Understanding the effects of spin-orbit coupling (SOC) and many-body interactions on spin transport is important in condensed matter physics and spintronics. This topic has been intensively studied for electrons as charged fermionic carriers of spin, but barely explored for charge-neutral bosonic quasiparticles or their condensates, which have recently become promising carriers for coherent spin transport over macroscopic distances. Here, we explore the effects of synthetic SOC (induced by optical Raman coupling) and atomic interactions on the spin transport in an atomic Bose-Einstein condensate (BEC), in which the out-of-phase oscillations (spin-dipole mode, SDM, actuated by quenching the Raman coupling) of two interacting BECs of different spin states constitute an alternating spin current in a trap. We experimentally observe that SOC can significantly enhance the SDM damping, while reducing the thermalization of the BEC. Our theory, consistent with the experimental observations, reveals that the interference, immiscibility, and interaction between the two colliding spin components can be notably modified by SOC and play a crucial role in spin transport. Accompanied by the SDM damping, we also observe the generation of different BEC collective excitations such as shape oscillations. Our work may contribute to the fundamental understanding of spin transport and quenched dynamics in spin-orbit coupled systems.

The measurement process is considered for quantum field theory on curved spacetimes. Measurements are carried out on one QFT, the "system", using another, the "probe" via a dynamical coupling of "system" and "probe" in a bounded spacetime region. The resulting "coupled theory" determines a scattering map on the uncoupled combination of the "system" and "probe" by reference to natural "in" and "out" spacetime regions. No specific interaction is assumed and all constructions are local and covariant.

Given any initial probe state in the "in" region, the scattering map determines a completely positive map from "probe" observables in the "out" region to "induced system observables", thus providing a measurement scheme for the latter. It is shown that the induced system observables may be localized in the causal hull of the interaction coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory. Post-selected states conditioned on measurement outcomes are obtained using Davies-Lewis instruments. Composite measurements involving causally ordered coupling regions are also considered. Provided that the scattering map obeys a causal factorization property, the causally ordered composition of the individual instruments coincides with the composite instrument; in particular, the instruments may be combined in either order if the coupling regions are causally disjoint. This is the central consistency property of the proposed framework.

The general concepts and results are illustrated by an example in which both "system" and "probe" are quantized linear scalar fields, coupled by a quadratic interaction term with compact spacetime support. System observables induced by simple probe observables are calculated exactly, for sufficiently weak coupling, and compared with first order perturbation theory.

One of the biggest challenges impeding the progress of Metal-Oxide-Silicon (MOS) quantum dot devices is the presence of disorder at the Si/SiO$_2$ interface which interferes with controllably confining single and few electrons. In this work we have engineered a low-disorder MOS quantum double-dot device with critical electron densities, i.e. the lowest electron density required to support a conducting pathway, approaching critical electron densities reported in high quality Si/SiGe devices and commensurate with the lowest critical densities reported in any MOS device. Utilizing a nearby charge sensor, we show that the device can be tuned to the single-electron regime where charging energies of $\approx$8 meV are measured in both dots, consistent with the lithographic size of the dot. Probing a wide voltage range with our quantum dots and charge sensor, we detect three distinct electron traps, corresponding to a defect density consistent with the ensemble measured critical density. Low frequency charge noise measurements at 300 mK indicate a 1/$f$ noise spectrum of 3.4 $\mu$eV/Hz$^{1/2}$ at 1 Hz and magnetospectroscopy measurements yield a valley splitting of 110$\pm$26 $\mu$eV. This work demonstrates that reproducible MOS spin qubits are feasible and represents a platform for scaling to larger qubit systems in MOS.

A sequential steering scenario is investigated, where multiple Bobs aim at demonstrating steering using successively the same half of an entangled quantum state. With isotropic entangled states of local dimension $d$, the number of Bobs that can steer Alice is found to be $N_\mathrm{Bob}\sim d/\log{d}$, thus leading to an arbitrary large number of successive instances of steering with independently chosen and unbiased inputs. This scaling is achieved when considering a general class of measurements along orthonormal bases, as well as complete sets of mutually unbiased bases. Finally, we show that similar results can be obtained in an anonymous sequential scenario, where none of the Bobs know their position in the sequence.

