A quantum neural network (QNN) is an object that extends the notion of a classical neural network to quantum models for quantum data. We can create a QNN by parametrizing a quantum process and then using it to model unknown relations between quantum states. In this paper, we explore how to use measurement-based quantum computation for quantum machine learning problems and propose a universal QNN in this framework which we call the multiple-triangle ansatz (MuTA). Using the proposed QNN, we solve several tasks, including learning a universal set of gates, optimizing measurement with post-processing, learning a quantum instrument, and the classification of classical data. Finally, we discuss how to train an ansatz under the hardware constraints imposed by photonic Gottesman-Kitaev-Preskill qubits. Our work demonstrates the feasibility of using measurement-based quantum computation as a framework for quantum machine learning algorithms.

Measurement-Based Quantum Computation (MBQC) is a model of quantum computation, which uses local measurements instead of unitary gates. Here we explain that the MBQC procedure has a fundamental basis in an underlying gauge theory. This perspective provides a theoretical foundation for global aspects of MBQC. The gauge transformations reflect the freedom of formulating the same MBQC computation in different local reference frames. The main identifications between MBQC and gauge theory concepts are: (i) the computational output of MBQC is a holonomy of the gauge field, (ii) the adaptation of measurement basis that remedies the inherent randomness of quantum measurements is effected by gauge transformations. The gauge theory of MBQC also plays a role in characterizing the entanglement structure of symmetry-protected topologically (SPT) ordered states, which are resources for MBQC. Our framework situates MBQC in a broader context of condensed matter and high energy theory.

We introduce a class of models, dubbed paired twist-defect networks, that generalize the structure of Kitaev's honeycomb model for which there is a direct equivalence between: i) Floquet codes (FCs), ii) adiabatic loops of gapped Hamiltonians, and iii) unitary loops or Floquet-enriched topological orders (FETs) many-body localized phases. This formalism allows one to apply well-characterized topological index theorems for FETs to understand the dynamics of FCs, and to rapidly assess the code properties of many FC models. As an application, we show that the Honeycomb Floquet code of Haah and Hastings is governed by an irrational value of the chiral Floquet index, which implies a topological obstruction to forming a simple, logical boundary with the same periodicity as the bulk measurement schedule. In addition, we construct generalizations of the Honeycomb Floquet code exhibiting arbitrary anyon-automorphism dynamics for general types of Abelian topological order.

We provide an intuitive understanding of the collective low-energy spin excitation of the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain, known as the spinon. To this end, we demonstrate how a single spinon can be excited by adding one extra spin to the ground state. This procedure accurately reproduces all key features of the spinon's dispersion. These follow from the vanishing norm of the excited state which is triggered by the ground state entanglement. Next, we show that the spinon dispersion can be approximately reproduced if we replace the true ground state with the simplest valence-bond solid. This proves that the spinon of the one-dimensional Heisenberg model can be understood as a single spin flowing through a valence-bond solid.

The superconducting order parameter is directly related to the pairing interaction, with the amplitude determined by the interaction strength, while the phase reflects the spatial structure of the interaction. However, given the large variety of materials and their rich physical properties within the iron-based high-Tc superconductors, the structure of the order parameter remains controversial in many cases. Here, we introduce Defect Bound State Quasi Particle Interference (DBS-QPI) as a new method to determine the superconducting order parameter. Using a low-temperature scanning tunneling microscope, we image in-gap bound states in the stoichiometric iron-based superconductor LiFeAs and show that the bound states induced by defect scattering are formed from Bogoliubov quasiparticles that have significant spatial extent. Quasiparticle interference from these bound states has unique signatures from which one can determine the phase of the order parameter as well as the nature of the defect, i.e. whether it is better described as a magnetic vs a nonmagnetic scatterer. DBS-QPI provides an easy but general method to characterize the pairing symmetry of superconducting condensates.

Spins in gated semiconductor quantum dots (QDs) are a promising platform for Hubbard model simulation inaccessible to computation. Precise control of the tunnel couplings by tuning voltages on metallic gates is vital for a successful QD-based simulator. However, the number of tunable voltages and the complexity of the relationships between gate voltages and the parameters of the resulting Hubbard models quickly increase with the number of quantum dots. As a consequence, it is not known if and how a particular gate geometry yields a target Hubbard model. To solve this problem, we propose a hybrid machine-learning approach using a combination of support vector machines (SVMs) and Bayesian optimization (BO) to identify combinations of voltages that realize a desired Hubbard model. SVM constrains the space of voltages by rejecting voltage combinations producing potentials unsuitable for tight-binding (TB) approximation. The target voltage combinations are then identified by BO in the constrained subdomain. For large QD arrays, we propose a scalable efficient iterative procedure using our SVM-BO approach, which optimises voltage subsets and utilises a two-QD SVM model for large systems. Our results use experimental gate lithography images and accurate integrals calculated with linear combinations of harmonic orbitals to train the machine learning algorithms.

