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Randomised measurements can efficiently characterise many-body quantum states by learning the expectation values of observables with low Pauli weights. In this paper, we generalise the theoretical tools of classical shadow tomography to the temporal domain to explore multi-time phenomena. This enables us to efficiently learn the features of multi-time processes such as correlated error rates, multi-time non-Markovianity, and temporal entanglement. We test the efficacy of these tools on a noisy quantum processor to characterise its noise features. Implementing these tools requires mid-circuit instruments, typically slow or unavailable in current quantum hardware. We devise a protocol to achieve fast and reliable instruments such that these multi-time distributions can be learned to a high accuracy. This enables a compact matrix product operator representation of large processes allowing us to showcase a reconstructed 20-step process (whose naive dimensionality is that of a 42-qubit state). Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of noisy intermediate-scale quantum devices., Comment: 26 pages, 7 figures; split off and expanded from earlier version of arXiv:2107.13934

We scheme an efficient and reusable approach to quantum teleportation that allows cyclic teleportation of a two-qubit graph state around a quantum hamster wheel -- a ring of qubits entangled as a one-dimensional line prepared on the 20-qubit Quantinuum H1-1 ion-trap quantum processor. The qubits on the ring are periodically measured and reused to achieve a teleportation depth that exceeds the total number of available qubits in the quantum processor. Using the outcomes measured during teleportation, we calculate and apply byproduct operators through dynamic circuits to correct local transformations induced on the teleported state. We evaluate the quality of teleportation by tracing the preserved entanglement and fidelity of the teleported two-qubit graph state from its density matrix. In the real-machine experiments, we demonstrate that 58% of the entanglement of the teleported state is sustained with a measured two-qubit negativity of $0.291\pm0.018$ after three complete revolutions around the hamster wheel, or equivalently, after hopping across 56 qubits. By performing teleportation along a regenerating graph state, our work is a step forward in demonstrating the feasibility of measurement-based quantum computation., Comment: 6 pages, 3 figures

Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of quantum neural networks becomes a key challenge in integrating quantum computing into AI. To provide a more fine-grained characterisation of the impact of quantum components on the performance of neural networks, we propose a framework where classical neural network layers are gradually replaced by quantum layers that have the same type of input and output while keeping the flow of information between layers unchanged, different from most current research in quantum neural network, which favours an end-to-end quantum model. We start with a simple three-layer classical neural network without any normalisation layers or activation functions, and gradually change the classical layers to the corresponding quantum versions. We conduct numerical experiments on image classification datasets such as the MNIST, FashionMNIST and CIFAR-10 datasets to demonstrate the change of performance brought by the systematic introduction of quantum components. Through this framework, our research sheds new light on the design of future quantum neural network models where it could be more favourable to search for methods and frameworks that harness the advantages from both the classical and quantum worlds., Comment: 50 pages (including Appendix), many figures, accepted as a poster on QTML2024. Code available at https://github.com/peiyong-addwater/Let-The-Quantum-Creep-In

When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the ``quantisation" of classical learning algorithms, such as using quantum linear algebra to implement important subroutines of classical algorithms, if not the entire algorithm, seeking to achieve quantum advantage through possible run-time accelerations brought by quantum computing. However, recent research has started questioning whether quantum advantage via speedup is the right goal for quantum machine learning [1]. Research also has been undertaken to exploit properties that are unique to quantum systems, such as quantum contextuality, to better design quantum machine learning models [2]. In this paper, we take an alternative approach by incorporating the heuristics and empirical evidences from the design of classical deep learning algorithms to the design of quantum neural networks. We first construct a model based on the data reuploading circuit [3] with the quantum Hamiltonian data embedding unitary [4]. Through numerical experiments on images datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN)[5] by a large margin (up to over 40% on MNIST test set). Based on the model design process and numerical results, we then laid out six principles for designing quantum machine learning models, especially quantum neural networks., Comment: 11 figures, 31 pages. Code available on https://github.com/peiyong-addwater/HamEmbedding. Author affiliation updated for v2. Acknowledgements and funding information added for v2

