A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[2^r, 2^r - C(r,t) - 2 sum_{i=0}^{t-1} C(r,i), 2^t + 2^{t-1} ]].

We construct a microscopic spin-exchange Hamiltonian for the quasi-1D Ising magnet CoNb$_2$O$_6$ that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in CoNb$_2$O$_6$ corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and `quasiparticle breakdown' in the polarized phase at high transverse field.

We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the control strategy required to achieve superadiabaticity. We apply our formalism to two examples consisting of a two-level system coupled to environments with time-dependent bath operators.

Motivated by the recent success of reinforcement learning in games such as Go and Dota2, we formulate Bell non-local games as a reinforcement learning problem. Such a formulation helps us to explore Bell non-locality in a range of scenarios. The measurement settings and the quantum states are selected by the learner randomly in the beginning. Still, eventually, it starts understanding the underlying patterns and discovers an optimal (or near-optimal) quantum configuration corresponding to the task at hand. We provide a proof of principle approach to learning quantum configurations for violating various Bell inequalities. The algorithm also works for non-convex optimization problems where convex methods fail, thus offering a possibility to explore optimal quantum configurations for Bell inequalities corresponding to large quantum networks. We also implement a hybrid quantum-classical variational algorithm with reinforcement learning.

Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.

Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisa- tion, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the analytical and sophisticated numerical methods required to tackle these systems is included.

10,000 simulations of 1000-particle realisations of the same cluster are computed by direct force summation. Over three crossing times the original Poisson noise is amplified more than tenfold by self-gravity. The cluster's fundamental dipole mode is strongly excited by Poisson noise, and this mode makes a major contribution to driving diffusion of stars in energy. The diffusive flow through action space is computed for the simulations and compared with the predictions of both local-scattering theory and the Balescu-Lenard (BL) equation. The predictions of local-scattering theory are qualitatively wrong because the latter neglects self-gravity. These results imply that local-scattering theory is of little value. Future work on cluster evolution should employ either N-body simulation or the BL equation. However, significant code development will be required to make use of the BL equation practicable.

Ion traps are often loaded from atomic beams produced by resistively heated ovens. We demonstrate an atomic oven which has been designed for fast control of the atomic flux density and reproducible construction. We study the limiting time constants of the system and, in tests with $^{40}\textrm{Ca}$, show we can reach the desired level of flux in 12s, with no overshoot. Our results indicate that it may be possible to achieve an even faster response by applying an appropriate one-off heat treatment to the oven before it is used.

One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is neither. The resolution to this paradox is to recognize that global unitary evolution of a multi-partite quantum state causes the state of local subsystems to evolve towards maximum-entropy states. In this work, we experimentally demonstrate this effect in linear quantum optics by simultaneously showing the convergence of local quantum states to a generalized Gibbs ensemble constituting a maximum-entropy state under precisely controlled conditions, while introducing an efficient certification method to demonstrate that the state retains global purity. Our quantum states are manipulated by a programmable integrated quantum photonic processor, which simulates arbitrary non-interacting Hamiltonians, demonstrating the universality of this phenomenon. Our results show the potential of photonic devices for quantum simulations involving non-Gaussian states.

We revisit the dynamics of razor-thin, stone-cold, self-gravitating discs. By recasting the equations into standard cylindrical coordinates, the linearised vertical dynamics of an exponential disc can be followed for several gigayears on a laptop in a few minutes. An initially warped disc rapidly evolves into a flat inner region and an outward-propagating spiral corrugation wave that rapidly winds up and would quickly thicken a disc with non-zero radial velocity dispersion. The Sgr dwarf galaxy generates a similar warp in the Galactic disc as it passes through pericentre, and the warp generated by the dwarf's last pericentre ~ 35 Myr ago is remarkably similar to the warp traced by the Galaxy's HI disc. The resemblance to the observed warp is fleeting but its timing is perfect. For the adopted parameters the amplitude of the model warp is a factor 3 too small, but there are several reasons for this being so. The marked flaring of our Galaxy's low-alpha disc just outside the solar circle can be explained as a legacy of earlier pericentres.

A popular class of models for interpreting quasi-periodic X-ray eruptions from galactic nuclei (QPEs) invoke collisions between an object on an extreme mass ratio inspiral (EMRI) and an accretion disk around a supermassive black hole. There are strong links between QPE systems and those disks which formed following a tidal disruption event (TDE), and at least two events (AT2019qiz and AT2022upj) are known to have occurred following an otherwise typical TDE. We show that the fact that these disks were formed following a TDE strongly constrains their properties, more so than previous models have assumed. Models based on steady-state AGN-like disks have mass contents which grow strongly with size $M_{\rm disk}\propto R_{\rm out}^{7/2}$ and do not conserve the mass or angular momentum of the disrupted star. A very different scaling must be satisfied by a TDE disk in order to conserve the disrupted stars angular momentum, $M_{\rm disk} \propto R_{\rm out}^{-1/2}$. These constraints substantially change the predicted scaling relationships between QPE observables (luminosity, duration, energy, temperature) and the QPE period. They also allow QPE observables to be written in terms of the properties of the two stars assumed to be involved (the one tidally disrupted and the one on an EMRI), making plausibility tests of these models possible. We show that these modifications to the disk structure imply that (i) QPEs cannot be powered by collisions between an orbiting black hole and a TDE disk, (ii) QPEs also cannot be powered by collisions between the surface of a stellar EMRI and a TDE disk. A framework in which the collisions are between a TDE disk and a star which has puffed up to fill its Hills sphere with a trailing debris stream (as seen in recent simulations) cannot be ruled out from the data, and should be the focus of further study.