The spin 1/2 entropy of electrons trapped in a quantum dot has previously been measured with great accuracy, but the protocol used for that measurement is valid only within a restrictive set of conditions. Here, we demonstrate a novel entropy measurement protocol that is universal for arbitrary mesoscopic circuits and apply this new approach to measure the entropy of a quantum dot hybridized with a reservoir, where Kondo correlations dominate spin physics. The experimental results match closely to numerical renormalization group (NRG) calculations for small and intermediate coupling. For the largest couplings investigated in this work, NRG predicts a suppression of spin entropy at the charge transition due to the formation of a Kondo singlet, but that suppression is not observed in the experiment.

We formalize a rigorous connection between barren plateaus (BP) in variational quantum algorithms and exponential concentration of quantum kernels for machine learning. Our results imply that recently proposed strategies to build BP-free quantum circuits can be utilized to construct useful quantum kernels for machine learning. This is illustrated by a numerical example employing a provably BP-free quantum neural network to construct kernel matrices for classification datasets of increasing dimensionality without exponential concentration.

Resonant inelastic x-ray scattering (RIXS) has become an important tool for studying elementary excitations in correlated materials. Here, we present a systematic theoretical investigation of the Cu L-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving (NSC) and spin-conserving (SC) channels. The spectra are rich and host many exotic excitations. In the NSC-channel of the undoped case, we identify one-triplon and bound $\textit{triplet}$ two-triplon excitations in the strong-rung coupling limit, as well as confined spinons in the weak-rung coupling limit. In the doped case, we observe a quasiparticle excitation formed from a bound charge and spin-$\frac{1}{2}$ in the strong-rung coupling limit. In the SC-channel, we also identify several new features, including bound $\textit{singlet}$ two-triplon excitations and confined spinons in the undoped ladders in the strong- and weak-rung coupling limits, respectively. Conversely, in the doped case, the SC channel primarily probes both gapless and gapped charge excitations. Finally, we revisit the available data for the ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ in the context of our results.

By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state and a variational approach à la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagnetically interacting with each other, with strength $J$, and coupled to a common bath of bosonic oscillators, with strength $\alpha$. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for $J=0$ the critical value of $\alpha$ decreases asymptotically with $1/N$ by increasing $N$, for nonvanishing $J$ it turns out to be practically independent on $N$, allowing to identify a finite range of values of $\alpha$ where spin phase coherence is preserved also for large $N$. Then, by using matrix product state simulations, and the Mori formalism and the variational approach à la Feynman jointly, we unveil the features of the relaxation, that, in particular, exhibits a non monotonic dependence on the temperature reminiscent of the Kondo effect. For the observed quantum phase transition we also establish a criterion analogous to that of the metal-insulator transition in solids.

Affleck, Kennedy, Lieb, and Tasaki constructed a spin-1 model that is isotropic in spins and possesses a provable finite gap above the ground state more than three decades ago. They also constructed models in two dimensions. Their construction has impacted subsequent research that is still active. In this review article, we review some selected the progresses, such as magnetic ordering of the AKLT models, emerging phases under deforming the AKLT Hamiltonians, symmetry-protected topological order in several AKLT models, their spectral gap, and applications for quantum computation.

Parametric converters are parametric amplifiers that mix two spatially separate nondegenerate modes and are commonly used for amplifying and squeezing microwave signals in quantum computing and sensing. In Josephson parametric converters, the strong localized nonlinearity of the Josephson Junction limits the amplification and squeezing, as well as the dynamic range, in current devices. In contrast, a weak distributed nonlinearity can provide higher gain and dynamic range, when implemented as a kinetic inductance (KI) nanowire of a dirty superconductor, and has additional benefits such as resilience to magnetic field, higher-temperature operation, and simplified fabrication. Here, we propose, demonstrate, and analyze the performance of a KI parametric converter that relies on the weak distributed nonlinearity of a KI nanowire. The device utilizes three-wave mixing induced by a DC current bias. We demonstrate its operation as a nondegenerate parametric amplifier with high phase-sensitive gain, reaching two-mode amplification and deamplification of $\sim$30 dB for two resonances separated by 0.8 GHz, in excellent agreement with our theory of the device. We observe a dynamic range of -108~dBm at 30 dB gain. Our device can significantly broaden applications of quantum-limited signal processing devices including phase-preserving amplification and two-mode squeezing.