Quantum teleportation is not merely a fascinating corollary of quantum entanglement, it also finds utility in quantum processing and circuit compilation. In this paper, we measure and track the entanglement and fidelity of two-qubit states prepared on a 127-qubit IBM Quantum device, as one of the qubits is teleported across 19 qubits. We design, evaluate and compare two distinct approaches to teleportation: post-selected measurement categorisation and dynamic circuit corrections based on mid-circuit measurements, and compare with direct state transportation using SWAP gates. By optimally choosing the teleportation path which exhibits the highest total negativity entanglement measure across nearest-neighbour pairs, we show the entanglement of a two-qubit graph state is sustained after at least 19 hops in teleportation using the post-selection approach and 17 hops using the dynamic circuit approach. We observe a higher level of teleported entanglement in paths determined from two-qubit negativities compared to those obtained from gate errors, demonstrating an advantage in using the negativity map over the gate error map for compiling quantum circuits.

We introduce several probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning by leveraging the Linear Combination of Unitaries (LCU) method. Among our investigations are quantum native implementations of Residual Networks (ResNet), where we show that residual connections between layers of a variational ansatz can prevent barren plateaus in models which would otherwise contain them. Secondly, we implement a quantum analogue of average pooling layers from convolutional networks using single qubit controlled basic arithmetic operators and show that the LCU success probability remains stable for the MNIST database. This method can be further generalised to convolutional filters, while using exponentially fewer controlled unitaries than previous approaches. Finally, we propose a general framework for applying a linear combination of irreducible subspace projections on quantum encoded data. This enables a quantum state to remain within an exponentially large space, while selectively amplifying specific subspaces relative to others, alleviating simulability concerns that arise when fully projecting to a polynomially sized subspace. We demonstrate improved classification performance for partially amplified permutation invariant encoded point cloud data when compared to non-invariant or fully permutation invariant encodings. We also demonstrate a novel rotationally invariant encoding for point cloud data via Schur-Weyl duality. These quantum computing frameworks are all constructed using the LCU method, suggesting that further novel quantum machine learning algorithms could be created by utilising the LCU technique., Comment: 43 pages, 23 figures

As quantum technology advances and the size of quantum computers grow, it becomes increasingly important to understand the extent of quality in the devices. As large-scale entanglement is a quantum resource crucial for achieving quantum advantage, the challenge in its generation makes it a valuable benchmark for measuring the performance of universal quantum devices. In this work, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and graph states prepared on the range of IBM Quantum devices. We generate GHZ states and investigate their coherence times with respect to state size and dynamical decoupling techniques. A GHZ fidelity of $0.519 \pm 0.014$ is measured on a 32-qubit GHZ state, certifying its genuine multipartite entanglement (GME). We show a substantial improvement in GHZ decoherence rates for a 7-qubit GHZ state after implementing dynamical decoupling, and observe a linear trend in the decoherence rate of $\alpha=(7.13N+5.54)10^{-3}\mu s^{-1}$ for up to $N=15$ qubits, confirming the absence of superdecoherence. Additionally, we prepare and characterize fully bipartite entangled native graph states on 22 superconducting quantum devices with qubit counts as high as 414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of the decay of 2-qubit entanglement within the prepared states shows suppression of coherent noise signals with the implementation of dynamical decoupling techniques. Additionally, we observe that the entanglement in some qubit pairs oscillates over time, which is likely caused by residual ZZ-interactions. Characterizing entanglement in native graph states, along with detecting entanglement oscillations, can be an effective approach to low-level device benchmarking that encapsulates 2-qubit error rates along with additional sources of noise, with possible applications to quantum circuit compilation., Comment: 25 pages, 21 figures

The determination of ground state properties of quantum systems is a fundamental problem in physics and chemistry, and is considered a key application of quantum computers. A common approach is to prepare a trial ground state on the quantum computer and measure observables such as energy, but this is often limited by hardware constraints that prevent an accurate description of the target ground state. The quantum computed moments (QCM) method has proven to be remarkably useful in estimating the ground state energy of a system by computing Hamiltonian moments with respect to a suboptimal or noisy trial state. In this paper, we extend the QCM method to estimate arbitrary ground state observables of quantum systems. We present preliminary results of using QCM to determine the ground state magnetisation and spin-spin correlations of the Heisenberg model in its various forms. Our findings validate the well-established advantage of QCM over existing methods in handling suboptimal trial states and noise, extend its applicability to the estimation of more general ground state properties, and demonstrate its practical potential for solving a wide range of problems on near-term quantum hardware., Comment: 5 pages, 2 figures. Accepted paper at the 2023 IEEE International Conference on Quantum Computing and Engineering (QCE23)

