Levitated nanoparticles are being intensively investigated from two different perspectives: as a potential realisation of macroscopic quantum coherence; and as ultra-sensitive sensors of force, down to the zeptoNewton level, with a range of various applications, including the search for Dark Matter. A future aim is to merge these two strands, enabling the development of quantum-limited sensors. Here we propose that mechanical cross-correlation spectra $S_{xy}(\omega)$ offer new possibilities: once detector misalignment errors are minimised, the spectral shape of $S_{xy}(\omega)$ directly points out the orientation of an external stochastic force, offering something akin to a compass in the $x-y$ plane. We analyse this for detection of microscopic gas currents, but any broad spectrum directed force will suffice, enabling straightforward investigation with laboratory test forces with or without cavities. For a cavity set-up, we analyse misalignment imprecisions between detectors and motional modes due to for example optical back-actions that mask the signature of the directed forces, and show how to suppress them. Near quantum regimes, we quantify the imprecision due to the $x-y$ correlating effect of quantum shot noise imprecision.

We propose a quantum annealing protocol that more effectively probes the dynamics of a single qubit on D-Wave's quantum annealing hardware. This protocol uses D-Wave's h-gain schedule functionality, which allows the rapid quenching of the longitudinal magnetic field at arbitrary points during the anneal. This features enables us to distinguish between open and closed system dynamics as well as the presence or absence of longitudinal magnetic field noise. We show that both thermal and magnetic field fluctuations are key sources of noise that need to be included in an open quantum system model to reproduce the output statistics of the hardware.

The 1d transverse-field Ising model, when projected to the $Z_2$ symmetric sector, is known to have a noninvertible gravitational anomaly that can be compensated by the $Z_2$ toric model in 2d. In this paper, we study the generalization of this type of bulk-boundary correspondence in a large class of qubit lattice models in arbitrary dimensions, called the generalized Ising (GI) models. We provide a systematic construction of exactly solvable bulk models, where the GI models can terminate on their boundaries. In each bulk model, any ground state is robust against local perturbations. If the model has degenerate ground states with periodic boundary condition, the phase is topological and/or fracton ordered. The construction generates abundant examples, including not only prototype ones such as $Z_2$ toric code models in any dimensions no less than two, and the X-cube fracton model, but also more diverse ones such as the $Z_2\times Z_2$ topological order, the 4d $Z_2$ topological order with pure-loop excitations, etc. The boundary of the solvable model is potentially anomalous and corresponds to precisely only sectors of the GI model that host certain total symmetry charges and/or satisfy certain boundary conditions. We derive a concrete condition for such bulk-boundary correspondence. The condition is violated only when the bulk model is either trivial or fracton ordered. A generalized notion of Kramers-Wannier duality plays an important role in the construction. Also, utilizing the duality, we find an example where a single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders. More generally, topological orders may also be generated starting with qubit lattice models beyond the GI models, such as those with SPT orders, through a variant bulk construction, which we provide in an appendix.

We propose a nuclear-spin polarization protocol in a general evolution-and-measurement framework. The technique works in a spin-star configuration, where the central spin is coupled to the surrounding bath (nuclear) spins by flip-flop interaction and subject to a sequence of projective measurements on its ground state. Then a nondeterministic nuclear-spin polarization could be implemented by entropy reduction through measurement. Optimized measurement-interval $\tau_{\rm opt}$ is analytically obtained in the near-resonant condition, which is particularly relevant to the nuclear spins' polarization degree of the last-round measurement, the number of nuclear spins, and the coupling strength between central spin and nuclear spins. Hundreds and even thousands of randomly aligned nuclear spins under thermal state could be almost fully polarized with an optimized sequence of less than twenty unequal-time-spacing measurements. In comparison to the conventional methods, our protocol is not sensitive to the ambient conditions and it is robust against the extra counter-rotating interaction in the near-resonant case.

