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Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum…

We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…

Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…

Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are…

Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…

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…

Quantum computers are emerging as a viable alternative to tackle certain computational problems that are challenging for classical computers. With the rapid development of quantum hardware such as those based on trapped ions, there is…

Quantum algorithms have gained increasing attention for addressing complex combinatorial problems in finance, notably portfolio optimization. This study systematically benchmarks two prominent variational quantum approaches, Variational…

Previously only considered a frontier area of Physics, nowadays quantum computing is one of the fastest growing research field, precisely because of its technological applications in optimization problems, machine learning, information…

The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…

Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…

Accurate prediction of future loan defaults is a critical capability for financial institutions that provide lines of credit. For institutions that issue and manage extensive loan volumes, even a slight improvement in default prediction…

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

Real-world applications of computing can be extremely time-sensitive. It would be valuable if we could accelerate such tasks by performing some of the work ahead of time. Motivated by this, we propose a cost model for quantum algorithms…

Risk assessment and in particular derivatives pricing is one of the core areas in computational finance and accounts for a sizeable fraction of the global computing resources of the financial industry. We outline a quantum-inspired…

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…

The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…

Molecular simulations are widely regarded as leading candidates to demonstrate quantum advantage--defined as the point at which quantum methods surpass classical approaches in either accuracy or scale. Yet the qubit counts and error rates…