The data encoding circuits used in quantum support vector machine (QSVM) kernels play a crucial role in their classification accuracy. However, manually designing these circuits poses significant challenges in terms of time and performance. To address this, we leverage the GASP (Genetic Algorithm for State Preparation) framework for gate sequence selection in QSVM kernel circuits. We explore supervised and unsupervised kernel loss functions' impact on encoding circuit optimisation and evaluate them on diverse datasets for binary and multiple-class scenarios. Benchmarking against classical and quantum kernels reveals GA-generated circuits matching or surpassing standard techniques. We analyse the relationship between test accuracy and quantum kernel entropy, with results indicating a positive correlation. Our automated framework reduces trial and error, and enables improved QSVM based machine learning performance for finance, healthcare, and materials science applications.

The accurate computation of properties of large molecular systems is classically infeasible and is one of the applications in which it is hoped that quantum computers will demonstrate an advantage over classical devices. However, due to the limitations of present-day quantum hardware, variational-hybrid algorithms introduced to tackle these problems struggle to meet the accuracy and precision requirements of chemical applications. Here, we apply the Quantum Computed Moments (QCM) approach combined with a variety of noise-mitigation techniques to an 8 qubit/spin-orbital representation of the water molecule (H$_2$O). A noise-stable improvement on the variational result for a 4-excitation trial-state (circuit depth 25, 22 CNOTs) was obtained, with the ground-state energy computed to be within $1.4\pm1.2$ mHa of exact diagonalisation in the 14 spin-orbital basis. Thus, the QCM approach, despite an increased number of measurements and noisy quantum hardware (CNOT error rates c.1% corresponding to expected error rates on the trial-state circuit of order 20%), is able to determine the ground-state energy of a non-trivial molecular system at the required accuracy (c.0.1%). To the best of our knowledge, these results are the largest calculations performed on a physical quantum computer to date in terms of encoding individual spin-orbitals producing chemically relevant accuracy, and a promising indicator of how such hybrid approaches might scale to problems of interest in the low-error/fault-tolerant regimes as quantum computers develop., Comment: 20 pages, 8 figures (incl. SI)

With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have assessed the performance of IBM superconducting quantum computer devices implementing heavy-hexagon code syndrome measurements with increasing circuit sizes up to 23 qubits, against the error assumptions underpinning code threshold calculations. Circuit operator change rate statistics in the presence of depolarizing and biased noise were modelled using analytic functions of error model parameters. Data from 16 repeated syndrome measurement cycles was found to be inconsistent with a uniform depolarizing noise model, favouring instead biased and inhomogeneous noise models. Spatial-temporal correlations investigated via $Z$ stabilizer measurements revealed significant temporal correlation in detection events. These results highlight the non-trivial structure which may be present in the noise of quantum error correction circuits, revealed by operator measurement statistics, and support the development of noise-tailored codes and decoders to adapt.

One of the fundamental tasks in information theory is the compression of information. To achieve this in the quantum domain, quantum autoencoders that aim to compress quantum states to low-dimensional ones have been proposed. When taking a pure state as the reference state, there exists an upper bound for the encoding fidelity. This bound limits the compression rate for high-rank states that have high entropy. To overcome the entropy inconsistency between the initial states and the reconstructed states, we allow the reference state to be a mixed state. A new cost function that combines the encoding fidelity and the quantum mutual information is proposed for compressing general input states. In particular, we consider the reference states to be a mixture of maximally mixed states and pure states. To achieve efficient compression for different states, two strategies for setting the ratio of mixedness (in the mixture of maximally mixed states and pure states) are provided based on prior knowledge about quantum states or observations obtained from the training process. Numerical results on thermal states of the transverse-field Ising model, Werner states, and maximally mixed states blended with pure states illustrate the effectiveness of the proposed method. In addition, quantum autoencoders using mixed reference states are experimentally implemented on IBM Quantum devices to compress and reconstruct thermal states and Werner states.

Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver quantum advantage, but its realisation for practical applications remains impeded by challenges. Amongst those, a key barrier is the computationally expensive task of encoding classical data into a quantum state, which could erase any prospective speed-ups over classical algorithms. In this work, we implement methods for the efficient preparation of quantum states representing encoded image data using variational, genetic and matrix product state based algorithms. Our results show that these methods can approximately prepare states to a level suitable for QML using circuits two orders of magnitude shallower than a standard state preparation implementation, obtaining drastic savings in circuit depth and gate count without unduly sacrificing classification accuracy. Additionally, the QML models trained and evaluated on approximately encoded data display an increased robustness to adversarially generated input data perturbations. This partial alleviation of adversarial vulnerability, possible due to the "drowning out" of adversarial perturbations while retaining the meaningful large-scale features of the data, constitutes a considerable benefit for approximate state preparation in addition to lessening the requirements of the quantum hardware. Our results, based on simulations and experiments on IBM quantum devices, highlight a promising pathway for the future implementation of accurate and robust QML models on complex datasets relevant for practical applications, bringing the possibility of NISQ-era QML advantage closer to reality., Comment: 14 pages, 8 figures

Magnetic van der Waals materials are often proposed for use in future spintronic devices, aiming to leverage the combination of long-range magnetic order and near-atomic thinness to produce energy-efficient components. One class of material that has been discussed in this context are the iron halides FeCl$_2$ and FeBr$_2$, which are A-type antiferromagnets with strong uniaxial magnetocrystalline anisotropy. However, despite characterization of the bulk materials, the possibility for sustaining the magnetic behaviors that would underpin such applications in thin flakes has not been investigated. In this work, we use nitrogen-vacancy (NV) center microscopy to quantitatively image magnetism in individual exfoliated flakes of these iron halides, revealing the absence of magnetic remanence, a weak induced magnetization under bias field and variable behavior versus temperature. We show that our results are consistent with the antiferromagnetic behavior of the bulk material with a soft ferromagnetic uncompensated layer, indicating that extended ($>1~\mu$m) ferromagnetic domains are not sustained even at low temperatures (down to 4 K). Finally, we find that the magnetic order is strongly affected by the sample preparation, with a surprising diamagnetic order observed in a thin, hydrated sample., Comment: 15 pages, 13 figures

Machine learning algorithms are powerful tools for data driven tasks such as image classification and feature detection, however their vulnerability to adversarial examples - input samples manipulated to fool the algorithm - remains a serious challenge. The integration of machine learning with quantum computing has the potential to yield tools offering not only better accuracy and computational efficiency, but also superior robustness against adversarial attacks. Indeed, recent work has employed quantum mechanical phenomena to defend against adversarial attacks, spurring the rapid development of the field of quantum adversarial machine learning (QAML) and potentially yielding a new source of quantum advantage. Despite promising early results, there remain challenges towards building robust real-world QAML tools. In this review we discuss recent progress in QAML and identify key challenges. We also suggest future research directions which could determine the route to practicality for QAML approaches as quantum computing hardware scales up and noise levels are reduced., Comment: 10 Pages, 4 Figures

Quantum Computing offers a potentially powerful new method for performing Machine Learning. However, several Quantum Machine Learning techniques have been shown to exhibit poor generalisation as the number of qubits increases. We address this issue by demonstrating a permutation invariant quantum encoding method, which exhibits superior generalisation performance, and apply it to point cloud data (three-dimensional images composed of points). Point clouds naturally contain permutation symmetry with respect to the ordering of their points, making them a natural candidate for this technique. Our method captures this symmetry in a quantum encoding that contains an equal quantum superposition of all permutations and is therefore invariant under point order permutation. We test this encoding method in numerical simulations using a Quantum Support Vector Machine to classify point clouds drawn from either spherical or toroidal geometries. We show that a permutation invariant encoding improves in accuracy as the number of points contained in the point cloud increases, while non-invariant quantum encodings decrease in accuracy. This demonstrates that by implementing permutation invariance into the encoding, the model exhibits improved generalisation., Comment: 10 pages, 9 figures

