arXiv subjects

Leonard Wossnig

Publications and source records attributed to Leonard Wossnig.

At least 19 recordsLinked to original sources

arXiv2026

Simulating a Post-Automation Economy

We develop an agent-based, stock-ow-consistent model of an economy undergoing automation, built to ask which scal instrument reaches the durable surplus that articial intelligence creates. The model separates two channels: a competitive return on reproducible robotic capital, and a mobile, foreign-held intellectual-property rent earned by AI. Production is an endogenous nested-CES technology; wealth concentration is microfounded through heterogeneous, persistent returns to wealth; and taxation and capital mobility are modelled as behavioural responses. The central result is that the durable surplus is the foreign-held AI rent, a cross-border licence fee that corporate, robot, and compute or token taxes largely miss and that only a source-based levy (a digital-services-style tax or a withholding) reaches. The appropriate policy depends decisively on whether a country owns the automation or imports it: for a host that owns the rent the problem is domestic inequality, reached by progressive and wealth taxes; for a rent-importing host the problem is base erosion and a gradual transfer of capital ownership abroad, which a residence-based wealth tax cannot reach. We report conditional orderings, stress-tested with global (Sobol) sensitivity and a formal stability analysis, rather than point forecasts.

econ.GN↗

arXiv2023

Best practices for machine learning in antibody discovery and development

Over the past 40 years, the discovery and development of therapeutic antibodies to treat disease has become common practice. However, as therapeutic antibody constructs are becoming more sophisticated (e.g., multi-specifics), conventional approaches to optimisation are increasingly inefficient. Machine learning (ML) promises to open up an in silico route to antibody discovery and help accelerate the development of drug products using a reduced number of experiments and hence cost. Over the past few years, we have observed rapid developments in the field of ML-guided antibody discovery and development (D&D). However, many of the results are difficult to compare or hard to assess for utility by other experts in the field due to the high diversity in the datasets and evaluation techniques and metrics that are across industry and academia. This limitation of the literature curtails the broad adoption of ML across the industry and slows down overall progress in the field, highlighting the need to develop standards and guidelines that may help improve the reproducibility of ML models across different research groups. To address these challenges, we set out in this perspective to critically review current practices, explain common pitfalls, and clearly define a set of method development and evaluation guidelines that can be applied to different types of ML-based techniques for therapeutic antibody D&D. Specifically, we address in an end-to-end analysis, challenges associated with all aspects of the ML process and recommend a set of best practices for each stage.

q-bio.BM↗

arXiv2022

The Variational Quantum Eigensolver: a review of methods and best practices

The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits. The VQE may be used to model complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm. All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation of errors, and best practices are suggested. We identify four main areas of future research:(1) optimal measurement schemes for reduction of circuit repetitions; (2) large scale parallelization across many quantum computers;(3) ways to overcome the potential appearance of vanishing gradients in the optimization process, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.

quant-ph↗

arXiv2021

Quantum Machine Learning For Classical Data

In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of research falls under the umbrella of quantum machine learning, a research area of computer science which has recently received wide attention. In particular, we investigate to what extent quantum computers can be used to accelerate supervised machine learning algorithms. The aim of this is to develop a clear understanding of the promises and limitations of the current state of the art of quantum algorithms for supervised machine learning, but also to define directions for future research in this exciting field. We start by looking at supervised quantum machine learning (QML) algorithms through the lens of statistical learning theory. In this framework, we derive novel bounds on the computational complexities of a large set of supervised QML algorithms under the requirement of optimal learning rates. Next, we give a new bound for Hamiltonian simulation of dense Hamiltonians, a major subroutine of most known supervised QML algorithms, and then derive a classical algorithm with nearly the same complexity. We then draw the parallels to recent "quantum-inspired" results, and will explain the implications of these results for quantum machine learning applications. Looking for areas which might bear larger advantages for QML algorithms, we finally propose a novel algorithm for Quantum Boltzmann machines, and argue that quantum algorithms for quantum data are one of the most promising applications for QML with potentially exponential advantage over classical approaches.