We present a theoretical and experimental study of superconducting ring resonators as an initial step towards their application to superconducting electronics and quantum technologies. These devices have the potentially valuable property of supporting two orthogonal electromagnetic modes that couple to a common Cooper pair, quasiparticle, and phonon system. We present here a comprehensive theoretical and experimental analysis of the superconducting ring resonator system. We have developed superconducting ring resonator models that describe the key features of microwave behaviour to first order, providing insights into how transmission line inhomogeneities give rise to frequency splitting and mode rotation. Furthermore, we constructed signal flow graphs for a four-port ring resonator to numerically validate the behaviour predicted by our theoretical analysis. Superconducting ring resonators were fabricated in both coplanar waveguide and microstrip geometries using Al and Nb thin films. Microwave characterisation of these devices demonstrates close agreement with theoretical predictions. Our study reveals that frequency splitting and mode rotation are prevalent in ring systems with coupled degenerate modes, and these phenomena become distinctly resolved in high quality factor superconducting ring resonators.

We realize a two-stage, hexagonal pyramid magneto-optical trap (MOT) with strontium, and demonstrate loading of cold atoms into cavity-enhanced 1D and 2D optical lattice traps, all within a single compact assembly of in-vacuum optics. We show that the device is suitable for high-performance quantum technologies, focusing especially on its intended application as a strontium optical lattice clock. We prepare $2\times 10^4$ spin-polarized atoms of $^{87}$Sr in the optical lattice within 500 ms; we observe a vacuum-limited lifetime of atoms in the lattice of 27 s; and we measure a background DC electric field of 12 Vm$^{-1}$ from stray charges, corresponding to a fractional frequency shift of $(-1.2\times 0.8)\times 10^{-18}$ to the strontium clock transition. When used in combination with careful management of the blackbody radiation environment, the device shows potential as a platform for realizing a compact, robust, transportable optical lattice clock with systematic uncertainty at the $10^{-18}$ level.

We demonstrate long-lived coherence in internal hyperfine states of a single \Ca{43} trapped-ion qubit $[T_2=1.2(2)\s]$, and in external motional states of a single \Ca{40} trapped-ion qubit $[T_2'=0.18(4)\s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state $T_2$ time that we observe in \Ca{43}, which has not previously been used as a trapped-ion qubit, is about one thousand times longer than that of physical qubits based on \Ca{40} ions. Using a single spin-echo pulse to ``re-phase'' the internal state, we can detect no decoherence after 1\s, implying an effective coherence time $T_2^{\mbox{\tiny SE}} \gtish 45\s$. This compares with timescales in this trap for single-qubit operations of \ish 1\us, and for two-qubit operations of \ish 10\us.

The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer. Methods of error correction in the quantum regime are presented, and their limitations assessed. A quantum channel can recover from arbitrary decoherence of x qubits if K bits of quantum information are encoded using n quantum bits, where K/n can be greater than 1-2 H(2x/n), but must be less than 1 - 2 H(x/n). This implies exponential reduction of decoherence with only a polynomial increase in the computing resources required. Therefore quantum computation can be made free of errors in the presence of physically realistic levels of decoherence. The methods also allow isolation of quantum communication from noise and evesdropping (quantum privacy amplification).

We show that interstitial hydrogen nucleii on a metallic lattice are strongly coupled to their near neighbours by the unscreened electromagnetic field mediating transitions between low-lying states. We then show that in almost-stoichiometric PdD clusters, in which most interstitial sites are occupied by a deuteron, certain specific superpositions of many-site product states exist that are lower in energy than the single-site ground state, suggesting the existence of a new low temperature phase. The modified behaviour of the two-particle wavefunction at small separations is investigated and prelimary results suggesting an over-canceling of the effective Coulomb barrier are presented.

Active stabilisation of a quantum system is the active suppression of noise (such as decoherence) in the system, without disrupting its unitary evolution. Quantum error correction suggests the possibility of achieving this, but only if the recovery network can suppress more noise than it introduces. A general method of constructing such networks is proposed, which gives a substantial improvement over previous fault tolerant designs. The construction permits quantum error correction to be understood as essentially quantum state synthesis. An approximate analysis implies that algorithms involving very many computational steps on a quantum computer can thus be made possible.

Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and degree of parallelism. I present an analysis of error correction with block codes, made fault-tolerant through the use of prepared ancilla blocks. The preparation and verification of the ancillas is described in detail. It is shown that the ancillas need only be verified against a small set of errors. This, combined with previously known advantages, makes this `ancilla factory' the best method to apply error correction, whether in concatenated or block coding. I then consider the resources required to achieve $2 \times 10^{10}$ computational steps reliably in a computer of 2150 logical qubits, finding that the simplest $[[n,1,d]]$ block codes can tolerate more noise with smaller overheads than the $7^L$-bit concatenated code. The scaling is such that block codes remain the better choice for all computations one is likely to contemplate.

A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already known how to phrase the first four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the solution to the more general Abelian `hidden subgroup problem' can also be described and analysed as such. We then point out how certain instances of these problems can be solved with only one control qubit, or `flying qubits', instead of entire registers of control qubits.