All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition over the history of the computation. We prove that all history-state Hamiltonians must be critical. More precisely, for any circuit-to-Hamiltonian mapping that maps quantum circuits to local Hamiltonians with low-energy history states, there is an increasing sequence of circuits that maps to a growing sequence of Hamiltonians with spectral gap closing at least as fast as O(1/n) with the number of qudits n in the circuit. This result holds for very general notions of history state, and also extends to quasi-local Hamiltonians with exponentially-decaying interactions.

This suggests that QMA-hardness for gapped Hamiltonians (and also BQP-completeness of adiabatic quantum computation with constant gap) either require techniques beyond history state constructions. Or gapped Hamiltonians cannot be QMA-hard (respectively, BQP-complete).

We demonstrate single-shot imaging and narrow-line cooling of individual alkaline earth atoms in optical tweezers; specifically, strontium-88 atoms trapped in $515.2~\text{nm}$ light. We achieve high-fidelity single-atom-resolved imaging by detecting photons from the broad singlet transition while cooling on the narrow intercombination line, and extend this technique to highly uniform two-dimensional arrays of $121$ tweezers. Cooling during imaging is based on a previously unobserved narrow-line Sisyphus mechanism, which we predict to be applicable in a wide variety of experimental situations. Further, we demonstrate optically resolved sideband cooling of a single atom close to the motional ground state of a tweezer. Precise determination of losses during imaging indicate that the branching ratio from $^1$P$_1$ to $^1$D$_2$ is more than a factor of two larger than commonly quoted, a discrepancy also predicted by our ab initio calculations. We also measure the differential polarizability of the intercombination line in a $515.2~\text{nm}$ tweezer and achieve a magic-trapping configuration by tuning the tweezer polarization from linear to elliptical. We present calculations, in agreement with our results, which predict a magic crossing for linear polarization at $520(2)~\text{nm}$ and a crossing independent of polarization at 500.65(50)nm. Our results pave the way for a wide range of novel experimental avenues based on individually controlled alkaline earth atoms in tweezers -- from fundamental experiments in atomic physics to quantum computing, simulation, and metrology implementations.

Reradiation of a spatially non-uniform ultrashort electromagnetic pulse interacting with the linear chain of multielectron atoms is studied in the framework of sudden perturbation approximation. Angular distributions of the reradiation spectrum for arbitrary number of atoms are obtained. It is shown that interference effects for the photon radiation amplitudes lead to appearing of "diffraction" maximums. The obtained results can be extended to the case of two- and three-dimensional crystal lattices and atomic chains. The approach developed allows also to take into account thermal vibrations of the lattice atoms.

We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic) Hamiltonians we are naturally led to see that the spectral gap can always be upper bounded by an isoperimetric ratio that depends only on the ground state probability distribution and the range of the terms in the Hamiltonian, but not on any other details of the interaction couplings. This means that for a given probability distribution the inequality constrains the spectral gap of any local Hamiltonian with this distribution as its ground state probability distribution in some basis (Eldar and Harrow derived a similar result in order to characterize the output of low-depth quantum circuits). Going further, we relate the Hilbert space localization properties of the ground state to higher energy eigenvalues by showing that the presence of k strongly localized ground state modes (i.e. clusters of probability, or subsets with small expansion) in Hilbert space implies the presence of k energy eigenvalues that are close to the ground state energy. Our results suggest that quantum adiabatic optimization using local Hamiltonians will inevitably encounter small spectral gaps when attempting to prepare ground states corresponding to multi-modal probability distributions with strongly localized modes, and this problem cannot necessarily be alleviated with the inclusion of non-stoquastic couplings.

Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose a machine learning assisted scheme to measure the entanglement between arbitrary subsystems of size $N_A$ and $N_B$, with $\mathcal{O}(N_A + N_B)$ measurements, and without any prior knowledge of the state. The method exploits a neural network to learn the unknown, non-linear function relating certain measurable moments and the logarithmic negativity. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the quantum state, and a decomposition of the measurement operator in a basis of operators with known discrete spectra. We then show how this algorithm can be combined with (a) Hamiltonian evolution to make quantum simulations efficient, (b) the Newton-Raphson method based solution of matrix inverse to efficiently solve linear simultaneous equations, and (c) Chebyshev expansion of matrix exponentials to efficiently evaluate thermal expectation values. The general strategy may be useful in solving many other linear algebra problems efficiently.

Nanomechanical resonators have demonstrated great potential for use as versatile tools in a number of emerging quantum technologies. For such applications, the performance of these systems is restricted by the decoherence of their fragile quantum states, necessitating a thorough understanding of their dissipative coupling to the surrounding environment. In bulk amorphous solids, these dissipation channels are dominated at low temperatures by parasitic coupling to intrinsic two-level system (TLS) defects, however, there remains a disconnect between theory and experiment on how this damping manifests in dimensionally-reduced nanomechanical resonators. Here, we present an optomechanically-mediated thermal ringdown technique, which we use to perform simultaneous measurements of the dissipation in four mechanical modes of a cryogenically-cooled silicon nanoresonator, with resonant frequencies ranging from 3 - 19 MHz. Analyzing the device's mechanical damping rate at fridge temperatures between 10 mK - 10 K, we demonstrate quantitative agreement with the standard tunneling model for TLS ensembles confined to one dimension. From these fits, we extract the defect density of states ($P_0 \sim$ 1 - 4 $\times$ 10$^{44}$ J$^{-1}$ m$^{-3}$) and deformation potentials ($\gamma \sim$ 1 - 2 eV), showing that each mechanical mode couples on average to less than a single thermally-active defect at 10 mK.

True on--demand high--repetition--rate single--photon sources are highly sought after for quantum information processing applications. However, any coherently driven two-level quantum system suffers from a finite re-excitation probability under pulsed excitation, causing undesirable multi--photon emission. Here, we present a solid--state source of on--demand single photons yielding a raw second--order coherence of $g^{(2)}(0)=(7.5\pm1.6)\times10^{-5}$ without any background subtraction nor data processing. To this date, this is the lowest value of $g^{(2)}(0)$ reported for any single--photon source even compared to the previously best background subtracted values. We achieve this result on GaAs/AlGaAs quantum dots embedded in a low--Q planar cavity by employing (i) a two--photon excitation process and (ii) a filtering and detection setup featuring two superconducting single--photon detectors with ultralow dark-count rates of $(0.0056\pm0.0007) s^{-1}$ and $(0.017\pm0.001) s^{-1}$, respectively. Re--excitation processes are dramatically suppressed by (i), while (ii) removes false coincidences resulting in a negligibly low noise floor.

We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cram\'er--Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely result in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times in the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.

It was recently found that it is theoretically possible for there to exist quantum processes in which the operations performed by separate parties cannot be ascribed a definite causal order. Some of these processes are believed to have a physical realization in standard quantum mechanics via coherent control of the times of the operations. A prominent example is the quantum SWITCH, which was recently demonstrated experimentally. However, up until now, there has been no rigorous justification for the interpretation of such an experiment as a genuine realization of a process with indefinite causal structure as opposed to a simulation of such a process. Where exactly are the local operations of the parties in such an experiment? On what spaces do they act given that their times are indefinite? Can we probe them directly rather than assume what they ought to be based on heuristic considerations? How can we reconcile the claim that these operations really take place, each once as required, with the fact that the structure of the presumed process implies that they cannot be part of any acyclic circuit? Here, I offer a precise answer to these questions: the input and output systems of the operations in such a process are generally nontrivial subsystems of Hilbert spaces that are tensor products of Hilbert spaces associated with different times---a fact that is directly experimentally verifiable. With respect to these time-delocalized subsystems, the structure of the process is one of a circuit with a cycle, which cannot be reduced to a (possibly dynamical) probabilistic mixture of acyclic circuits. I further show that all bipartite processes that admit a certain type of isometric extension have a physical realization on such time-delocalized subsystems. These results unveil a novel structure within quantum mechanics, which may have important implications for physics and information processing.

