Roman Orus

Donostia International Physics Center / Multiverse Computing

Here we introduce an improved approach to Variational Quantum Attack Algorithms (VQAA) on crytographic protocols. Our methods provide robust quantum attacks to well-known cryptographic algorithms, more efficiently and with remarkably fewer qubits than previous approaches. We implement simulations of our attacks for symmetric-key protocols such as S...

Here we analyze three well-known conjectures: (i) the existence of infinitely-many twin primes, (ii) Goldbach's strong conjecture, and (iii) Polignac's conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of the Goldbach's strong conjecture, one must consider also the existen...

Machine learning models capable of handling the large data sets collected in the financial world can often become black boxes expensive to run. The quantum computing paradigm suggests new optimization techniques that, combined with classical algorithms, may deliver competitive, faster, and more interpretable models. In this paper we propose a quant...

Simulating IBM's largest quantum processors using Tensor Networks.

Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum devices. The idea of the algorithm relies on reducing the clustering problem to an optimization, and then solving it via...

Quantum technologies have the potential to solve computationally hard problems that are intractable via classical means. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolera...

In this work, we investigate the interplay between dissipation and symmetry-protected topological order. We considered the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki model interacting with an environment where the dissipative dynamics are described by the Lindladian master equation. The Markovian dynamics is solved by the implementation of...

Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum optimization scheme where discrete classical variables are encoded in non-orthogonal states of the quantum system. We de...

In this paper we perform a detailed analysis of Riemann’s hypothesis, dealing with the zeros of the analytically-extended zeta function. We use the functional equation ζ(s) = 2^s π^(s−1) sin(πs/2)Γ(1 − s)ζ(1 − s) for complex numbers s such that 0 < Re(s) < 1 and the reduction to the absurd method where we use an analytical study based on a complex...

The Cheyette model is a quasi-Gaussian volatility interest rate model widely used to price interest rate derivatives such as European and Bermudan Swaptions for which Monte Carlo simulation has become the industry standard. In low dimensions, these approaches provide accurate and robust prices for European Swaptions but, even in this computationall...

Machine learning algorithms, both in their classical and quantum versions, heavily rely on optimization algorithms based on gradients, such as gradient descent and alike. The overall performance is dependent on the appearance of local minima and barren plateaus, which slow-down calculations and lead to non-optimal solutions. In practice, this resul...

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The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be spe...

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to sto...

Machine Learning models capable of handling the large datasets collected in the financial world can often become black boxes expensive to run. The quantum computing paradigm suggests new optimization techniques, that combined with classical algorithms, may deliver competitive, faster and more interpretable models. In this work we propose a quantum-...

In this paper we perform a detailed analysis of Riemann's hypothesis, dealing with the zeros of the analytically-extended zeta function. We use the functional equation ζ(s) = 2^s π^(s−1)sin(πs/2)Γ(1 − s)ζ(1 − s) for complex numbers s such that 0 < Re(s) < 1, as well as reduction to the absurd in combination with a deep numerical analysis, to show t...

Deep neural networks (NN) suffer from scaling issues when considering a large number of neurons, in turn limiting also the accessible number of layers. To overcome this, here we propose the integration of tensor networks (TN) into NNs, in combination with variational DMRG-like optimization. This results in a scalable tensor neural network (TNN) arc...

In this work, we investigate the interplay between dissipation and symmetry-protected topological order. We considered the one-dimensional Spin-1 Affleck-Kennedy-Lieb-Tasaki model interacting with an environment where the dissipative dynamics are described by the Lindladian master equation. The Markovian dynamics is solved by the implementation of...

The entanglement entropy is a unique probe to reveal universal features of strongly interacting many-body systems. In two or more dimensions these features are subtle, and detecting them numerically requires extreme precision, a notoriously difficult task. This is especially challenging in models of interacting fermions, where many such universal f...

Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic building block of our approach is a variational quantum circuit where each qubit encodes up to three continuous var...

Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum optimization scheme where discrete classical variables are encoded in non-orthogonal states of the quantum system. We de...

In this work, we demonstrate how to apply non-linear cardinality constraints, important for real-world asset management, to quantum portfolio optimization. This enables us to tackle non-convex portfolio optimization problems using quantum annealing that would otherwise be challenging for classical algorithms. Being able to use cardinality constrain...

https://arxiv.org/abs/2208.05916 In this work, we develop a new quantum algorithm to solve a combinatorial problem with significant practical relevance occurring in clutch manufacturing. It is demonstrated how quantum optimization can play a role in real industrial applications in the manufacturing sector. Using the quantum annealer provided by D-...

In this paper we consider several algorithms for quantum computer vision using Noisy Intermediate-Scale Quantum (NISQ) devices, and benchmark them for a real problem against their classical counterparts. Specifically, we consider two approaches: a quantum Support Vector Machine (QSVM) on a universal gate-based quantum computer, and QBoost on a quan...

