The Problem with Quantum Computers

László Gyöngyösi

Quantum computers provide a valuable resource to solve computational problems. The maximization of the objective function of a computational problem is a crucial problem in gate-model quantum computers. The objective function estimation is a high-cost procedure that requires several rounds of quantum computations and measurements. Here, we define a method for objective function estimation of arbitrary computational problems in gate-model quantum computers. The proposed solution significantly reduces the costs of the objective function estimation and provides an optimized estimate of the state of the quantum computer for solving optimization problems.

B. Skuse

M. I. Dyakonov

Samyak Jhaveri, A. Krone-Martins, Cristina Videira Lopes

Quantum computers are becoming a reality. The advantage of quantum computing is that it has the potential to solve computationally complex problems in a fixed amount time, independent of the size of the problem. However, the kinds of problems for which these computers are a good fit, and the ways to express those problems, are substantially different from the kinds of problems and expressions used in classical computing. Quantum annealers, in particular, are currently the most promising and available quantum computing devices in the short term. However, they are also the most foreign compared to classical programs, as they require a different kind of computational thinking. In order to ease the transition into this new world of quantum computing, we present a novel quantum approach to a well-known software problem: code clone detection. We express code clone detection as a subgraph isomorphism problem that is mapped into a quadratic optimization problem, and solve it using a DWave quantum annealing computer. We developed a quantum annealing algorithm that compares Abstract Syntax Trees (AST) and reports an energy value that indicates how similar they are.

Vyacheslav Yu. Korolyov, Oleksandr Khodzinskyi

Introduction. Quantum computers provide several times faster solutions to several NP-hard combinatorial optimization problems in comparison with computing clusters. The trend of doubling the number of qubits of quantum computers every year suggests the existence of an analog of Moore's law for quantum computers, which means that soon they will also be able to get a significant acceleration of solving many applied large-scale problems. The purpose of the article is to review methods for creating algorithms of quantum computer mathematics for combinatorial optimization problems and to analyze the influence of the qubit-to-qubit coupling and connections strength on the performance of quantum data processing. Results. The article offers approaches to the classification of algorithms for solving these problems from the perspective of quantum computer mathematics. It is shown that the number and strength of connections between qubits affect the dimensionality of problems solved by algorithms of quantum computer mathematics. It is proposed to consider two approaches to calculating combinatorial optimization problems on quantum computers: universal, using quantum gates, and specialized, based on a parameterization of physical processes. Examples of constructing a half-adder for two qubits of an IBM quantum processor and an example of solving the problem of finding the maximum independent set for the IBM and D-wave quantum computers are given. Conclusions. Today, quantum computers are available online through cloud services for research and commercial use. At present, quantum processors do not have enough qubits to replace semiconductor computers in universal computing. The search for a solution to a combinatorial optimization problem is performed by achieving the minimum energy of the system of coupled qubits, on which the task is mapped, and the data are the initial conditions. Approaches to solving combinatorial optimization problems on quantum computers are considered and the results of solving the problem of finding the maximum independent set on the IBM and D-wave quantum computers are given. Keywords: quantum computer, quantum computer mathematics, qubit, maximal independent set for a graph.

Scott Aaronson