Contextuality and inductive bias in quantum machine learning

Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the types of data structures that lend themselves naturally to quantum models. In this work we look to quantum contextuality -- a form of nonclassicality with links to computational advantage -- for answers to this question. We introduce a framework for studying contextuality in machine learning, which leads us to a definition of what it means for a learning model to be contextual. From this, we connect a central concept of contextuality, called operational equivalence, to the ability of a model to encode a linearly conserved quantity in its label space. A consequence of this connection is that contextuality is tied to expressivity: contextual model classes that encode the inductive bias are generally more expressive than their noncontextual counterparts. To demonstrate this, we construct an explicit toy learning problem -- based on learning the payoff behaviour of a zero-sum game -- for which this is the case. By leveraging tools from geometric quantum machine learning, we then describe how to construct quantum learning models with the associated inductive bias, and show through our toy problem that they outperform their corresponding classical surrogate models. This suggests that understanding learning problems of this form may lead to useful insights about the power of quantum machine learning.Comment: comments welcom

The influence of entrepreneurial bricolage and design thinking on opportunity development

Background: Entrepreneurial activity in an efficiency-driven economy is fundamental to economic growth, yet its sustainability and opportunities are concerning. Both entrepreneurial bricolage and design thinking could enhance opportunity development, but their effectiveness and incorporation into an integrated approach to opportunity advancement require further investigation. Aim: This study explores design thinking and entrepreneurial bricolage as facilitating constructs for entrepreneurial opportunity development, employing the design-centred entrepreneurship perspective and the conceptual framework offered by various authors; it investigates the effectiveness of the theoretical frameworks mentioned; and lastly it explores the potential of amalgamating these frameworks into a more comprehensive structure for entrepreneurial opportunity development. Setting: The sample consisted of entrepreneurs in South Africa. Methods: Fourteen semi-structured interviews with founders of small and medium entrepreneurial ventures in various South African industry sectors were conducted. Results: Current frameworks pertaining to bricolage and design thinking proficiencies were appropriate for opportunity development and could be effectively integrated. However, some contributory factors should be included, such as organisational culture, business partners and a non-linear rather than a methodical approach. Conclusion: Entrepreneurial bricolage has a significant influence on developing and establishing opportunities. The value of design thinking was confirmed with a specific focus on a human-centred approach, creativity and innovation. However, contradictory to design thinking authors, entrepreneurs described the design thinking process as non-linear and disordered. Contribution: This study provides empirical evidence to enrich the understanding of the elusive entrepreneurial opportunity development process by integrating the design-centred entrepreneurship framework with the entrepreneurial bricolage perspective into a single, more comprehensive framework

Machine learning and the physical sciences

Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on the interface between machine learning and physical sciences. This includes conceptual developments in machine learning (ML) motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross-fertilization between the two fields. After giving basic notion of machine learning methods and principles, we describe examples of how statistical physics is used to understand methods in ML. We then move to describe applications of ML methods in particle physics and cosmology, quantum many body physics, quantum computing, and chemical and material physics. We also highlight research and development into novel computing architectures aimed at accelerating ML. In each of the sections we describe recent successes as well as domain-specific methodology and challenges

Convex optimization of programmable quantum computers

A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any finite-dimensional design of this model is known to be non-universal, meaning that the processor cannot perfectly simulate an arbitrary quantum channel over the input. Characterizing how close the simulation is and finding the optimal program state have been open questions for the past 20 years. Here, we answer these questions by showing that the search for the optimal program state is a convex optimization problem that can be solved via semi-definite programming and gradient-based methods commonly employed for machine learning. We apply this general result to different types of processors, from a shallow design based on quantum teleportation, to deeper schemes relying on port-based teleportation and parametric quantum circuits

The Born supremacy: quantum advantage and training of an Ising Born machine

The search for an application of near-term quantum devices is widespread. Quantum Machine Learning is touted as a potential utilisation of such devices, particularly those which are out of the reach of the simulation capabilities of classical computers. In this work, we propose a generative Quantum Machine Learning Model, called the Ising Born Machine (IBM), which we show cannot, in the worst case, and up to suitable notions of error, be simulated efficiently by a classical device. We also show this holds for all the circuit families encountered during training. In particular, we explore quantum circuit learning using non-universal circuits derived from Ising Model Hamiltonians, which are implementable on near term quantum devices. We propose two novel training methods for the IBM by utilising the Stein Discrepancy and the Sinkhorn Divergence cost functions. We show numerically, both using a simulator within Rigetti's Forest platform and on the Aspen-1 16Q chip, that the cost functions we suggest outperform the more commonly used Maximum Mean Discrepancy (MMD) for differentiable training. We also propose an improvement to the MMD by proposing a novel utilisation of quantum kernels which we demonstrate provides improvements over its classical counterpart. We discuss the potential of these methods to learn `hard' quantum distributions, a feat which would demonstrate the advantage of quantum over classical computers, and provide the first formal definitions for what we call `Quantum Learning Supremacy'. Finally, we propose a novel view on the area of quantum circuit compilation by using the IBM to `mimic' target quantum circuits using classical output data only.Comment: v3 : Close to journal published version - significant text structure change, split into main text & appendices. See v2 for unsplit version; v2 : Typos corrected, figures altered slightly; v1 : 68 pages, 39 Figures. Comments welcome. Implementation at https://github.com/BrianCoyle/IsingBornMachin