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of dimensionality in new ways. However, deep learning methods are constrained by training time and memory. To tackle these sho...

In this paper we briefly review two recent use-cases of quantum optimization algorithms applied to hard problems in finance and economy. Specifically, we discuss the prediction of financial crashes as well as dynamic portfolio optimization. We comment on the different types of quantum strategies to carry on these optimizations, such as those based...

Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ) devices. The idea of the algorithm relies on reducing the clustering problem to an optimization, and then solving...

En este artículo resumimos brevemente y de manera no técnica varios avances recientes en el estudio del lenguaje desde la perspectiva de la física. En particular, comentamos resultados referentes a la equivalencia entre MERGE y renormalización, así como de la teoría de Matrix Syntax. Proponemos también un experimento que pueden llevar a cabo estudi...

Here we consider some well-known facts in syntax from a physics perspective, allowing us to establish analogies between both fields with many consequences. Mainly, we observe that the operation MERGE, put forward by Chomsky (in: Evolution and Revolution in Linguistic Theory, Essays in honor of Carlos Otero., eds. Hector Campos and Paula Kempchinsky...

In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints. This problem is central to quantitative finance. After a detailed introduction to the problem, we i...

We show that the problem of political forecasting, i.e, predicting the result of elections and referendums, can be mapped to finding the ground-state configuration of a classical spin system. Depending on the required prediction, this spin system can be a combination of XY, Ising and vector Potts models, always with two-spin interactions, magnetic...

«Matrix syntax» es un modelo formal de relaciones sintácticas en el lenguaje. La estructura matemática resultante se asemeja a algunos aspectos de la mecánica cuántica. «Matrix syntax» nos permite describir una serie de fenómenos del lenguaje que de otro modo serían muy difíciles de explicar, como las cadenas lingüísticas, y podría decirse que es u...

The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain wheth...

We present an algorithm which efficiently estimates the intrinsic long-term value of a portfolio of assets on a quantum computer. The method relies on quantum amplitude estimation to estimate the mean of a novel implementation of the Gordon-Shapiro formula. The choice of loading and readout algorithms makes it possible to price a five-asset portfol...

We combine tensor-network approaches and high-order linked-cluster expansions to investigate the quantum phase diagram of the antiferromagnetic Kitaev's honeycomb model in a magnetic field for general spin values. For the pure Kitaev model, tensor network calculations confirm the absence of fluxes and spin-spin correlations beyond nearest neighbor...

In this paper we propose a hybrid quantum-classical algorithm for dynamic portfolio optimization with minimal holding period. Our algorithm is based on sampling the near-optimal portfolios at each trading step using a quantum processor, and efficiently post-selecting to meet the minimal holding constraint. We found the optimal investment trajectory...

We study the 3D Kitaev and Kitaev-Heisenberg models, respectively, on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit. Our analysis relies on advanced tensor network (TN) simulations based on graph projected entangled-pair states (gPEPS). We map out the TN phase diagrams of the models an...

In this paper we show how to implement in a simple way some complex real-life constraints on the portfolio optimization problem, so that it becomes amenable to quantum optimization algorithms. Specifically, first we explain how to obtain the best investment portfolio with a given target risk. This is important in order to produce portfolios with di...

The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain wheth...

Coupling a quantum many-body system to an external environment dramatically changes its dynamics and offers novel possibilities not found in closed systems. Of special interest are the properties of the steady state of such open quantum many-body systems, as well as the relaxation dynamics toward the steady state. However, new computational tools a...

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter...

We study the zero-temperature phase diagram of the spin-$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entan...

In this paper we propose a hybrid quantum-classical algorithm for dynamic portfolio optimization with minimal holding period. Our algorithm is based on sampling the near-optimal portfolios at each trading step using a quantum processor, and efficiently post-selecting to meet the minimal holding constraint. We found the optimal investment trajectory...

We implement and benchmark tensor network algorithms with SU(2) symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement SU(2)-invariant versions of the infinite projected entangled pair states and infinite projected entangled simplex states methods. Our implementation of SU(2) symmetry follows the f...

We study the 3D Kitaev and Kitaev-Heisenberg models respectively on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit. Our analysis relies on advanced tensor network (TN) simulations based on graph Projected Entangled-Pair States (gPEPS). We map out the TN phase diagrams of the models and...

Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate t...

In this paper we briefly review two recent use-cases of quantum optimization algorithms applied to hard problems in finance and economy. Specifically, we discuss the prediction of financial crashes as well as dynamic portfolio optimization. We comment on the different types of quantum strategies to carry on these optimizations, such as those based...

