Review on the study of entanglement in quantum computation speedup

Ding, ShengChao, Jin +1 more

量纠纷在量计算加速起的作用广泛地被争论了，相信那量计算“如果纠纷是不在的，在古典计算上的 s 加速是不可能的，当其它宣称纠纷的存在不是为一些量算法的一个必要条件时。这篇论文系统地讨论这个问题。与古典资源模仿量计算被分析，在已知的算法的纠纷被考察。纠纷的存在是处于纯状态或伪 pure 状态量计算加速的一个必要然而并非足够的条件，这被结束。有混合状态的盒子仍然保持开。进一步从介绍结果研究量计算愿望利益。

Guifré Vidal

ARTUR K. EKERT, Richard Jozsa

We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speedup in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2n in the quantum context, showing how the group–theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms.

Arun Kumar Pati, Samuel L. Braunstein

Benoît Vermersch

Dr. Chandra Sekhar Rajanala

Quantum computing (QC) stands at the forefront of a technological revolution poised to disrupt the global banking industry. By harnessing superposition, entanglement, and quantum interference, QC offers exponential or quadratic speedups for complex financial computations that challenge classical systems. This study provides a comprehensive empirical analysis of QC’s dual impact—transformative opportunities in portfolio optimization, risk modeling, derivative pricing, fraud detection, and Monte Carlo simulations, alongside substantial risks including cryptographic vulnerabilities (e.g., Shor’s algorithm threatening RSA/ECC), high capital costs, talent shortages, and NISQ-era noise limitations. Adopting a mixed-methods approach, the research integrates an extensive literature review, a survey of 120 banking and fintech professionals, expert insights, and hybrid quantum-classical simulations using frameworks like Qiskit and PennyLane on benchmark datasets (50–10,000 assets/scenarios). Findings indicate potential speedups of 20–30x in optimization and risk calculations, with 15–40% improvements in metrics such as Sharpe ratios and fraud detection accuracy. McKinsey projects $400–600 billion in annual value for finance by 2035, yet “harvest now, decrypt later” (HNDL) attacks pose systemic threats if post-quantum cryptography (PQC) migration lags. The study highlights hybrid approaches as the pragmatic near-term path and proposes a quantum readiness framework tailored for banks, with emphasis on emerging markets. Strategic recommendations address governance, investment prioritization, talent development, and regulatory collaboration. This research contributes actionable insights for bank executives, policymakers, and researchers navigating the quantum transition. Keywords: Quantum computing, banking disruption, portfolio optimization, risk management, post-quantum cryptography, hybrid quantum-classical systems, financial innovation, quantum readiness, empirical simulation