Development of the Quantum Inverse Problem Method. (Talk, Abstract Only)

Nickolay V Maletin, M. Tokarev, Dmitry V Minaev +1 more

Abstract The paper provides a brief overview of the current state of development of quantum, hybrid and quantum-inspired annealers and the problems that can be solved with their help. We propose a method for reducing high-degree polynomial optimization problems from a large number of continuous variables to quadratic unconstrained binary optimization (QUBO) problems, developed by the authors and not previously encountered in the literature. The QUBO formulation of the 1D problem of synchronous model-based inversion of seismic data, obtained through this method, is presented. Evaluations are carried out that demonstrate a significantly higher efficiency of the introduced technique in comparison with the standard one, as well as the possibility of solving the 1D problem of synchronous model-based inversion of industrial-scale seismic data (containing ∼1000 time steps) on the latest models of the D-Wave hybrid annealer.

Evgeny Konstantinovich Sklyanin, Leon Armenovich Takhtadzhyan, Lyudvig Dmitrievich Faddeev

Sharada Narsingrao Ohatkar

Quantum computing is a new and exciting area of computational mathematics that has the ability to solve very hard problems that traditional computing methods have not been able to solve for a long time. This abstract goes into detail about how quantum computing can be used in numerical linear algebra, which is an important part of computational mathematics that is used in many fields, such as science, engineering, and data analysis. The idea behind quantum computing is new. It uses quantum bits (qubits) and quantum gates to do calculations in a very different way, based on the rules of quantum physics. Because of this change in thinking, quantum computers might be able to solve some numerical linear algebra problems a lot faster than traditional computers. The outline then talks about some of the most important quantum computing methods and algorithms that are made for numerical linear algebra problems. There are quantum versions of standard algorithms like matrix multiplication, Gaussian elimination, and singular value decomposition. There are also new algorithms that are intended to use quantum parallelism and interference to speed up computations. For situations where full-scale quantum gear is not yet available, quantum-inspired methods are also talked about. These blend conventional and quantum techniques. The abstract talks about the difficulties and chances of using quantum algorithms for numerical linear algebra on quantum hardware systems that are available now and in the near future. It talks about things like error correction, qubit coherence times, and making efficient quantum circuit implementations. Lastly, the abstract talks about how quantum computing might change computational mathematics. It imagines that advances in quantum computing could help solve numerical linear algebra problems that were previously impossible to solve. This could have huge effects on many fields, from machine learning and optimization to quantum chemistry and cryptography. In the end, it stresses how important it is for mathematicians, computer scientists, physicists, and engineers to work together across disciplines in order to fully utilize the transformative power of quantum computing in numerical linear algebra and other areas.

Ningping Cao, Jie Xie, Aonan Zhang +3 more

Abstract Quantum inverse problem (QIP) is the problem of estimating an unknown quantum system from a set of measurements, whereas the classical counterpart is the inverse problem of estimating a distribution from a set of observations. In this paper, we present a neural-network-based method for QIPs, which has been widely explored for its classical counterpart. The proposed method utilizes the quantumness of the QIPs and takes advantage of the computational power of neural networks to achieve remarkable efficiency for the quantum state estimation. We test the method on the problem of maximum entropy estimation of an unknown state ρ from partial information both numerically and experimentally. Our method yields high fidelity, efficiency and robustness for both numerical experiments and quantum optical experiments.

Jean Michel Maillet, V. Terras