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A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more…

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…

Quantum Physics · Physics 2020-05-13 Alexander M. Dalzell , Aram W. Harrow , Dax Enshan Koh , Rolando L. La Placa

Quantum computers have now surpassed classical simulation limits, yet noise continues to limit their practical utility. As the field shifts from proof-of-principle demonstrations to early deployments, there is no standard method for…

Quantum Physics · Physics 2025-05-29 J. A. Montanez-Barrera , Kristel Michielsen , David E. Bernal Neira

The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…

Quantum Physics · Physics 2023-08-16 Willie Aboumrad , Dominic Widdows , Ananth Kaushik

An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…

Quantum Physics · Physics 2007-05-23 Wim van Dam

We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…

Computational Complexity · Computer Science 2015-03-20 Richard J. Lipton , Kenneth W. Regan , Atri Rudra

This paper presents a new method to reduce the optimization of a pseudo-Boolean function to QUBO problem which can be solved by quantum annealer. The new method has two aspects, one is coefficient optimization and the other is variable…

Cryptography and Security · Computer Science 2022-11-21 Anpeng Zhang , Xiutao Feng

Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing are prominent approaches for solving combinatorial optimization problems, such as those formulated as Quadratic Unconstrained Binary Optimization (QUBO). These…

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…

This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout…

Quantum Physics · Physics 2007-05-23 Austin G. Fowler

Running quantum circuits on quantum computers does not always generate "clean" results, unlike on a simulator, as noise plays a significant role in any quantum device. To explore this, we experimented with the Quantum Approximate…

Quantum Physics · Physics 2025-10-09 Abyan Khabir Irfan , Chansu Yu

Prime factorization (P = M*N) is considered to be a promising application in quantum computations. We perform 4-bit factorization in experiments using a superconducting flux qubit toward quantum annealing. Our proposed method uses a…

Quantum Physics · Physics 2023-08-15 Daisuke Saida , Mutsuo Hidaka , Yuki Yamanashi

In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…

Quantum Physics · Physics 2016-09-08 I. Chuang , Raymond Laflamme , P. Shor , W. Zurek

A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses,…

Quantum Physics · Physics 2022-05-25 Minghui Li , Wei Wang , Zikang Tang , Hou Ian

We study the results of a compiled version of Shor's factoring algorithm on the ibmqx5 superconducting chip, for the particular case of $N=15$, $21$ and $35$. The semi-classical quantum Fourier transform is used to implement the algorithm…

Quantum Physics · Physics 2019-07-17 Mirko Amico , Zain H. Saleem , Muir Kumph

Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…

Quantum Physics · Physics 2009-10-28 Robert B. Griffiths , Chi-Sheng Niu

Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of…

Quantum Physics · Physics 2022-07-21 Yuwei Jin , Jason Luo , Lucent Fong , Yanhao Chen , Ari B. Hayes , Chi Zhang , Fei Hua , Eddy Z. Zhang

We show how the execution time of algorithms on quantum computers depends on the architecture of the quantum computer, the choice of algorithms (including subroutines such as arithmetic), and the ``clock speed'' of the quantum computer. The…

Quantum Physics · Physics 2007-05-23 Rodney Van Meter , Kohei M. Itoh , Thaddeus D. Ladd

Cryptography in the modern era is very important to prevent a cyber attack, as the world tends to be more and more digitalized. Classical cryptographic protocols mainly depend on the mathematical complicacy of encoding functions and the…

Quantum Physics · Physics 2021-10-04 Sinchan Ghosh , Harsh Mishra , Bikash K. Behera , Prasanta K. Panigrahi

Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…

Quantum Physics · Physics 2025-06-13 Yuchen Guo , Shuo Yang