We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in a complex neighborhood of 0. On a set of canonical examples, with bounded and unbounded perturbations, we show that our ultraviolet conditions are essentially necessary. If the form factor of the perturbation does not meet our assumptions, the heat variation distribution exhibits heavy tails. The tails can be as heavy as preventing the existence of a fourth moment of the heat variation.

We report a single-stage bi-directional interface capable of linking Sr+ trapped ion qubits in a long-distance quantum network. Our interface converts photons between the Sr+ emission wavelength at 422 nm and the telecoms C-band to enable low-loss transmission over optical fiber. We have achieved both up- and down-conversion at the single photon level with efficiencies of 9.4% and 1.1% respectively. Furthermore we demonstrate noise levels that are low enough to allow for genuine quantum operation in the future.

Non-equilibrium quasiparticle excitations degrade the performance of a variety of superconducting circuits. Understanding the energy distribution of these quasiparticles will yield insight into their generation mechanisms, the limitations they impose on superconducting devices, and how to efficiently mitigate quasiparticle-induced qubit decoherence. To probe this energy distribution, we systematically correlate qubit relaxation and excitation with charge-parity switches in an offset-charge-sensitive transmon qubit, and find that quasiparticle-induced excitation events are the dominant mechanism behind the residual excited-state population in our samples. By itself, the observed quasiparticle distribution would limit $T_1$ to $\approx200~\mu\mathrm{s}$, which indicates that quasiparticle loss in our devices is on equal footing with all other loss mechanisms. Furthermore, the measured rate of quasiparticle-induced excitation events is greater than that of relaxation events, which signifies that the quasiparticles are more energetic than would be predicted from a thermal distribution describing their apparent density.

Hierarchical sets such as the Pythagorean triplets ($\cal{PT}$) and the integral Apollonian gaskets ($\cal{IAG}$) are iconic mathematical sets made up of integers that resonate with a wide spectrum of inquisitive minds. Here we show that these abstract objects are related with a quantum fractal made up of integers, known as the {\it Hofstadter Butterfly}. The "butterfly fractal" describes a {\it physical system} of electrons in a crystal in a magnetic field, representing exotic states of matter known as {\it integer quantum Hall} states. Integers of the butterfly are the quanta of Hall conductivity that appear in a highly convoluted form in the integers of the $\cal{PT}$ and the $\cal{IAG}$. Scaling properties of these integers, as we zoom into the self-similar butterfly fractal are given by a class of quadratic irrationals that lace the butterfly in a highly intricate and orderly pattern, some describing a

{\it mathematical kaleidoscope}. The number theoretical aspects are all concealed in Lorentz transformations along the light cone in abstract Minkowski space where subset of these are related to the celebrated {\it Pell's equation}.

Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a decoder which can adapt to the wide variety of error models present in experiments. The typical approach to the problem of decoding the surface code is to reduce it to minimum-weight perfect matching in a way that provides a suboptimal threshold error rate, and is specialized to correct a specific error model. Recently, optimal threshold error rates for a variety of error models have been obtained by methods which do not use minimum-weight perfect matching, showing that such thresholds can be achieved in polynomial time. It is an open question whether these results can also be achieved by minimum-weight perfect matching. In this work, we use belief propagation and a novel algorithm for producing edge weights to increase the utility of minimum-weight perfect matching for decoding surface codes. This allows us to correct depolarizing errors using the rotated surface code, obtaining a threshold of $17.76 \pm 0.02 \%$. This is larger than the threshold achieved by previous matching-based decoders ($14.88 \pm 0.02 \%$), though still below the known upper bound of $\sim 18.9 \%$.