Heffernan J, Mintert F, Nyman RA, Oulton RFet al., 2024,

    Bose–Einstein condensation of light in a semiconductor quantum well microcavity

    , Nature Photonics, Vol: 18, ISSN: 1749-4885

    When particles with integer spin accumulate at low temperature and high density, they undergo Bose–Einstein condensation (BEC). Atoms, magnons, solid-state excitons, surface plasmon polaritons and excitons coupled to light exhibit BEC, which results in high coherence due to massive occupation of the respective system’s ground state. Surprisingly, photons were shown to exhibit BEC recently in organic-dye-flled optical microcavities, which—owing to the photon’s low mass—occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalize and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalization in our system where we can clearly distinguish laser action from BEC. Semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. In practical terms, photon BECs ofer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages: the lack of dark electronic states in inorganic semiconductors allows these BECs to be sustained continuously; and quantum wells ofer stronger photon–photon scattering. We measure an unoptimized interaction parameter ( g̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfuid light.

  • Journal article
    Yu S, Jia Z, Zhang A, Mer E, Li Z, Crescimanna V, Chen K-C, Patel RB, Walmsley IA, Kaszlikowski Det al., 2024,

    Shedding Light on the Future: Exploring Quantum Neural Networks through Optics

    , ADVANCED QUANTUM TECHNOLOGIES
  • Journal article
    Lee JP, Avni T, Alexander O, Maimaris M, Ning H, Bakulin AA, Burden PG, Moutoulas E, Georgiadou DG, Brahms C, Travers JC, Marangos JP, Ferchaud Cet al., 2024,

    Few-femtosecond soft X-ray transient absorption spectroscopy with tuneable DUV-Vis pump pulses

    , Optica, Vol: 11, Pages: 1320-1323, ISSN: 2334-2536

    Achieving few-femtosecond resolution for a pump-probe experiment is crucial to measuring the fastest electron dynamics and for creating superpositions of valence states in quantum systems. However, traditional UV-Vis pump pulses cannot achieve few-fs durations and usually operate at fixed wavelengths. Here, we present, to our knowledge, an unprecedented temporal resolution and pump tuneability for UV-Vis-pumped soft X-ray transient absorption spectroscopy. We have combined few-fs deep-UV to visible tuneable pump pulses from resonant dispersive wave emission in hollow capillary fiber with attosecond soft X-ray probe pulses from high harmonic generation. We achieve sub-5-fs time resolution, sub-fs interferometric stability, and continuous tuneability of the pump pulses from 230 to 700 nm. We demonstrate that the pump can initiate an ultrafast photochemical reaction and that the dynamics at different atomic sites can be resolved simultaneously. These capabilities will allow studies of the fastest electronic dynamics in a large range of photochemical, photobiological and photovoltaic reactions.

  • Journal article
    Gemmell NR, Ma Y, Pearce E, Flórez J, Czerwinski O, Kim MS, Oulton RF, Clark AS, Phillips CCet al., 2024,

    Coupling undetected sensing modes by quantum erasure

    , APL Quantum, Vol: 1

    <jats:p>Imaging with undetected photons (IUP) enables the possibility of sensing changes in the phase and the transmission of a beam of light that need never be detected. This has led to the possibility of infrared sensing with visible silicon camera technology, for example. Relying on the interference of two identical pairs of photons, IUP was initially achieved using unidirectional paths through two nonlinear crystal pair sources. More recently, folded arrangements using bidirectional paths through a single-crystal have become common for their simplicity. Here, we theoretically model and experimentally implement a novel setup involving three interference paths through a single nonlinear crystal. This establishes two independent IUP sensing modes in addition to a third linear interference mode. We achieve this using a polarization state quantum eraser approach, with excellent agreement between experiment and theory. This system provides a new route to control and optimize IUP interference in a single-crystal folded arrangement by using controllable quantum erasure to balance the interferometer, opening the door to new implementations and applications for IUP.</jats:p>

