Why is quantum computing useful for optimization problems

1 2 Quantum computers are better at guessing, new study demonstrates Researchers leverage techniques to manage error accumulation, demonstrating the potential of quantum computing in the error-prone NISQ era Date: June 5, 2023 Source: University of Southern California Summary: Researchers have demonstrated a quantum speedup over the most efficient classical computer algorithm possible for what is believed to be the first time. The accomplishment was performed on an IBM Montreal Quantum Falcon r4 27-qubit device. Share: Daniel Lidar, the Viterbi Professor of Engineering at USC and Director of the USC Center for Quantum Information Science & Technology, and first author Dr. Bibek Pokharel, a Research Scientist at IBM Quantum, achieved this quantum speedup advantage in the context of a "bitstring guessing game." They managed strings up to 26 bits long, significantly larger than previously possible, by effectively suppressing errors typically seen at this scale. (A bit is a binary number that is either zero or one). Quantum computers promise to solve certain problems with an advantage that increases as the problems increase in complexity. However, they are also highly prone to errors, or noise. The challenge, says Lidar, is "to obtain an advantage in the real world where today's quantum computers are still 'noisy.'" This noise-prone condition of current quantum computing is termed the "NISQ" (Noisy Intermediate-Scale Quantum) era, a term adapted from the RISC architecture used...

Quantum computing is often famous as the solution to all problems. However, they are expected to alleviate world hunger, cure disease, and even help mitigate the effects of climate change. It is the reason several quantum computing companies have started joining established markets. It is widely known that quantum computing is useful for solving optimization problems. Apart from this interest, there is still plenty of uncertainty around the near-term uses of quantum computing. However, a crucial question that most quantum researchers face is fundamental: Why is Quantum Computing Useful for Optimization Problems? Quantum computing has already managed to beat ordinary computers in resolving some optimization problems. However, the next milestone is to get them to perform some practical stuff. Some researchers have demonstrated that a very small yet well-functioning quantum computer can solve a small part of the real logistics dilemma in the aviation industry. Keep in mind that optimization problems are very different from others. You don’t search for a correct answer. You don’t want to put a label on something unknown, but you aim to find the best among several suitable solutions. It will force you to take a different approach. In addition to this, you have to encode the problem into qubits. It will allow you to figure out the solution and evaluate its effectiveness. Table of Contents • • • • • • • • Reasons Quantum Computing is Useful for Optimization Problems Quantum compu...

Contents • 1 Introduction • 2 Theory, methodology, and/or algorithmic discussions • 2.1 Quantum Approximate Optimization Algorithm • 2.2 Quadratic Unconstrained Binary Optimization • 2.3 Hybrid QC-based Optimization Algorithm • 2.4 Quantum Annealing • 3 Numerical Example • 4 Applications • 4.1 Energy Systems • 4.2 Finance • 4.3 Fault Detection and Diagnosis • 4.4 Quantum Data Fitting • 5 Conclusion • 6 References Introduction Recent scientific advances have made quantum computing (QC) the next frontier in computation. A novel feature of QC is that it offers a significant speed advantage over classical methods in solving some of the most complex optimization problems. Theory, methodology, and/or algorithmic discussions Quantum Approximate Optimization Algorithm Quantum Approximate Optimization Algorithm (QAOA) introduced by Farhi et al. Quadratic Unconstrained Binary Optimization QUBO, also called unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem that has applications in finance, economics, and machine learning. In addition to incorporating network flows, scheduling, max cuts, max cliques, vertex covers, and other graph and management science problems into a unified modeling framework, QUBO has been extensively studied and used to model and solve numerous types of optimization problems. Given is the graph G = [N, E] with node set N = where 𝑄 is an n-by-n square symmetric matrix of coefficients. Hybrid QC-based Optimization Algorithm...

Optimization algorithms using quantum computing Quantum optimization algorithms are Quantum data fitting [ ] Quantum least squares fitting [ ] One of the most common types of data fitting is solving the The algorithm is given N is required for scalable advantage. See also [ ] • • References [ ] • Moll, Nikolaj; Barkoutsos, Panagiotis; Bishop, Lev S.; Chow, Jerry M.; Cross, Andrew; Egger, Daniel J.; Filipp, Stefan; Fuhrer, Andreas; Gambetta, Jay M.; Ganzhorn, Marc; Kandala, Abhinav; Mezzacapo, Antonio; Müller, Peter; Riess, Walter; Salis, Gian; Smolin, John; Tavernelli, Ivano; Temme, Kristan (2018). "Quantum optimization using variational algorithms on near-term quantum devices". Quantum Science and Technology. 3 (3): 030503. • Wiebe, Nathan; Braun, Daniel; Lloyd, Seth (2 August 2012). "Quantum Algorithm for Data Fitting". Physical Review Letters. 109 (5): 050505. • Montanaro, Ashley (12 January 2016). "Quantum algorithms: an overview". 2: 15023. • Ramana, Motakuri V. (1997). Mathematical Programming. 77: 129–162. • Brandao, Fernando G. S. L.; • Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam (2014). "A Quantum Approximate Optimization Algorithm". • Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam (2014). "A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem". • Barak, Boaz; Moitra, Ankur; O'Donnell, Ryan; Raghavendra, Prasad; Regev, Oded; Steurer, David; Trevisan, Luca; Vijayaraghavan, Aravindan; Witmer, David; Wright, John (2015)...

Don’t Go It Alone. Gurobi and Its Partners Provide the Continuum of Support You Need. While the mathematical optimization field is more than 70 years old, many customers are still learning how to make the most of its capabilities. That’s why, at Gurobi, we have established the Gurobi Alliance partner network—a group of trusted partners who can support you in achieving your optimization goals. Learn More • What is Quantum Computing Optimization? The world is abuzz about quantum computing, and rightfully so. By exploiting the power of subatomic phenomena, quantum computing has the potential to solve some of humanity’s greatest challenges—and companies and governments want to be ready to take full advantage of these capabilities. As a result, organizations are investing heavily in quantum computing. According to Why Is Quantum Useful for Optimization? Quantum computing promises to be the solution to today’s most complex problems, and it’s expected to make an especially transformative impact in simulation problems—such as organic chemistry, materials science, and biochemistry—and security. But optimization is the area where quantum computing is expected to create breakthrough performance first. This is of particular interest to business leaders, in particular, since optimization can solve common business problems—enabling organizations to do more with their limited resources. Some common quantum optimization use cases include: • Factory layout planning • Renewable energy grid ...