quant-ph↗

arXiv2021

Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver

Solving for molecular excited states remains one of the key challenges of modern quantum chemistry. Traditional methods are constrained by existing computational capabilities, limiting the complexity of the molecules that can be studied or the accuracy of the results that can be obtained. Several quantum computing methods have been suggested to address this limitation. However, these typically have hardware requirements which may not be achieved in the near term. We propose a variational quantum machine learning based method to determine molecular excited states aiming at being as resilient as possible to the defects of early Noisy Intermediate Scale Quantum (NISQ) computers and demonstrate an implementation for H2 on IBMQ. Our method uses a combination of two parametrized quantum circuits, working in tandem, combined with a Variational Quantum Eigensolver (VQE) to iteratively find the eigenstates of a molecular Hamiltonian.

quant-ph↗

arXiv2020

Statistical Limits of Supervised Quantum Learning

Within the framework of statistical learning theory it is possible to bound the minimum number of samples required by a learner to reach a target accuracy. We show that if the bound on the accuracy is taken into account, quantum machine learning algorithms for supervised learning---for which statistical guarantees are available---cannot achieve polylogarithmic runtimes in the input dimension. We conclude that, when no further assumptions on the problem are made, quantum machine learning algorithms for supervised learning can have at most polynomial speedups over efficient classical algorithms, even in cases where quantum access to the data is naturally available.

quant-ph↗

arXiv2020

Quantum State Discrimination Using Noisy Quantum Neural Networks

Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term quantum devices as it fulfils the above criteria. We find that when simulating gradient calculation on a noisy device, a large number of parameters is disadvantageous. By introducing a new smaller circuit ansatz we overcome this limitation, and find that the QNN performs well at noise levels of current quantum hardware. We also show that networks trained at higher noise levels can still converge to useful parameters. Our findings show that noisy quantum computers can be used in applications for state discrimination and for classifiers of the output of quantum generative adversarial networks.

quant-ph↗

arXiv2020

A quantum algorithm for simulating non-sparse Hamiltonians

We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random access memory (qRAM) which allows for the efficient preparation of states that encode the rows of the Hamiltonian. We use a linear combination of quantum walks to achieve poly-logarithmic dependence on precision. The time complexity of our algorithm, measured in terms of the circuit depth, is $O(t\sqrt{N}\|H\|\,\mathrm{polylog}(N, t\|H\|, 1/ε))$, where $t$ is the evolution time, $N$ is the dimension of the system, and $ε$ is the error in the final state, which we call precision. Our algorithm can be directly applied as a subroutine for unitary implementation and quantum linear systems solvers, achieving $\widetilde{O}(\sqrt{N})$ dependence for both applications.

quant-ph↗

arXiv2020

Approximating Hamiltonian dynamics with the Nyström method

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be efficiently classically simulated under specific structural conditions. Our main technical contribution is a randomized algorithm for approximating Hermitian matrix exponentials. The proof leverages a low-rank, symmetric approximation via the Nyström method. Our results suggest that under strong sampling assumptions there exist classical poly-logarithmic time simulations of quantum computations.

quant-ph↗

arXiv2019

An initialization strategy for addressing barren plateaus in parametrized quantum circuits

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. In turn, this makes some of the most compact ansätze usable in practice, which was not possible before even for rather basic problems. We show empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method.

quant-ph↗

arXiv2019

Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits

Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum (NISQ) devices, parametrized quantum circuits (PQCs) have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We also demonstrate the ability to evaluate the gradient of the encoded cost function in a quantum state.

quant-ph↗

arXiv2019

Generative training of quantum Boltzmann machines with hidden units

In this article we provide a method for fully quantum generative training of quantum Boltzmann machines with both visible and hidden units while using quantum relative entropy as an objective. This is significant because prior methods were not able to do so due to mathematical challenges posed by the gradient evaluation. We present two novel methods for solving this problem. The first proposal addresses it, for a class of restricted quantum Boltzmann machines with mutually commuting Hamiltonians on the hidden units, by using a variational upper bound on the quantum relative entropy. The second one uses high-order divided difference methods and linear-combinations of unitaries to approximate the exact gradient of the relative entropy for a generic quantum Boltzmann machine. Both methods are efficient under the assumption that Gibbs state preparation is efficient and that the Hamiltonian are given by a sparse row-computable matrix.