  • Journal article
    Alexander O, Egun F, Rego L, Martinez Gutierrez A, Garratt D, Adolfo Cardenes G, Nogueira JJ, Lee J, Zhao K, Wang R-P, Ayuso D, Barnard J, Beauvarlet S, Bucksbaum PH, Cesar D, Coffee R, Duris J, Frasinski L, Huse N, Kowalczyk K, Larsen K, Matthews M, Mukamel S, O'Neal J, Penfold T, Thierstein E, Tisch JWG, Turner JR, Vogwell J, Driver T, Berrah N, Lin M-F, Dakovski G, Moeller S, Cryan JP, Marinelli A, Picón A, Marangos JPet al., 2024,

    Attosecond impulsive stimulated x-ray Raman scattering in liquid water

    , Science Advances, Vol: 10, ISSN: 2375-2548

    We report the measurement of impulsive stimulated x-ray Raman scattering in neutral liquid water. An attosecond pulse drives the excitations of an electronic wavepacket in water molecules. The process comprises two steps: a transition to core-excited states near the oxygen atoms accompanied by transition to valence-excited states. Thus, the wavepacket is impulsively created at a specific atomic site within a few hundred attoseconds through a nonlinear interaction between the water and the x-ray pulse. We observe this nonlinear signature in an intensity-dependent Stokes Raman sideband at 526 eV. Our measurements are supported by our state-of-the-art calculations based on the polarization response of water dimers in bulk solvation and propagation of attosecond x-ray pulses at liquid density.

  • Journal article
    Driver T, Mountney M, Wang J, Ortmann L, Al-Haddad A, Berrah N, Bostedt C, Champenois EG, DiMauro LF, Duris J, Garratt D, Glownia JM, Guo Z, Haxton D, Isele E, Ivanov I, Ji J, Kamalov A, Li S, Lin M-F, Marangos JP, Obaid R, O'Neal JT, Rosenberger P, Shivaram NH, Wang AL, Walter P, Wolf TJA, Woerner HJ, Zhang Z, Bucksbaum PH, Kling MF, Landsman AS, Lucchese RR, Emmanouilidou A, Marinelli A, Cryan JPet al., 2024,

    Attosecond delays in X-ray molecular ionization

    , NATURE, Vol: 632, ISSN: 0028-0836
  • Journal article
    Bressanini G, Genoni MG, Kim MS, Paris MGAet al., 2024,

    Multi-parameter quantum estimation of single- and two-mode pure Gaussian states

    , Journal of Physics A: Mathematical and Theoretical, Vol: 57, ISSN: 1751-8113

    We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cramér–Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.

  • Journal article
    Haug T, Kim MS, 2024,

    Generalization of quantum machine learning models using quantum Fisher information metric

    , Physical Review Letters, Vol: 133, ISSN: 0031-9007

    Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we introduce the data quantum Fisher information metric (DQFIM). It describes the capacity of variational quantum algorithms depending on variational ansatz, training data, and their symmetries. We apply the DQFIM to quantify circuit parameters and training data needed to successfully train and generalize. Using the dynamical Lie algebra, we explain how to generalize using a low number of training states. Counterintuitively, breaking symmetries of the training data can help to improve generalization. Finally, we find that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work provides a useful framework to explore the power of quantum machine learning models.

  • Journal article
    Knight PL, Gerry CC, Birrittella RJ, Alsing PMet al., 2024,

    Enduring relevance of the Jaynes-Cummings model: a personal perspective [Invited]

    , JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, Vol: 41, ISSN: 0740-3224
  • Journal article
    Latacz BM, Fleck M, Jaeger JI, Umbrazunas G, Arndt BP, Erlewein SR, Wursten EJ, Devlin JA, Micke P, Abbass F, Schweitzer D, Wiesinger M, Will C, Yildiz H, Blaum K, Matsuda Y, Mooser A, Ospelkaus C, Smorra C, Soter A, Quint W, Walz J, Yamazaki Y, Ulmer Set al., 2024,