Quantum circuits with many photons on a programmable nanophotonic chip

Growing interest in quantum computing for practical applications has led to a surge in the availability of programmable machines for executing quantum algorithms. Present day photonic quantum computers have been limited either to non-deterministic operation, low photon numbers and rates, or fixed random gate sequences. Here we introduce a full-stack hardware-software system for executing many-photon quantum circuits using integrated nanophotonics: a programmable chip, operating at room temperature and interfaced with a fully automated control system. It enables remote users to execute quantum algorithms requiring up to eight modes of strongly squeezed vacuum initialized as two-mode squeezed states in single temporal modes, a fully general and programmable four-mode interferometer, and genuine photon number-resolving readout on all outputs. Multi-photon detection events with photon numbers and rates exceeding any previous quantum optical demonstration on a programmable device are made possible by strong squeezing and high sampling rates. We verify the non-classicality of the device output, and use the platform to carry out proof-of-principle demonstrations of three quantum algorithms: Gaussian boson sampling, molecular vibronic spectra, and graph similarity

Solving a Higgs optimization problem with quantum annealing for machine learning

The discovery of Higgs-boson decays in a background of standard-model processes was assisted by machine learning methods. The classifiers used to separate signals such as these from background are trained using highly unerring but not completely perfect simulations of the physical processes involved, often resulting in incorrect labelling of background processes or signals (label noise) and systematic errors. Here we use quantum and classical annealing (probabilistic techniques for approximating the global maximum or minimum of a given function) to solve a Higgs-signal-versus-background machine learning optimization problem, mapped to a problem of finding the ground state of a corresponding Ising spin model. We build a set of weak classifiers based on the kinematic observables of the Higgs decay photons, which we then use to construct a strong classifier. This strong classifier is highly resilient against overtraining and against errors in the correlations of the physical observables in the training data. We show that the resulting quantum and classical annealing-based classifier systems perform comparably to the state-of-the-art machine learning methods that are currently used in particle physics. However, in contrast to these methods, the annealing-based classifiers are simple functions of directly interpretable experimental parameters with clear physical meaning. The annealer-trained classifiers use the excited states in the vicinity of the ground state and demonstrate some advantage over traditional machine learning methods for small training datasets. Given the relative simplicity of the algorithm and its robustness to error, this technique may find application in other areas of experimental particle physics, such as real-time decision making in event-selection problems and classification in neutrino physics

EEG alterations during treatment with olanzapine

The aim of this naturalistic observational study was to investigate EEG alterations in patients under olanzapine treatment with a special regard to olanzapine dose and plasma concentration. Twenty-two in-patients of a psychiatric university ward with the monodiagnosis of paranoid schizophrenia (ICD-10: F20.0), who received a monotherapy of olanzapine were included in this study. All patients had a normal alpha-EEG before drug therapy, and did not suffer from brain-organic dysfunctions, as verified by clinical examination and cMRI scans. EEG and olanzapine plasma levels were determined under steady-state conditions (between 18 and 22 days after begin of treatment). In 9 patients (40.9%), pathological EEG changes (one with spike-waves) consecutive to olanzapine treatment were observed. The dose of olanzapine was significantly higher in patients with changes of the EEG than in patients without changes (24.4 mg/day (SD: 8.1) vs. 12.7 mg/day (SD: 4.8); T = −4.3, df = 21, P < 0.001). In patients with EEG changes, the blood plasma concentration of olanzapine (45.6 μg/l (SD: 30.9) vs. 26.3 μg/l (SD: 21.6) tended to be also higher. The sensitivity of olanzapine dosage to predict EEG changes was 66.7%, the specificity 100% (Youden-index: 0.67). EEG abnormalities during olanzapine treatment are common. These are significantly dose dependent. Thus, EEG control recordings should be mandatory during olanzapine treatment with special emphasis on dosages exceeding 20 mg per day, although keeping in mind that EEGs have only a limited predictive power regarding future epileptic seizures

On the Principles of Differentiable Quantum Programming Languages

Variational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also because of their feasibility on near-term noisy intermediate-size quantum (NISQ) machines. The need for gradient information in the training procedure of VQC applications has stimulated the development of auto-differentiation techniques for quantum circuits. We propose the first formalization of this technique, not only in the context of quantum circuits but also for imperative quantum programs (e.g., with controls), inspired by the success of differentiable programming languages in classical machine learning. In particular, we overcome a few unique difficulties caused by exotic quantum features (such as quantum no-cloning) and provide a rigorous formulation of differentiation applied to bounded-loop imperative quantum programs, its code-transformation rules, as well as a sound logic to reason about their correctness. Moreover, we have implemented our code transformation in OCaml and demonstrated the resource-efficiency of our scheme both analytically and empirically. We also conduct a case study of training a VQC instance with controls, which shows the advantage of our scheme over existing auto-differentiation for quantum circuits without controls.Comment: Codes are available at https://github.com/LibertasSpZ/adcompil