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We present a quantum algorithm for portfolio optimisation. Specifically, We present an end-to-end quantum approximate optimisation algorithm (QAOA) to solve the discrete global minimum variance portfolio (DGMVP) model. This model finds a portfolio of risky assets with the lowest possible risk contingent on the number of traded assets being discrete. We provide a complete pipeline for this model and analyses its viability for noisy intermediate-scale quantum computers. We design initial states, a cost operator, and ans\"atze with hard mixing operators within a binary encoding. Further, we perform numerical simulations to analyse several optimisation routines, including layerwise optimisation, utilising COYBLA and dual annealing. Finally, we consider the impacts of thermal relaxation and stochastic measurement noise. We find dual annealing with a layerwise optimisation routine provides the most robust performance. We observe that realistic thermal relaxation noise levels preclude quantum advantage. However, stochastic measurement noise will dominate when hardware sufficiently improves. Within this regime, we numerically demonstrate a favourable scaling in the number of shots required to obtain the global minimum -- an indication of quantum advantage in portfolio optimisation., Comment: 35 pages, 23 figures

We present a detailed analysis of JWST/NIRSpec and NIRCam observations of ZF-UDS-7329, a massive, quiescent galaxy at redshift $z=3.2$, which has been put forward to challenge cosmology and galaxy formation physics. Our study extends previous works by focusing on the impact of different star formation history (SFH) priors, stellar libraries, metallicity, and initial mass function assumptions. Our results show that ZF-UDS-7329, with a formed stellar mass of $M_{\star} \approx 10^{11.4}~M_{\odot}$ and a specific star formation rate of $\mathrm{sSFR} \approx 0.03$ Gyr$^{-1}$, formed efficiently in the first billion years of the Universe. In agreement with previous work, we find that the spectrum is consistent with mass-weighted stellar ages of $1.3-1.8$ Gyr, depending on the SFH prior used. A physically motivated rising SFH prior makes the formation history of ZF-UDS-7329 compatible with stellar mass and star-formation rate estimates of high-redshift ($z>6$) galaxies. Using NIRCam imaging, we identify a colour gradient indicative of an old, quiescent bulge and a younger disc component, as expected from a complex formation history. The inferred SFH is consistent a high stellar fraction of $f_{\star}=M_{\star}/(f_b \cdot M_{\rm h}) \approx 100\%$ at $z=7-12$, implying an extremely high integrated star-formation efficiency. However, when considering cosmic variance and possible mergers as expected in over-dense environments - as traced by ZF-UDS-7329 - the stellar fractions could be reduced to $f_{\star} \approx 50\%$, which is more consistent with galaxy formation models and the stellar-to-halo mass relation at lower redshifts. We conclude that ZF-UDS-7329 forms extremely efficient in the early universe, but does not necessitate unseen galaxies at higher redshifts since the inferred SFR of ancestors are consistent with those seen in $z>6$ galaxies., Comment: 15 pages and 8 figures (+appendix), submitted to MNRAS

Medical image analysis tasks often focus on regions or structures located in a particular location within the patient's body. Often large parts of the image may not be of interest for the image analysis task. When using deep-learning based approaches, this causes an unnecessary increases the computational burden during inference and raises the chance of errors. In this paper, we introduce CTARR, a novel generic method for CT Anatomical Region Recognition. The method serves as a pre-processing step for any deep learning-based CT image analysis pipeline by automatically identifying the pre-defined anatomical region that is relevant for the follow-up task and removing the rest. It can be used in (i) image segmentation to prevent false positives in anatomically implausible regions and speeding up the inference, (ii) image classification to produce image crops that are consistent in their anatomical context, and (iii) image registration by serving as a fast pre-registration step. Our proposed method is based on atlas registration and provides a fast and robust way to crop any anatomical region encoded as one or multiple bounding box(es) from any unlabeled CT scan of the brain, chest, abdomen and/or pelvis. We demonstrate the utility and robustness of the proposed method in the context of medical image segmentation by evaluating it on six datasets of public segmentation challenges. The foreground voxels in the regions of interest are preserved in the vast majority of cases and tasks (97.45-100%) while taking only fractions of a seconds to compute (0.1-0.21s) on a deep learning workstation and greatly reducing the segmentation runtime (2.0-12.7x). Our code is available at https://github.com/ThomasBudd/ctarr.