    Orders of Magnitude Improved Cyclotron-Mode Cooling for Nondestructive Spin Quantum Transition Spectroscopy with Single Trapped Antiprotons

    , PHYSICAL REVIEW LETTERS, Vol: 133, ISSN: 0031-9007
  • Journal article
    Tofful A, Baynham CFA, Curtis EA, Parsons AO, Robertson B, Schioppo M, Tunesi J, Margolis HS, Hendricks RJ, Whale J, Thompson RC, Godun RMet al., 2024,

    <SUP>171</SUP>Yb<SUP>+</SUP> optical clock with 2.2 x 10<SUP>-18</SUP> systematic uncertainty and absolute frequency measurements

    , METROLOGIA, Vol: 61, ISSN: 0026-1394
  • Journal article
    Taylor A, Bressanini G, Kwon H, Kim MSet al., 2024,

    Quantum error cancellation in photonic systems: undoing photon losses

    , Physical Review A, Vol: 110, ISSN: 2469-9926

    Real photonic devices are subject to photon losses that can decohere quantum information encoded in the system. In the absence of full fault tolerance, quantum error mitigation techniques have been introduced to help manage errors in noisy quantum devices. In this paper, we introduce an error mitigation protocol inspired by probabilistic error cancellation (a popular error mitigation technique in discrete variable systems) for continuous variable systems. We show that our quantum error cancellation protocol can undo photon losses in expectation value estimation tasks. To do this, we analytically derive the (nonphysical) inverse photon loss channel and decompose it into a sum over physically realizable channels with potentially negative coefficients. The bias of our ideal expectation value estimator can be made arbitrarily small at the cost of increasing the sampling overhead. The protocol requires a noiseless amplification followed by a series of photon subtractions. While these operations can be implemented probabilistically, for certain classes of initial state one can avoid the burden of carrying out the amplification and photon subtractions by leveraging Monte Carlo methods to give an unbiased estimate of the ideal expectation value. We validate our proposed mitigation protocol by simulating the scheme on squeezed vacuum states, cat states, and entangled coherent states.

  • Journal article
    Athanasakis-Kaklamanakis M, Wilkins SG, Lassegues P, Lalanne L, Reilly JR, Ahmad O, Au M, Bai SW, Berbalk J, Bernerd C, Borschevsky A, Breier AA, Chrysalidis K, Cocolios TE, de Groote RP, Fajardo-Zambrano CM, Flanagan KT, Franchoo S, Ruiz RFG, Hanstorp D, Heinke R, Imgram P, Koszorus A, Kyuberis AA, Lim J, Liu YC, Lynch KM, Mcglone A, Mei WC, Neyens G, Nies L, Oleynichenko AV, Raggio A, Rothe S, Skripnikov LV, Smets E, van den Borne B, Warbinek J, Wessolek J, Yang XFet al., 2024,

    Radiative lifetime of the <i>A</i> <SUP>2</SUP>Π <sub>1 / 2</sub> state in RaF with relevance to laser cooling

    , PHYSICAL REVIEW A, Vol: 110, ISSN: 2469-9926
  • Journal article
    Xiao X, Yang JJ, Millard TS, Zhu S, Kowalczyk KM, Tisch JWG, Matthews M, Maier SA, Oulton RFet al., 2024,

    Nanofocusing in critically coupled nanogap waveguide resonators

    , ACS Photonics, Vol: 11, Pages: 2836-2842, ISSN: 2330-4022

    Coupling between optical antenna resonances is a powerful way to control the distribution of light in nanoscale systems. When the strength of coupling is fine-tuned against resonance loss, a critical coupling condition is often met, where energy can be efficiently directed between the system’s components. In this work, we use this concept to nanofocus optical energy into the 50 nm gap of a waveguide resonator, which on its own cannot be excited by external illumination. Light couples to the waveguide antenna via Fano interference with a bar antenna dimer. As a composite antenna, the shifting of the dimer relative to the waveguide resonator enables the precise tuning of their mutual coupling. We find a critical coupling condition where light is maximally focused into the waveguide’s gap corresponding to unity coupling cooperativity. Our interpretation of critical-coupling-induced nanofocusing is supported by the simultaneous maximization of both second and third harmonic generation at the critical condition.