Affleck, Kennedy, Lieb, and Tasaki constructed a spin-1 model that is isotropic in spins and possesses a provable finite gap above the ground state more than three decades ago. They also constructed models in two dimensions. Their construction has impacted subsequent research that is still active. In this review article, we review some selected the progresses, such as magnetic ordering of the AKLT models, emerging phases under deforming the AKLT Hamiltonians, symmetry-protected topological order in several AKLT models, their spectral gap, and applications for quantum computation.

Impurity bound states and quasi-particle scattering from these can serve as sensitive probes for identifying the pairing state of a superconducting condensate. We introduce and discuss defect bound state quasi-particle interference (DBS-QPI) imaging as a tool to extract information about the symmetry of the order parameter from spatial maps of the density of states around magnetic and non-magnetic impurities. We show that the phase information contained in the scattering patterns around impurities can provide valuable information beyond what is obtained through conventional QPI imaging. Keeping track of phase, rather than just magnitudes, in the Fourier transforms is achieved through phase-referenced Fourier transforms that preserve both real and imaginary parts of the QPI images. We further compare DBS-QPI to other approaches which have been proposed to use either QPI or defect scattering to distinguish different symmetries of the order parameter.

We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation with magic states, the size of this state space only depends on the number of magic states used in the quantum computation, and not on the length of the gate and measurement sequence.

We describe a joint cohomological framework for measurement-based quantum computation (MBQC) and the corresponding contextuality proofs. The central object in this framework is an element in the second cohomology group of the chain complex describing a given MBQC. It contains the function computed, up to gauge equivalence, and at the same time is a contextuality witness. The present cohomological description only applies to temporally flat MBQCs, and we outline an approach for extending it to the temporally ordered case.

Electrochemical CO2 reduction offers a method to use renewable electricity to convert CO2 into CO and other carbon-based chemical building blocks. While nearly all studies rely on a CO2 feed, we show herein that aqueous bicarbonate solutions can also be electrochemically converted into CO gas at meaningful rates in a flow cell. We achieved this result in a flow cell containing a bipolar membrane (BPM) and a silver nanoparticle catalyst on a porous carbon support. Electrolysis upon a N2-saturated 3.0-M potassium bicarbonate electrolyte solution yields CO with a faradaic efficiency (this http URL) of 81% at 25 mA cm-2 and 37% at 100 mA cm-2. This output is comparable to the analogous experiment where the electrolyte is saturated with gaseous CO2 (faradaic efficiency for CO is 78% at 25 mA cm-2 and 35% at 100 mA cm-2). The H+ flux from the BPM is critical to this chemistry in that it reacts with the bicarbonate feed to generate CO2, which is then reduced to CO at the gas diffusion electrode. These results are important in that they show that the addition of gaseous CO2 to bicarbonate electrolytes is not necessary in order to obtain reduced carbon products with a flow cell architecture. This process offers a means of using electrolysis to bypass the thermally-intensive step of extracting CO2 from bicarbonate solutions generated in carbon capture schemes.

A microwave-optical photon converter with high efficiency ($>50$ %) and low added noise ($\ll 1$ photon) could enable the creation of scalable quantum networks where quantum information is distributed optically and processed in the microwave regime. However, integrated converters demonstrated to date lack sufficient co-operativity or are too lossy to provide the required performance. Here we propose a bi-directional microwave-optical converter employing an ensemble of spin-bearing color centers hosted within a high-Q Si photonic resonator and coupled magnetically to a high-Q superconducting microwave resonator. We develop a theory for microwave-optical conversion when the ensemble of centers is strongly hybridized with one or both cavities, and find a counterintuitive operating point where microwave and optical photons are tuned to bare center/cavity resonances. Compared to the perturbative coupling regime, we find a substantially enhanced nonlinearity, making it possible to obtain the required co-operativity with reduced pump- and center-induced losses, and improved robustness to optical inhomogeneous broadening. Taking color center and optical pump-induced losses into account in both the Si photonic and superconducting resonators, we find that $\sim 95$ % total efficiency and added noise $\ll 1$ quanta is possible at low ($\mu$W) pump powers for both Er- and T-centers in Si. Our results open new pathways towards quantum networks using microwave-optical converters.

In this work, we generalize the algebraic framework for measurement-based quantum computation (MBQC) in one-dimensional symmetry protected topological states recently developed in [Quantum 7, 1215 (2023)], such that in addition to half-odd-integer spins, the integer spin chains can also be incorporated in the framework. The computational order parameter characterizing the efficiency of MBQC is identified, which, for spin-$1$ chains in the Haldane phase, coincides with the conventional string order parameter in condensed matter physics.