arXiv subjects

Del Rajan

Publications and source records attributed to Del Rajan.

11 recordsLinked to original sources

arXiv2026

Gaussian Boson Sampling for Asset Clustering in Statistical Arbitrage Portfolios

Gaussian Boson Sampling (GBS) provides a native photonic quantum heuristic for sampling dense subgraphs from adjacency matrices, offering a scalable physical approach to combinatorial graph search problems. Simultaneously, correlation matrix clustering algorithms, such as Spectral and SPONGE, have established robust benchmarks for identifying co-moving assets from correlation matrices in statistical arbitrage (StatArb) strategies. In this work, we map S&P 500 residual correlation data into GBS-compatible adjacency matrices. We benchmark those classical clustering algorithms against two quantum clustering algorithms, GBS Boost and our novel GBS Roots, to construct dynamic, market-neutral portfolios over a rolling one-year window. Simulations across distinct macroeconomic regimes reveal that quantum clustering generates superior alpha within large stock universes during periods of high volatility, effectively isolating structural market idiosyncrasies. Crucially, this economic advantage persists under simulated low-loss conditions and extends into high-loss regimes via the application of coherent displacement to compensate for photon loss. Our findings underscore the efficacy of GBS-derived graph clustering in constructing robust StatArb portfolios, establishing a quantum foundation for broader quantitative finance applications.

quant-ph↗

arXiv2025

Enhanced fill probability estimates in institutional algorithmic bond trading using statistical learning algorithms with quantum computers

The estimation of fill probabilities for trade orders represents a key ingredient in the optimization of algorithmic trading strategies. It is bound by the complex dynamics of financial markets with inherent uncertainties, and the limitations of models aiming to learn from multivariate financial time series that often exhibit stochastic properties with hidden temporal patterns. In this paper, we focus on algorithmic responses to trade inquiries in the corporate bond market and investigate fill probability estimation errors of common machine learning models when given real production-scale intraday trade event data, transformed by a quantum algorithm running on IBM Heron processors, as well as on noiseless quantum simulators for comparison. We introduce a framework to embed these quantum-generated data transforms as a decoupled offline component that can be selectively queried by models in low-latency institutional trade optimization settings. A trade execution backtesting method is employed to evaluate the fill prediction performance of these models in relation to their input data. We observe a relative gain of up to ~ 34% in out-of-sample test scores for those models with access to quantum hardware-transformed data over those using the original trading data or transforms by noiseless quantum simulation. These empirical results suggest that the inherent noise in current quantum hardware contributes to this effect and motivates further studies. Our work demonstrates the emerging potential of quantum computing as a complementary explorative tool in quantitative finance and encourages applied industry research towards practical applications in trading.

quant-ph↗

arXiv2024

Effects of the entropy source on Monte Carlo simulations

In this paper we show how different sources of random numbers influence the outcomes of Monte Carlo simulations. We compare industry-standard pseudo-random number generators (PRNGs) to a quantum random number generator (QRNG) and show, using examples of Monte Carlo simulations with exact solutions, that the QRNG yields statistically significantly better approximations than the PRNGs. Our results demonstrate that higher accuracy can be achieved in the commonly known Monte Carlo method for approximating $\pi$. For Buffon's needle experiment, we further quantify a potential reduction in approximation errors by up to $1.89\times$ for optimal parameter choices when using a QRNG and a reduction of the sample size by $\sim 8\times$ for sub-optimal parameter choices. We attribute the observed higher accuracy to the underlying differences in the random sampling, where a uniformity analysis reveals a tendency of the QRNG to sample the solution space more homogeneously.

physics.comp-ph↗

arXiv2022

Quantum Analogue of Entropy Based DDoS Detection

Distributed Denial-of-Service (DDoS) attacks can occur in quantum networks, which can pose a significant threat to its key distribution protocols. We introduce a quantum analogue of a classical entropic DDoS detection system, and apply it in the context of detecting an attack on a quantum network. In particular, we examine DDoS attacks on a quantum repeater and harness the associated entanglement entropy for the detection system. Our method contributes to the applicability of quantum information from the domain of data security to the area of network security.

quant-ph↗

arXiv2020

Quantum Entanglement in Time

In this doctoral thesis we provide one of the first theoretical expositions on a quantum effect known as entanglement in time. It can be viewed as an interdependence of quantum systems across time, which is stronger than could ever exist between classical systems. We explore this temporal effect within the study of quantum information and its foundations as well as through relativistic quantum information. An original contribution of this thesis is the design of one of the first applications of entanglement in time.

quant-ph↗

arXiv2019

Quantum PBR Theorem as a Monty Hall Game

The quantum Pusey--Barrett--Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a $ψ$-ontic model (system's physical state) or to a $ψ$-epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a $ψ$-ontic or $ψ$-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability.

quant-ph↗

arXiv2019

Quantum Blockchain using entanglement in time

We propose a conceptual design for a quantum blockchain. Our method involves encoding the blockchain into a temporal GHZ (Greenberger-Horne-Zeilinger) state of photons that do not simultaneously coexist. It is shown that the entanglement in time, as opposed to an entanglement in space, provides the crucial quantum advantage. All the subcomponents of this system have already been shown to be experimentally realized. Furthermore, our encoding procedure can be interpreted as nonclassically influencing the past.

quant-ph↗

arXiv2019

Kochen-Specker theorem revisited

The Kochen-Specker theorem is a basic and fundamental 50 year old non-existence result affecting the foundations of quantum mechanix, strongly implying the lack of any meaningful notion of "quantum realism", and typically leading to discussions of "contextuality" in quantum physics. Original proofs of the Kochen-Specker theorem proceeded via brute force counter-examples; often quite complicated and subtle (albeit mathematically "elementary") counter-examples. Only more recently have somewhat more "geometrical" proofs been developed. We present herein yet another simplified geometrical proof of the Kochen-Specker theorem, one that is valid for any number of dimensions, that minimizes the technical machinery involved, and makes the seriousness of the issues raised manifest.

quant-ph↗

arXiv2019

Explicit construction of the density matrix in Gleason's theorem

Gleason's theorem is a fundamental 60 year old result in the foundations of quantum mechanix, setting up and laying out the surprisingly minimal assumptions required to deduce the existence of quantum density matrices and the Born rule. Now Gleason's theorem and its proof have been continuously analyzed, simplified, and revised over the last 60 years, and we will have very little to say about the theorem and proof themselves. Instead, we find it useful, (and hopefully interesting), to make some clarifying comments concerning the explicit construction of the quantum density matrix that Gleason's theorem proves exists, but that Gleason's theorem otherwise says relatively little about.

quant-ph↗

arXiv2017

Complex Spacetimes and the Newman-Janis trick

In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions

gr-qc↗

arXiv2017

Cartesian Kerr-Schild variation on the Newman-Janis ansatz

The Newman-Janis trick is a procedure, (not even really an ansatz), for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old trick continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an algorithm, or even an inspired ansatz, or is it just a random trick of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not answer these deeper questions, we shall instead present a much simpler alternative variation on the theme of the Newman--Janis trick that might be easier to work with. We shall present a 2-step version of the Newman-Janis trick that works directly with the Kerr-Schild "Cartesian" metric presentation of the Kerr spacetime. That is, we show how the original 4-step Newman-Janis procedure can, (using the interplay between oblate spheroidal and Cartesian coordinates), be reduced to a considerably cleaner 2-step process.

gr-qc↗