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This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover's algorithm for unstructured search to build intuition. We then…

Quantum Physics · Physics 2025-09-24 Jose Blanchet , Mark S. Squillante , Mario Szegedy , Guanyang Wang

Over the last decade, Quantum Computing hardware has rapidly developed and become a very intriguing, promising, and active research field among scientists worldwide. To achieve the desired quantum functionalities, quantum algorithms require…

Quantum Physics · Physics 2022-09-05 Shamminuj Aktar , Abdel-Hameed A. Badawy , Nandakishore Santhi

Quantum annealing (QA) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. In QA process, a bottleneck that may prevent QA to scale up is minor embedding step in which we embed…

Quantum Physics · Physics 2023-07-06 Hoang M. Ngo , Tamer Kahveci , My T. Thai

Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…

Optimization and Control · Mathematics 2022-01-21 Chin-Yao Chang , Eric Jones , Yiyun Yao , Peter Graf , Rishabh Jain

Analog quantum simulation leverages native hardware dynamics to emulate complex quantum systems with great efficiency by bypassing the quantum circuit abstraction. However, conventional compilation methods for analog simulators are…

Quantum Physics · Physics 2025-07-01 Junyu Zhou , Yuhao Liu , Shize Che , Anupam Mitra , Efekan Kökcü , Ermal Rrapaj , Costin Iancu , Gushu Li

There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover's algorithm has been commonly attributed to…

Quantum Physics · Physics 2007-08-27 Adrian Gepp , Phil Stocks

We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…

High Energy Physics - Phenomenology · Physics 2022-06-01 Selomit Ramírez-Uribe , Andrés E. Rentería-Olivo , Germán Rodrigo , German F. R. Sborlini , Luiz Vale Silva

The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…

Quantum Physics · Physics 2009-11-13 Avatar Tulsi

Quantum hardware continues to advance, yet finding new quantum algorithms - quantum software - remains a challenge, with classically trained computer programmers having little intuition of how computational tasks may be performed in the…

Quantum Physics · Physics 2018-12-12 Václav Potoček , Alan P. Reynolds , Alessandro Fedrizzi , David W. Corne

Quantum annealing offers a promising paradigm for solving NP-hard combinatorial optimization problems, but its practical application is severely hindered by two challenges: the complex, manual process of translating problem descriptions…

Machine Learning · Computer Science 2025-09-03 Huixiang Zhang , Mahzabeen Emu , Salimur Choudhury

The quantum circuit model essentially treats every quantum algorithm as a straight-line program. While this view is universal, recent work has shown that it is inconvenient for using different-length quantum subroutines in superposition.…

Quantum Physics · Physics 2026-05-11 Stacey Jeffery , Manideep Mamindlapally , Alex Baudoin Nguetsa Tankeu

Quantum computation constitutes a rapidly expanding subfield of computer science. Development quantum algorithms is facilitated by the availability of efficient quantum programming languages, and a plethora of approaches has been already…

Quantum Physics · Physics 2015-03-19 Arnab Chakraborty

It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…

Programming Languages · Computer Science 2009-11-07 S. Bettelli , L. Serafini , T. Calarco

Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…

Quantum Physics · Physics 2023-02-02 Bin Yan , Nikolai A. Sinitsyn

We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge…

Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…

Quantum Physics · Physics 2019-08-20 Rituparna Maji , Bikash K. Behera , Prasanta K. Panigrahi

Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However,…

Quantum Physics · Physics 2022-04-15 Qiuhao Chen , Yuxuan Du , Qi Zhao , Yuling Jiao , Xiliang Lu , Xingyao Wu

We investigate the implementation of an oracle for the Subset Sum problem for quantum search using Grover's algorithm. Our work concerns reducing the number of qubits, gates, and multi-controlled gates required by the oracle. We describe…

Emerging Technologies · Computer Science 2024-10-03 Angelo Benoit , Sam Schwartz , Ron K. Cytron

We present a new algorithm for reducing an arbitrary unitary matrix into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of…

Quantum Physics · Physics 2007-05-23 Robert R. Tucci