The efficient preparation of quantum states is an important step in the execution of many quantum algorithms. In the noisy intermediate-scale quantum (NISQ) computing era, this is a significant challenge given quantum resources are scarce and typically only low-depth quantum circuits can be implemented on physical devices. We present a genetic algorithm for state preparation (GASP) which generates relatively low-depth quantum circuits for initialising a quantum computer in a specified quantum state. The method uses a basis set of R_x, R_y, R_z, and CNOT gates and a genetic algorithm to systematically generate circuits to synthesize the target state to the required fidelity. GASP can produce more efficient circuits of a given accuracy with lower depth and gate counts than other methods. This variability of the required accuracy facilitates overall higher accuracy on implementation, as error accumulation in high-depth circuits can be avoided. We directly compare the method to the state initialisation technique based on an exact synthesis technique by implemented in IBM Qiskit simulated with noise and implemented on physical IBM Quantum devices. Results achieved by GASP outperform Qiskit's exact general circuit synthesis method on a variety of states such as Gaussian states and W-states, and consistently show the method reduces the number of gates required for the quantum circuits to generate these quantum states to the required accuracy.

Machine learning (ML) methods such as artificial neural networks are rapidly becoming ubiquitous in modern science, technology and industry. Despite their accuracy and sophistication, neural networks can be easily fooled by carefully designed malicious inputs known as adversarial attacks. While such vulnerabilities remain a serious challenge for classical neural networks, the extent of their existence is not fully understood in the quantum ML setting. In this work, we benchmark the robustness of quantum ML networks, such as quantum variational classifiers (QVC), at scale by performing rigorous training for both simple and complex image datasets and through a variety of high-end adversarial attacks. Our results show that QVCs offer a notably enhanced robustness against classical adversarial attacks by learning features which are not detected by the classical neural networks, indicating a possible quantum advantage for ML tasks. Contrarily, and remarkably, the converse is not true, with attacks on quantum networks also capable of deceiving classical neural networks. By combining quantum and classical network outcomes, we propose a novel adversarial attack detection technology. Traditionally quantum advantage in ML systems has been sought through increased accuracy or algorithmic speed-up, but our work has revealed the potential for a new kind of quantum advantage through superior robustness of ML models, whose practical realisation will address serious security concerns and reliability issues of ML algorithms employed in a myriad of applications including autonomous vehicles, cybersecurity, and surveillance robotic systems., Comment: 10 pages, 5 Figures

In the lead up to fault tolerance, the utility of quantum computing will be determined by how adequately the effects of noise can be circumvented in quantum algorithms. Hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) have been designed for the short-term regime. However, as problems scale, VQE results are generally scrambled by noise on present-day hardware. While error mitigation techniques alleviate these issues to some extent, there is a pressing need to develop algorithmic approaches with higher robustness to noise. Here, we explore the robustness properties of the recently introduced quantum computed moments (QCM) approach to ground state energy problems, and show through an analytic example how the underlying energy estimate explicitly filters out incoherent noise. Motivated by this observation, we implement QCM for a model of quantum magnetism on IBM Quantum hardware to examine the noise-filtering effect with increasing circuit depth. We find that QCM maintains a remarkably high degree of error robustness where VQE completely fails. On instances of the quantum magnetism model up to 20 qubits for ultra-deep trial state circuits of up to ~500 CNOTs, QCM is still able to extract reasonable energy estimates. The observation is bolstered by an extensive set of experimental results. To match these results, VQE would need hardware improvement by some 2 orders of magnitude on error rates., Comment: 14 pages, 4 figures

Dense, near-surface (within 10 nm) ensembles of nitrogen-vacancy (NV) centres in diamond are rapidly moving into prominence as the workhorse of a variety of envisaged applications, ranging from the imaging of fast-fluctuating magnetic signals to the facilitation of nuclear hyperpolarisation. Unlike their bulk counterparts, near-surface ensembles suffer from charge stability issues and reduced NV formation efficiency due to the diamond surface's role as a vacancy sink during annealing and an electron sink afterwards. To this end, work is ongoing to determine the best methods for producing high-quality ensembles in this regime. Here we examine the prospects for creating such ensembles cost-effectively by implanting nitrogen-rich type Ib diamond with electron donors, aiming to exploit the high bulk nitrogen density to combat surface-induced band bending in the process. This approach has previously been successful at creating deeper ensembles, however we find that in the near-surface regime there are fewer benefits over nitrogen implantation into pure diamond substrates. Our results suggest that control over diamond surface termination during annealing is key to successfully creating high-yield near-surface NV ensembles generally, and implantation into type Ib diamond may be worth revisiting once that has been accomplished., Comment: 7 pages, 3 figures