We show that the problem of political forecasting, i.e, predicting the result of elections and referendums, can be mapped to finding the ground state configuration of a classical spin system. Depending on the required prediction, this spin system can be a combination of XY, Ising and vector Potts models, always with two-spin interactions, magnetic...

In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints. This problem, well-known to be NP-Hard, is central to quantitative finance. After a detailed introd...

This paper is a manual with tips and tricks for programming tensor network algorithms with global SU(2) symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of codes, such as useful data structures to store the tensors, practical ways of manipulating them, and adapting typica...

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse graining, provide the original ones. Thanks to this procedure, the original latt...

We implement and benchmark tensor network algorithms with $SU(2)$ symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement $SU(2)$-invariant versions of the infinite Projected Entangled Pair States (iPEPS) and infinite Projected Entangled Simplex States (iPESS) methods. Our implementation of $SU(2)$...

Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate t...

We construct a short-range resonating-valence-bond (RVB) state on the ruby lattice, using projected entangled-pair states with bond dimension D=3. By introducing nonlocal moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave func...

A Bloch sphere is the geometrical representation of an arbitrary two-dimensional Hilbert space. Possible classes of entanglement and separability for the pure and mixed states on the Bloch sphere were suggested by [Boyer et al 2017 PRA 95 032 308]. Here we construct a Bloch sphere for the Hilbert space spanned by one of the ground states of Kitaev’...

We study the zero-temperature phase diagram of the spin-$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entan...

La sintaxi de matrius és un model formal de relacions sintàctiques en el llenguatge que va sorgir del desig de modelar les cadenes. L’objectiu d’aquest treball és explicar les idees bàsiques d’aquest model a un públic lingüístic, sense entrar en gaires detalls formals (vegeu Orús et al. 2017). L’estructura matemàtica resultant s’assembla a alguns a...

We construct a short-range resonating valence-bond state (RVB) on the ruby lattice, using projected entangled-pair states (PEPS) with bond dimension $D=3$. By introducing non-local moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB...

In structured indexes, classification systems, thesauri, conceptual structures or semantic networks, relationships are too often vague. For instance, in terminology, the relationships between concepts are often reduced to the distinction established by standard between hierarchical relationships (genus-species relationships and part/whole relations...

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse-graining, provide the original ones. Thanks to this procedure, the original latt...

Originally developed in the context of condensed-matter physics and based on renormalization group ideas, tensor networks have been revived thanks to quantum information theory and the progress in understanding the role of entanglement in quantum many-body systems. Moreover, tensor network states have turned out to play a key role in other scientif...

Coupling a quantum many-body system to an external environment dramatically changes its dynamics and offers novel possibilities not found in closed systems. Of special interest are the properties of the steady state of such open quantum many-body systems, as well as the relaxation dynamics towards the steady state. However, new computational tools...

A key problem in financial mathematics is the forecasting of financial crashes: If we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator which has complete information abo...

In this paper we study the ground-state properties of a ladder Hamiltonian with chiral SU(2)-invariant spin interactions, a possible first step toward the construction of truly two-dimensional nontrivial systems with chiral properties starting from quasi-one-dimensional ones. Our analysis uses a recent implementation by us of SU(2) symmetry in tens...

We present a general graph-based projected entangled-pair state (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural matrix, which codifies the details of tensor networks on any graphs in any dimension d, we are able to produce a code that can b...

Prediction of financial crashes in a complex financial network is known to be an NP-hard problem, i.e., a problem which cannot be solved efficiently with a classical computer. We experimentally explore a novel approach to this problem by using a D-Wave quantum computer to obtain financial equilibrium more efficiently. To be specific, the equilibriu...

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time-evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter...

Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice s...

We discuss how quantum computation can be applied to financial problems, providing an overview of current approaches and potential prospects. We review quantum optimization algorithms, and expose how quantum annealers can be used to optimize portfolios, find arbitrage opportunities, and perform credit scoring. We also discuss deep-learning in finan...

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory and the understanding of entanglement in quantum many-body systems. Moreover, it has been not-so-long realized...

In this paper we study the ground state properties of a ladder Hamiltonian with chiral $SU(2)$-invariant spin interactions, a possible first step towards the construction of truly two dimensional non-trivial systems with chiral properties starting from quasi-one dimensional ones. Our analysis uses a recent implementation by us of $SU(2)$ symmetry i...

A Bloch sphere is the geometrical representation of an arbitrary two-dimensional Hilbert space. Possible classes of entanglement and separability for the pure and mixed states on the Bloch sphere were suggested by [M. Boyer, R. Liss, T. Mor, PRA, 032308 (2017)]. Here we construct a Bloch sphere for the Hilbert space spanned by one of the ground sta...