Quantum key distribution (QKD) is a cryptographic protocol to enable two parties to share a secure key string, which can be used in one-time pad cryptosystem. There has been an ongoing surge of interest in implementing long-haul photonic-implementation of QKD protocols. However, the endeavour is challenging in many aspects. In particular, one of the major challenges is the polarization degree of freedom of single-photons getting affected while transmission through optical fibres, or atmospheric turbulence. Conventionally, an active feedback-based mechanism is employed to achieve real-time polarization tracking. In this work, we propose an alternative approach where we first perform a state tomography to reconstruct the output density matrix. We then evaluate the optimal measurement bases at Bob's end that leads to the maximum (anti-)correlation in the measurement outcomes of both parties. As a proof-of-principle demonstration, we implement an in-lab BBM92 protocol -- a particular variant of a QKD protocol using quantum entanglement as a resource -- to exemplify the performance of our technique. We experimentally generate polarization-entangled photon pairs having $94\%$ fidelity with $\ket{\psi}_1 = 1/\sqrt{2}\,(\ket{HV}+\ket{VH})$ state and a concurrence of $0.92$. By considering a representative 1 ns coincidence window span, we are able to achieve a quantum-bit-error-rate (QBER) of $\approx 5\%$, and a key rate of $\approx 35$ Kbps. The protocol performance is independent of local polarization rotations through optical fibres. We also develop an algorithmic approach to optimize the trade-off between the key rate and QBER. Our approach obviates the need for active polarization tracking. Our method is also applicable to entanglement-based QKD demonstrations using partially mixed as well as non-maximally entangled states, and extends to single-photon implementations over fibre channels.

A scalable quantum information processing architecture based on silicon metal-oxide-semiconductor technology is presented, combining quantum hardware elements from planar and 3D silicon-on-insulator technologies. This architecture is expressed in the ``unit cell'' approach, where tiling cells in two dimensions and allowing inter-cellular nearest-neighbour interactions makes the architecture compatible with the surface code for fault tolerant quantum computation. The architecture utilises global control methods, substantially reducing processor complexity with scale: Single-qubit control is achieved using globally applied spin-resonance techniques and two-qubit interactions are mediated by large quantum dots. Further, a solution to device variation is proposed through integration of electronics for individual trimming of quantum dot voltage references. Such a combined set of solutions addresses several major barriers to scaling quantum machines within completely silicon based architectures.

The process of thermalization in many-body systems is driven by complex interactions among sub-systems and with the surrounding environment. Here we lay the theoretical foundations for the active control of local thermal states in these systems close to their equilibrium state. In particular we describe how to (i) force some part of the system to evolve according to a prescribed law during the relaxation process (i.e. thermal targeting probem), (ii) insulate some elements from the rest of the system or (iii) synchronize their evolution during the relaxation process. We also derive the general conditions a system must fullfill in order that some parts relax toward a minimal temperature with a minimum energetic cost or relax toward a prescribed temperature with a minimum time. Finally, we consider several representative examples in the context of systems exchanging heat radiatively.

A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to the von Neumann equation for the density matrix. The transform reduces to the Weyl transform in the electrostatic limit, when the vector potential and thus the magnetic field are zero. Both cases involve a center-of-mass transform followed by a Fourier integral on the relative coordinate introducing the momentum variable. The latter is continuous if the limits of the integral are infinite, or, equivalently, the coherence length is infinite. However, the quantum theory involves Fourier transforms of the electromagnetic field components, which imposes conditions on their behavior at infinity. Conversely, quantum systems are bounded and often very small, as is, for instance, the case in modern nanoelectronics. This implies a finite coherence length, which avoids the need to regularize non-converging Fourier integrals. Accordingly, the momentum space becomes discrete, giving rise to momentum quantization and to a semi-discrete gauge-invariant Wigner equation. To gain insights into the peculiarities of this theory one needs to analyze the equation for specific electromagnetic conditions. We derive the evolution equation for the linear electromagnetic case and show that it significantly simplifies for a limit dictated by the long coherence length behavior, which involves momentum derivatives: In the discrete momentum picture these derivatives are presented by finite difference quantities which, together with further approximations, allow to develop a computationally feasible model which offering physical insights into the involved quantum processes. In particular, a Fredholm integral equation of the second kind is obtained, where the 'power' of the kernel components, measuring their rate of modification of the quantum evolution, can be evaluated.

We propose superluminal solitons residing in the momentum gap (k-gap) of nonlinear photonic time-crystals. These gap solitons are structured as plane-waves in space while being periodically self-reconstructing wavepackets in time. The solitons emerge from modes with infinite group velocity causing superluminal evolution, which is opposite to the stationary nature of the analogous Bragg gap soliton residing at the edge of an energy gap (or a spatial gap) with zero group velocity. We explore the faster-than-light pulsed propagation of these k-gap solitons in view of Einstein's causality by introducing a truncated input seed as a precursor of signal velocity forerunner, and find that the superluminal propagation of k-gap solitons does not break causality.

