Quantum computers have the potential to provide quadratic speedup for Monte Carlo methods currently used in various classical applications. In this work, we examine the advantage of quantum computers for financial option pricing with the Monte Carlo method. Systematic and statistical errors are handled in a joint framework, and a relationship to quantum gate error is established. New metrics are introduced for the assessment of quantum advantage based on sample count and optimized error handling. We implement and analyze a Fourier series based approach and demonstrate its benefit over the more traditional rescaling method in function approximation. Our numerical calculations reveal the unpredictable nature of systematic errors, making consistent quantum advantage difficult with current quantum hardware. Our results indicate that very low noise levels, a two-qubit gate error rate below 10⁻⁶, are necessary for the quantum method to outperform the classical one, but a low number of logical qubits (ca. 20) may be sufficient to see quantum advantage already.

A limited number of studies have focused on the mutational landscape of breast cancer in different ethnic populations within Europe and compared the data with other ethnic groups and databases. We performed whole-genome sequencing of 63 samples from 29 Hungarian breast cancer patients. We validated a subset of the identified variants at the DNA level using the Illumina TruSight Oncology (TSO) 500 assay. Canonical breast-cancer-associated genes with pathogenic germline mutations were CHEK2 and ATM. Nearly all the observed germline mutations were as frequent in the Hungarian breast cancer cohort as in independent European populations. The majority of the detected somatic short variants were single-nucleotide polymorphisms (SNPs), and only 8% and 6% of them were deletions or insertions, respectively. The genes most frequently affected by somatic mutations were KMT2C (31%), MUC4 (34%), PIK3CA (18%), and TP53 (34%). Copy number alterations were most common in the NBN, RAD51C, BRIP1, and CDH1 genes. For many samples, the somatic mutational landscape was dominated by mutational processes associated with homologous recombination deficiency (HRD). Our study, as the first breast tumor/normal sequencing study in Hungary, revealed several aspects of the significantly mutated genes and mutational signatures, and some of the copy number variations and somatic fusion events. Multiple signs of HRD were detected, highlighting the value of the comprehensive genomic characterization of breast cancer patient populations.

We present a model of classical binary time series derived from a matrix product state (MPS) Ansatz widely used in one-dimensional quantum systems. We discuss how this quantum Ansatz allows us to generate classical time series in a sequential manner. Our time series are built in two steps: First, a lower-level series (the driving noise or the increments) is created directly from the MPS representation, which is then integrated to create our ultimate higher-level series. The lower- and higher-level series have clear interpretations in the quantum context, and we elaborate on this correspondence with specific examples such as the spin-1/2 Ising model in a transverse field (ITF model), where spin configurations correspond to the increments of discrete-time, discrete-level stochastic processes with finite or infinite autocorrelation lengths, Gaussian or non-Gaussian limit distributions, nontrivial Hurst exponents, multifractality, asymptotic self-similarity, etc. Our time series model is a parametric model, and we investigate how flexible the model is in some synthetic and real-life calibration problems.

Entangled quantum mechanical states in one dimension can be used to represent and simulate classical stochastic processes with nontrivial statistical properties. Long-range quantum correlations translate into fractional processes with their asymptotic Hurst exponents characterizing roughness and persistence. We explore this analogy in the case of the spin-1/2 XXZ chain and investigate properties of four different classical two-state processes that this quantum system can generate. These processes show fractional characteristics with varying Hurst exponents. We argue that the continuous quantum symmetries such as U(1) or SU(2) of the XXZ chain give rise to $H=0$ with logarithmic scaling. Processes generated without these symmetries can produce $H \geq0.5$ but likely not $H < 0.5$ unless the dominant term responsible for $H=0.5$ gets canceled. This does not seem to happen for the XXZ model. We use standard quantum methods, including MERA and TEBD, to numerically substantiate our findings.