quant-ph↗

arXiv2019

Adversarial quantum circuit learning for pure state approximation

Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approximating an unknown quantum pure state. Although this could be done on universal quantum computers, the adversarial formulation enables us to execute the algorithm on near-term quantum computers. Two parametrized circuits are optimized in tandem: One tries to approximate the target state, the other tries to distinguish between target and approximated state. Supported by numerical simulations, we show that resilient backpropagation algorithms perform remarkably well in optimizing the two circuits. We use the bipartite entanglement entropy to design an efficient heuristic for the stopping criterion. Our approach may find application in quantum state tomography.

quant-ph↗

arXiv2018

Quantum gradient descent and Newton's method for constrained polynomial optimization

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into account curvature information and thereby often improves convergence. Here, we develop quantum versions of these iterative optimization algorithms and apply them to polynomial optimization with a unit norm constraint. In each step, multiple copies of the current candidate are used to improve the candidate using quantum phase estimation, an adapted quantum principal component analysis scheme, as well as quantum matrix multiplications and inversions. The required operations perform polylogarithmically in the dimension of the solution vector and exponentially in the number of iterations. Therefore, the quantum algorithm can be beneficial for high-dimensional problems where a small number of iterations is sufficient.

quant-ph↗

arXiv2018

Universal discriminative quantum neural networks

Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by non-orthogonal quantum probability distributions using the Adam stochastic optimization algorithm. This is achieved by iterative interactions of a classical device with a quantum processor to discover the parameters of an unknown non-unitary quantum circuit. This circuit learns to simulates the unknown structure of a generalized quantum measurement, or Positive-Operator-Value-Measure (POVM), that is required to optimally distinguish possible distributions of quantum inputs. Notably we use universal circuit topologies, with a theoretically motivated circuit design, which guarantees that our circuits can in principle learn to perform arbitrary input-output mappings. Our numerical simulations show that shallow quantum circuits could be trained to discriminate among various pure and mixed quantum states exhibiting a trade-off between minimizing erroneous and inconclusive outcomes with comparable performance to theoretically optimal POVMs. We train the circuit on different classes of quantum data and evaluate the generalization error on unseen mixed quantum states. This generalization power hence distinguishes our work from standard circuit optimization and provides an example of quantum machine learning for a task that has inherently no classical analogue.

quant-ph↗

arXiv2018

Quantum linear systems algorithms: a primer

The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of applications, and thus HHL constitutes an important algorithmic primitive. In these notes, we present the HHL algorithm and its improved versions in detail, including explanations of the constituent sub- routines. More specifically, we discuss various quantum subroutines such as quantum phase estimation and amplitude amplification, as well as the important question of loading data into a quantum computer, via quantum RAM. The improvements to the original algorithm exploit variable-time amplitude amplification as well as a method for implementing linear combinations of unitary operations (LCUs) based on a decomposition of the operators using Fourier and Chebyshev series. Finally, we discuss a linear solver based on the quantum singular value estimation (QSVE) subroutine.

quant-ph↗

arXiv2018

Quantum machine learning: a classical perspective

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.

quant-ph↗

arXiv2017

Quantum-classical truncated Newton method for high-dimensional energy landscapes

We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due to a recent formulation of semi-supervised learning as an optimization problem, the algorithm can further be used to find the optimal model parameters for deep generative models. In particular, we present a truncated saddle-free Newton's method based on recent insight from optimization, analysis of deep neural networks and random matrix theory. By combining these with the specific quantum subroutines we are able to exhaust quantum computing in order to arrive at a new quantum-classical hybrid algorithm design. Our algorithm is expected to perform at least as well as existing classical algorithms while achieving a polynomial speedup. The speedup is limited by the required classical read-out. Omitting this requirement can in theory lead to an exponential speedup.

quant-ph↗