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Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
This work introduces a novel approach to price rainbow options, a type of path-independent multi-asset derivatives, with quantum computers. Leveraging the Iterative Quantum Amplitude Estimation method, we present an end-to-end quantum…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…
Quantum optimization is the most mature quantum computing technology to date, providing a promising approach towards efficiently solving complex combinatorial problems. Methods such as adiabatic quantum computing (AQC) have been employed in…
This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that…
Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…
The application of quantum computing to the field of image processing has produced several promising applications: quantum image representation techniques have been developed showing how, by taking advantage of quantum properties like…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…
In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a…
We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…
Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant…