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Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations…
Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task,…
Understanding the capabilities of classical simulation methods is key to identifying where quantum computers are advantageous. Not only does this ensure that quantum computers are used only where necessary, but also one can potentially…
We present the Quantum Monte Carlo Integration (QMCI) engine developed by Quantinuum. It is a quantum computational tool for evaluating multi-dimensional integrals that arise in various fields of science and engineering such as finance.…
While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a…
Quantum machine learning is emerging as a promising application of quantum computing due to its distinct way of encoding and processing data. It is believed that large-scale quantum machine learning demonstrates substantial advantages over…
We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater…
We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…
Quantum computing (QC) offers a new computing paradigm that has the potential to provide significant speedups over classical computing. Each additional qubit doubles the size of the computational state space available to a quantum…
The problem of simulatability of quantum processes using classical resources plays a cornerstone role for quantum computing. Quantum circuits can be simulated classically, e.g., using Monte Carlo sampling techniques applied to…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
We propose a quantum machine learning framework for estimating classical covariance matrices using parameterized quantum circuits within the Pauli-Correlation-Encoding (PCE) paradigm. We introduce two quantum covariance estimators: the…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
We present an implementation of Quantum Annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin-glass in transverse field. In particular, we study whether or not such method is more…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of…
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the…
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…