  • Journal article
    Will C, Wiesinger M, Micke P, Yildiz H, Driscoll T, Kommu S, Abbass F, Arndt BP, Bauer BB, Erlewein S, Fleck M, Jaeger JI, Latacz BM, Mooser A, Schweitzer D, Umbrazunas G, Wursten E, Blaum K, Devlin JA, Ospelkaus C, Quint W, Soter A, Walz J, Smorra C, Ulmer Set al., 2024,

    Image-Current Mediated Sympathetic Laser Cooling of a Single Proton in a Penning Trap Down to 170 mK Axial Temperature

    , PHYSICAL REVIEW LETTERS, Vol: 133, ISSN: 0031-9007
  • Journal article
    Jae J, Lee J, Kim MS, Lee K-G, Lee Jet al., 2024,

    Contextual quantum metrology

    , npj Quantum Information, Vol: 10, ISSN: 2056-6387

    We demonstrate that the contextuality of measurement selection can enhance the precision of quantum metrology with a simple linear optical experiment. Contextuality is a nonclassical property known as a resource for various quantum information processing tasks. Recent studies show that contextuality by anomalous weak values can be utilized to enhance metrological precision, unraveling the role of contextuality in quantum metrology. Our contextual quantum metrology (coQM) scheme can elevate the precision of the optical polarimetry as much as 6 times the precision limit given by the Quantum Fisher Information. We achieve the contextuality-enabled enhancement with two mutually complementary measurements, whereas, in the conventional method, some optimal measurements to achieve the precision limit are either theoretically challenging to find or experimentally infeasible to realize. These results highlight that the contextuality of measurement selection is applicable in practice for quantum metrology.

  • Journal article
    Michniewicz J, Kim MS, 2024,

    Leveraging off-the-shelf silicon chips for quantum computing

    , APPLIED PHYSICS LETTERS, Vol: 124, ISSN: 0003-6951
  • Journal article
    Haug T, Lee S, Kim MS, 2024,

    Efficient quantum algorithms for stabilizer entropies

    , Physical Review Letters, Vol: 132, ISSN: 0031-9007

    Stabilizer entropies (SEs) are measures of nonstabilizerness or “magic” that quantify the degree to whicha state is described by stabilizers. SEs are especially interesting due to their connections to scrambling,localization and property testing. However, applications have been limited so far as previously knownmeasurement protocols for SEs scale exponentially with the number of qubits. Here, we efficiently measureSEs for integer R´enyi index n > 1 via Bell measurements. The SE of N-qubit quantum states can bemeasured with OðnÞ copies and OðnNÞ classical computational time, where for even n we additionallyrequire the complex conjugate of the state. We provide efficient bounds of various nonstabilizernessmonotones that are intractable to compute beyond a few qubits. Using the IonQ quantum computer, wemeasure SEs of random Clifford circuits doped with non-Clifford gates and give bounds for the stabilizerfidelity, stabilizer extent, and robustness of magic. We provide efficient algorithms to measure Clifford averaged 4n-point out-of-time-order correlators and multifractal flatness. With these measures we study thescrambling time of doped Clifford circuits and random Hamiltonian evolution depending on nonstabilizer ness. Counterintuitively, random Hamiltonian evolution becomes less scrambled at long times, which wereveal with the multifractal flatness. Our results open up the exploration of nonstabilizerness with quantumcomputers.

  • Journal article
    Zhu R, Pike-Burke C, Mintert F, 2024,

    Active learning for quantum mechanical measurements

    , PHYSICAL REVIEW A, Vol: 109, ISSN: 2469-9926

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