Correlations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by \textit{assemblages} of unnormalised quantum states, have recently caught the attention of the community, both from a foundational and an information-theoretic perspective. The set of quantum-realisable assemblages, or abbreviated to quantum assemblages, are those that arise from multiple parties performing local measurements on a shared quantum system. In general, deciding whether or not a given assemblage is a quantum assemblage, i.e. membership of the set of quantum assemblages, is a hard problem, and not always solvable. In this paper we introduce a hierarchy of tests where each level either determines non-membership of the set of quantum assemblages or is inconclusive. The higher the level of the hierarchy the better one can determine non-membership, and this hierarchy converges to a particular set of assemblages. Furthermore, this set to which it converges contains the quantum assemblages. Each test in the hierarchy is formulated as a semidefinite program. This hierarchy allows one to upper bound the quantum violation of a steering inequality and the quantum advantage provided by quantum EPR assemblages in a communication or information-processing task.

Today's most precise optical instruments -- gravitational-wave interferometers and optical atomic clocks -- rely on long storage times for photons to realize their exquisite sensitivity. Optical fiber technology is the most widely deployed platform for realizing long-distance optical propagation. Yet, their application to precision optical measurements is sparse. We review the state-of-the-art in the noise performance of conventional (solid-core) optical fibers from the perspective of precision optical measurements and quantum technology that rely on precise transfer of information over long distances. In doing so, we highlight the limitations of this platform and point to the opportunities that structured fiber technology offers to overcome some of these limitations.

We present a general protocol to control closed quantum systems that is based on minimising the adiabatic action. Using tools based on the geometry of quantum evolutions through the quantum adiabatic brachistochrone, we show that high fidelity control of the ground state of critical quantum systems can be achieved and requires only a reasonable approximation for the ground state spectral gap. We demonstrate our results for three widely applicable systems: the Landau-Zener, Ising, and fully connected spin models.

Spectral statistics of quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF) which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at bifurcation point is found to show anomalous accumulation which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space, which contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller trace formula.

We propose that an unsharp measurement-based process to generate genuine multipartite entanglement from an entangled initial state with a fewer number of qubits can be classified in two ways -- biased and unbiased inflation protocols. In the biased case, genuine multipartite entanglement (GME) of the resulting state obtained after a single measurement outcome is optimized, thereby creating a possibility of states with high GME while in the unbiased case, average GME is optimized over all possible outcomes. Interestingly, we show that the set of two-qubit unsharp measurements can generate multipartite states having different features according to GME measure, generalized geometric measure, the monogamy-based entanglement measure, tangle and robustness against particle loss quantified via persistency depending on the rank of the unsharp measurement operators. Specifically, in the process of producing three-qubit pure states, we prove that rank-$2$ measurements can create only Greenberger Horne Zeilinger (GHZ)-class states while only W-class states are produced with rank-$4$ measurements although rank-$3$ measurements are capable to generate both. In the case of multipartite states with an arbitrary number of qubits, we report that the average content of genuine multipartite entanglement increases with the decrease of the rank in the measurement operators although the persistency decreases with the rank, both in the biased as well as unbiased protocols.

Twin-field (TF) quantum key distribution (QKD) has rapidly risen as the most viable solution to long-distance secure fibre communication thanks to its fundamentally repeater-like rate-loss scaling. However, its implementation complexity, if not successfully addressed, could impede or even prevent its advance into real-world. To satisfy its requirement for twin-field coherence, all present setups adopted essentially a gigantic, resource-inefficient interferometer structure that lacks scalability that mature QKD systems provide with simplex quantum links. Here we introduce a novel technique that can stabilise an open channel without using a closed interferometer and has general applicability to phase-sensitive quantum communications. Using locally generated frequency combs to establish mutual coherence, we develop a simple and versatile TF-QKD setup that does not need service fibre and can operate over links of 100 km asymmetry. We confirm the setup's repeater-like behaviour and obtain a finite-size rate of 0.32 bit/s at a distance of 615.6 km.

Quantum computers with hundreds of qubits will be available soon. Unfortunately, high device error-rates pose a significant challenge in using these near-term quantum systems to power real-world applications. Executing a program on existing quantum systems generates both correct and incorrect outcomes, but often, the output distribution is too noisy to distinguish between them. In this paper, we show that erroneous outcomes are not arbitrary but exhibit a well-defined structure when represented in the Hamming space. Our experiments on IBM and Google quantum computers show that the most frequent erroneous outcomes are more likely to be close in the Hamming space to the correct outcome. We exploit this behavior to improve the ability to infer the correct outcome.