The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to attain expressional and computational advantage. In this work we extend the linear quantum support vector machine (QSVM) with kernel function computed through quantum kernel estimation (QKE), to form a decision tree classifier constructed from a decision directed acyclic graph of QSVM nodes - the ensemble of which we term the quantum random forest (QRF). To limit overfitting, we further extend the model to employ a low-rank Nystr\"{o}m approximation to the kernel matrix. We provide generalisation error bounds on the model and theoretical guarantees to limit errors due to finite sampling on the Nystr\"{o}m-QKE strategy. In doing so, we show that we can achieve lower sampling complexity when compared to QKE. We numerically illustrate the effect of varying model hyperparameters and finally demonstrate that the QRF is able obtain superior performance over QSVMs, while also requiring fewer kernel estimations., Comment: 33 pages, 11 figures

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability., Comment: 32 pages, 24 figures

Interest in van der Waals materials often stems from a desire to miniaturise existing technologies by exploiting their intrinsic layered structure to create near atomically-thin components that do not suffer from surface defects. One appealing property is easily-switchable yet robust magnetic order, a quality only sparsely demonstrated in the case of in-plane anisotropy. In this work, we use widefield nitrogen-vacancy (NV) center magnetic imaging to measure the properties of individual flakes of CuCrP$_2$S$_6$, a multiferroic van der Waals magnet known to exhibit weak easy-plane anisotropy in the bulk. We chart the crossover between in-plane ferromagnetism in thin flakes down to the trilayer, and the bulk behaviour dominated by a low-field spin-flop transition. Further, by exploiting the directional dependence of NV center magnetometry, we are able to observe an instance of a predominantly out-of-plane ferromagetic phase near zero field, in contradiction with expectation and previous experiments on the bulk material. We attribute this to the presence of surface anisotropies arising from the sample preparation process or exposure to the ambient environment, which is expected to have more general implications for a broader class of weakly anisotropic van der Waals magnets., Comment: 24 pages, 20 figures (including supplementary information)

Magnetic imaging with nitrogen-vacancy centers in diamond, also known as quantum diamond microscopy, has emerged as a useful technique for the spatial mapping of charge currents in solid-state devices. In this work, we investigate an application to photovoltaic (PV) devices, where the currents are induced by light. We develop a widefield nitrogen-vacancy microscope that allows independent stimulus and measurement of the PV device, and test our system on a range of prototype crystalline silicon PV devices. We first demonstrate micrometer-scale vector magnetic field imaging of custom PV devices illuminated by a focused laser spot, revealing the internal current paths in both short-circuit and open-circuit conditions. We then demonstrate time-resolved imaging of photocurrents in an interdigitated back-contact solar cell, detecting current build-up and subsequent decay near the illumination point with microsecond resolution. This work presents a versatile and accessible analysis platform that may find distinct application in research on emerging PV technologies., Comment: 14 pages, 9 figures

Quantum process tomography (QPT), where a quantum channel is reconstructed through the analysis of repeated quantum measurements, is an important tool for validating the operation of a quantum processor. We detail the combined use of an existing QPT approach based on tensor networks (TNs) and unsupervised learning with TN contraction path finding algorithms in order to use TNs of arbitrary topologies for reconstruction. Experiments were conducted on the 7-qubit IBM Quantum Falcon Processor ibmq_casablanca, where we demonstrate this technique by matching the topology of the tensor networks used for reconstruction with the topology of the processor, allowing us to extend past the characterisation of linear nearest neighbour circuits. Furthermore, we conduct single-qubit gate set tomography (GST) on each individual qubit to correct for separable errors during the state preparation and measurement phases of QPT, which are separate from the channel under consideration but may negatively impact the quality of its reconstruction. We are able to report a fidelity of 0.89 against the ideal unitary channel of a single-cycle random quantum circuit performed on ibmq_casablanca, after obtaining just $1.1 \times 10^5$ measurements for the reconstruction of this 7-qubit process. This represents more than five orders of magnitude fewer total measurements than the number needed to conduct full, traditional QPT on a 7-qubit process., Comment: 8 pages, 7 figures