Survival analysis is a branch of statistics used for modeling the time until a specific event occurs and is widely used in medicine, engineering, finance, and many other fields. When choosing survival models, there is typically a trade-off between performance and interpretability, where the highest performance is achieved by black-box models based on deep learning. This is a major problem in fields such as medicine where practitioners are reluctant to blindly trust black-box models to make important patient decisions. Kolmogorov-Arnold Networks (KANs) were recently proposed as an interpretable and accurate alternative to multi-layer perceptrons (MLPs). We introduce CoxKAN, a Cox proportional hazards Kolmogorov-Arnold Network for interpretable, high-performance survival analysis. We evaluate the proposed CoxKAN on 4 synthetic datasets and 9 real medical datasets. The synthetic experiments demonstrate that CoxKAN accurately recovers interpretable symbolic formulae for the hazard function, and effectively performs automatic feature selection. Evaluation on the 9 real datasets show that CoxKAN consistently outperforms the Cox proportional hazards model and achieves performance that is superior or comparable to that of tuned MLPs. Furthermore, we find that CoxKAN identifies complex interactions between predictor variables that would be extremely difficult to recognise using existing survival methods, and automatically finds symbolic formulae which uncover the precise effect of important biomarkers on patient risk.

High-harmonic generation (HHG) has recently emerged as a promising method for generating non-classical states of light with frequencies spanning from the infrared up to the extreme ultraviolet regime. In this work, we theoretically investigate the generation of squeezed states of light through HHG processes in atomic systems that had been initially driven to their first excited state. Our study reveals significant single-mode squeezing in both the driving field and low-order harmonic modes. Additionally, we characterize two-mode squeezing features in the generated states, both between fundamental and harmonic modes, and among the harmonic modes themselves. Using these correlations, we demonstrate the generation of optical Schr\"odinger kitten states through heralding measurements, specifically via photon subtraction in one of the modes influenced by two-mode squeezing., Comment: 17 pages (10 main text + 7 appendix), 6 figures (4 main text + 2 appendix). Comments are welcome

In this paper, we focus on the associated primes of powers of monomial ideals and asymptotic behavior properties such as normally torsion-freeness, normality, the strong persistence property, and the persistence property. In particular, we introduce the concept of monomial ideals of well-nearly normally torsion-free type, and show that these ideals are normal. After that, we present some results on the existence of embedded associated prime ideals in the associated primes set of powers of monomial ideals. Further, we employ them in investigating the edge and cover ideals of cones of graphs. Next, we present counterexamples to several questions concerning the relations between relevant algebraic properties of the edge ideals of clutters and complement clutters. We conclude by providing counterexamples to questions on the possible connections between normally torsion-freeness and normality of monomial ideals under polarization., Comment: 20 pages, 3 figures, This paper will appear in "AMS Contemporary Mathematics"

High-grade serous ovarian carcinoma (HGSOC) is characterised by significant spatial and temporal heterogeneity, typically manifesting at an advanced metastatic stage. A major challenge in treating advanced HGSOC is effectively monitoring localised change in tumour burden across multiple sites during neoadjuvant chemotherapy (NACT) and predicting long-term pathological response and overall patient survival. In this work, we propose a self-supervised deformable image registration algorithm that utilises a general-purpose image encoder for image feature extraction to co-register contrast-enhanced computerised tomography scan images acquired before and after neoadjuvant chemotherapy. This approach addresses challenges posed by highly complex tumour deformations and longitudinal lesion matching during treatment. Localised tumour changes are calculated using the Jacobian determinant maps of the registration deformation at multiple disease sites and their macroscopic areas, including hypo-dense (i.e., cystic/necrotic), hyper-dense (i.e., calcified), and intermediate density (i.e., soft tissue) portions. A series of experiments is conducted to understand the role of a general-purpose image encoder and its application in quantifying change in tumour burden during neoadjuvant chemotherapy in HGSOC. This work is the first to demonstrate the feasibility of a self-supervised image registration approach in quantifying NACT-induced localised tumour changes across the whole disease burden of patients with complex multi-site HGSOC, which could be used as a potential marker for ovarian cancer patient's long-term pathological response and survival.

Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon hardware. We investigate two state preparation tasks. First, we consider the preparation of molecular ground states and find the METs for H$_2$, HeH$^+$, and LiH to be 2.4 ns, 4.4 ns, and 27.2 ns, respectively. Second, we consider transitions between arbitrary states and find the METs for transitions between arbitrary four-qubit states to be below 50 ns. For comparison, connecting arbitrary two-qubit states via one- and two-qubit gates on the same silicon processor requires approximately 200 ns. This comparison indicates that pulse-based state preparation is likely to utilize the coherence times of silicon hardware more efficiently than gate-based state preparation. Finally, we quantify the effect of silicon device parameters on the MET. We show that increasing the maximal exchange amplitude from 10 MHz to 1 GHz accelerates the METs, e.g., for H$_2$ from 84.3 ns to 2.4 ns. This demonstrates the importance of fast exchange. We also show that increasing the maximal amplitude of the microwave drive from 884 kHz to 56.6 MHz shortens state transitions, e.g., for two-qubit states from 1000 ns to 25 ns. Our results bound both the state-preparation times for general quantum algorithms and the execution times of variational quantum algorithms with silicon spin qubits., Comment: 9 + (7) pages, 6 figs, comments are welcomed

This study introduces an automated pipeline for renal cancer (RC) detection in non-contrast computed tomography (NCCT). In the development of our pipeline, we test three detections models: a shape model, a 2D-, and a 3D axial-sample model. Training (n=1348) and testing (n=64) data were gathered from open sources (KiTS23, Abdomen1k, CT-ORG) and Cambridge University Hospital (CUH). Results from cross-validation and testing revealed that the 2D axial sample model had the highest small ($\leq$40mm diameter) RC detection area under the curve (AUC) of 0.804. Our pipeline achieves 61.9\% sensitivity and 92.7\% specificity for small kidney cancers on unseen test data. Our results are much more accurate than previous attempts to automatically detect small renal cancers in NCCT, the most likely imaging modality for RC screening. This pipeline offers a promising advance that may enable screening for kidney cancers.

Let $I\subset R=K[x_1, \ldots, x_n]$ be a square-free monomial ideal, $\mathfrak{q}$ be a prime monomial ideal in $R$, $h$ be a square-free monomial in $R$ with $\mathrm{supp}(h) \cap (\mathrm{supp}(\mathfrak{q}) \cup \mathrm{supp}(I))=\emptyset$, and $L:=I\cap (\mathfrak{q}, h)$. In this paper, we first focus on the associated primes of powers of $L$ and explore the normally torsion-freeness of $L$. We also give an application on a comb inatorial result. Next, we study when a square-free monomial ideal is minimally not normally torsion-free. Particularly, we introduce a class of square-free monomial ideals, which are minimally not normally torsion-free., Comment: This paper will appear in "Journal of Algebra and its Applications" (accepted)

We study how to use the surface states in a Bi$_{2}$Se$_{3}$ topological insulator ultra-thin film that are affected by finite size effects for the purpose of quantum computing. We demonstrate that: (i) surface states under the finite size effect can effectively form a two-level system where their energy levels lie in between the bulk energy gap and a logic qubit can be constructed, (ii) the qubit can be initialized and manipulated using electric pulses of simple forms, (iii) two-qubit entanglement is achieved through a $\sqrt{\text{SWAP}}$ operation when the two qubits are in a parallel setup, and (iv) alternatively, a Floquet state can be exploited to construct a qubit and two Floquet qubits can be entangled through a Controlled-NOT operation. The Floquet qubit offers robustness to background noise since there is always an oscillating electric field applied, and the single qubit operations are controlled by amplitude modulation of the oscillating field, which is convenient experimentally., Comment: 12 pages, 9 figures, submitted to the journal Frontiers of Physics

Adaptive variational quantum eigensolvers (ADAPT-VQEs) are promising candidates for simulations of strongly correlated systems on near-term quantum hardware. To further improve the noise resilience of these algorithms, recent efforts have been directed towards compactifying, or layering, their ansatz circuits. Here, we broaden the understanding of the algorithmic layering process in three ways. First, we investigate the non-commutation relations between the different elements that are used to build ADAPT-VQE ans\"atze. Doing so, we develop a framework for studying and developing layering algorithms, which produce shallower circuits. Second, based on this framework, we develop a new subroutine that can reduce the number of quantum-processor calls by optimizing the selection procedure with which a variational quantum algorithm appends ansatz elements. Third, we provide a thorough numerical investigation of the noise-resilience improvement available via layering the circuits of ADAPT-VQE algorithms. We find that layering leads to an improved noise resilience with respect to amplitude-damping and dephasing noise, which, in general, affect idling and non-idling qubits alike. With respect to depolarizing noise, which tends to affect only actively manipulated qubits, we observe no advantage of layering., Comment: 19 + (21) pages, 16 + (4) figs, comments are welcomed

In quantum metrology, information about unknown parameters $\mathbf{\theta} = (\theta_1,\ldots,\theta_M)$ is accessed by measuring probe states $\hat{\rho}_{\mathbf{\theta}}$. In experimental settings where copies of $\hat{\rho}_{\mathbf{\theta}}$ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high post-processing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in $\hat{\rho}_{\mathbf{\theta}} \, ^{\otimes n}$ into $m

High-quality cavities are crucial for various fundamental physical studies and applications. Here we find that by coupling two cavities directly or via a phase-tunable coupling channel, the photon lifetime of the local field can exceed that of the bare cavities. The cavity photon lifetime is modified by the phases of the initial states and the phase accumulation on the coupling channel which affect the interference between cavities. In experiments, by coupling superconducting radio-frequency cavities via phase-tunable cables, we realize a factor of two improvement in the cavity photon lifetime. The results can bring rich revenue to quantum information science, sensing, and high-energy physics., Comment: 6 pages, 4 figures

Modern particle accelerators and high-energy physics experiments that deployed up to several hundred of accelerating superconducting RF cavities require accurate frequency control. This is achieved by using cavity tuners typically actuated with the piezoelectric ceramic actuators. Piezoelectric ceramic actuators have become "standard" components of the SRF cavity tuner and depending on the application could be operated in different environments: in air, at cryogenic temperature, in vacuum, and submerged in liquid helium. Different applications place different requirements on the piezo actuators, but the important parameters common to all applications are the lifetime and reliability of the actuators. Several programs targeting the development of reliable piezo actuators are presented in this contribution., Comment: euspen's 23rd International Conference & Exhibition, Copenhagen, DK, June 2023

We present a numerically-optimized multipulse framework for the quantum control of a single-electron charge qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates., Comment: 9 pages, 9 figures

Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or entanglement to sample the unitary $N_{\mathrm{tot}}$ times, the variance of the estimates can scale as $O(1/{N^2_{\mathrm{tot}}})$, compared to the best ``classical'' strategy with $O(1/{N_{\mathrm{tot}}})$. The original algorithm for quantum phase estimation cannot be implemented on near-term hardware as it requires large-scale entangled probes and fault-tolerant quantum computing. Therefore, alternative algorithms have been introduced that rely on coherence and statistical inference. These algorithms produce quantum-boosted phase estimates without inter-probe entanglement. This family of phase-estimation algorithms have, until now, never exhibited the possibility of achieving optimal scaling $O(1/{N^2_{\mathrm{tot}}})$. Moreover, previous works have not considered the effect of noise on these algorithms. Here, we present a coherence-based phase-estimation algorithm which can achieve the optimal quadratic scaling in the mean absolute error and the mean squared error. In the presence of noise, our algorithm produces errors that approach the theoretical lower bound. The optimality of our algorithm stems from its adaptive nature: Each step is determined, iteratively, using a Bayesian protocol that analyses the results of previous steps.