We propose Hamming Reconstruction (HAMMER), a post-processing technique that leverages the observation of Hamming behavior to reconstruct the noisy output distribution, such that the resulting distribution has higher fidelity. We evaluate HAMMER using experimental data from Google and IBM quantum computers with more than 500 unique quantum circuits and obtain an average improvement of 1.37x in the quality of solution. On Google's publicly available QAOA datasets, we show that HAMMER sharpens the gradients on the cost function landscape.

The progress of miniaturisation in integrated electronics has led to atomic and nanometre-sized dopant devices in silicon. Such structures can be fabricated routinely by hydrogen resist lithography, using various dopants such as phosphorous and arsenic. However, the ability to non-destructively obtain atomic-species-specific images of the final structure, which would be an indispensable tool for building more complex nano-scale devices, such as quantum co-processors, remains an unresolved challenge. Here we exploit X-ray fluorescence to create an element-specific image of As dopants in silicon, with dopant densities in absolute units and a resolution limited by the beam focal size (here $\sim1~\mu$m), without affecting the device's low temperature electronic properties. The As densities provided by the X-ray data are compared to those derived from Hall effect measurements as well as the standard non-repeatable, scanning tunnelling microscopy and secondary ion mass spectroscopy, techniques. Before and after the X-ray experiments, we also measured the magneto-conductance, dominated by weak localisation, a quantum interference effect extremely sensitive to sample dimensions and disorder. Notwithstanding the $1.5\times10^{10}$ Sv ($1.5\times10^{16}$ Rad/cm$^{-2}$) exposure of the device to X-rays, all transport data were unchanged to within experimental errors, corresponding to upper bounds of 0.2 Angstroms for the radiation-induced motion of the typical As atom and 3$\%$ for the loss of activated, carrier-contributing dopants. With next generation synchrotron radiation sources and more advanced optics, we foresee that it will be possible to obtain X-ray images of single dopant atoms within resolved radii of 5 nm.

We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy that attains the quantum Fisher information, whereas the customarily used homodyne detection becomes useless in the limit of small displacements, due to the same effect that gives Rayleigh's curse in optical superresolution. There is a quantum advantage: a squeezed or a Fock state with $N$ average photons allow to asymptotically estimate the parameter with a $\sqrt{N}$ better precision than classical states with same energy.

All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics, over holographic duality in high-energy physics, to annealing algorithms in quantum computing. Typically, these models are abstractions that do not find unambiguous physical realisations in nature. Here, we realise an all-to-all interacting, disordered spin system by subjecting an atomic cloud in a cavity to a controllable light shift. Adjusting the detuning between atom resonance and cavity mode, we can tune between disordered versions of a central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically probing the low-energy excitations of the system, we explore the competition of interactions with disorder across a broad parameter range. We show how disorder in the central-mode model breaks the strong collective coupling, making the dark state manifold cross over to a random distribution of weakly-mixed light-matter, "grey", states. In the Lipkin-Meshkov-Glick model the ferromagnetic finite-size ground state evolves towards a paramagnet as disorder is increased. In that regime, semi-localised eigenstates emerge, as we observe by extracting bounds on the participation ratio. These results present significant steps towards freely programmable cavity-mediated interactions for the design of arbitrary spin Hamiltonians.

We introduce a family of quantum R\'enyi fidelities and discuss their symmetry resolution. We express the symmetry-resolved fidelities as Fourier transforms of charged fidelities, for which we derive exact formulas for Gaussian states. These results also yield a formula for the total fidelities of Gaussian states, which we expect to have applications beyond the scope of this paper. We investigate the total and symmetry-resolved fidelities in the XX spin chain, and focus on (i) fidelities between thermal states, and (ii) fidelities between reduced density matrices at zero temperature. Both thermal and reduced fidelities can detect the quantum phase transition of the XX spin chain. Moreover, we argue that symmetry-resolved fidelities are sensitive to the inner structure of the states. In particular, they can detect the phase transition through the reorganisation of the charge sectors at the critical point. This a main feature of symmetry-resolved fidelities which we expect to be general. We also highlight that reduced fidelities can detect quantum phase transitions in the thermodynamic limit.