Quantum Computing Lab

VQAs in Quantum Chemistry & Physics

We are focused on developing algorithms for calculations in Chemistry and Physics that can use hybrid quantum-classical infrastructures so that with the development of NISQ infrastructures, they gain a computational advantage over classical algorithms. The main topic of the research is the State-Averaged Orbital Optimized Variational Quantum Eigensolver (SAOOVQE). This new method allows obtaining potential surface areas of molecules, their gradients, electron couplings, non-adiabatic couplings, and other quantities for the ground and lower excited states with a "democratic" approach to all states. Within the group, we develop not only additional theory in this direction but also the software solution itself published on the Internet in open-source mode. Apart from SAOOVQE, we are devoted to the application of classical Variational Quantum Eigensolver (VQE) to the calculations of the properties of topological insulators both in the adiabatic regime and with the use of quantum entanglement theory. As part of these activities, we also participate in developing the well-established Quantics and Qiskit toolkits.

Solving Optimization Problems Using QAOA

The Quantum Approximate Optimization Algorithm (QAOA) is another type of Variational Quantum Algorithm (VQA). Similar to VQE, it aims to find the minimum eigenvalue, but in this case, the corresponding value of the state vector is of greater importance. This eigenvector should ideally represent the solution to the optimization problem encoded in the operator used. The applicability of this algorithm is only limited by the feasibility of encoding the given optimization problem into such an operator. Therefore, it can be utilized for a broad spectrum of combinatorial optimization problems, including Set Packing, Graph Partitioning, Job Sequencing, and Traveling Salesman, among others. Moreover, there are intriguing possibilities for employing QAOA in various domains such as finance (portfolio optimization), power engineering (enhancing grid resilience), communication (binary symbol detection), biochemistry (protein folding), computer vision (object detection), machine learning (model training), and more. Our experimentation involves tuning this algorithm to achieve improved accuracy and faster convergence towards the correct solution to the problem.

Quantum Machine Learning

Quantum machine learning is a research and engineering area that explores the interplay of phenomena of quantum mechanics and machine learning. Such intrinsic features of quantum mechanics as linearity, randomness, superposition, and entanglement can be naturally employed to process data using quantum resources. Many classical machine learning techniques use linear algebra and probability theory as their foundations; therefore, a natural mapping exists between the mathematical theory of machine learning and the two first features of quantum mechanics. Yet those last two phenomena open the door to a new era of computational power, allowing us to tackle previously too complex or time-consuming challenges.

• Devising certification and learning techniques for quantum operations
• Creating new validation and benchmarking methods of NISQ architectures
• Using Quantum networks to quantum algorithms
• Developing the causal structure theory

Quantum Factorization of Semiprimes

The exponential computational complexity of the factorization of large semiprimes is the basis of the security of RSA – the most widespread current cryptosystem used for secure data transmission. The best current factorization algorithms, programmable on classical computers, are of sub-exponential complexity. Today's supercomputers would take billions of years to successfully factorize an RSA key of 2048 bits (the currently recommended and most used length).

It is, therefore, essential for the security of global data transmission to know that even quantum computers cannot factor such a long key in a reasonable time and thus get to the transmitted information.

There are basically two ways to factorize semiprimes using a quantum computer. The first uses the well-known Shor's algorithm, which complicates the need for a quantum implementation of a modular exponentiation function. Therefore, this algorithm has so far been able to factorize only the number 21 on a quantum computer, and ambiguous results were measured when trying to factorize the number 35. Our efforts aim to factorize much larger numbers using this algorithm successfully.

The second way is to convert the factorization problem into an optimization problem. This can then be solved by quantum annealing or adiabatic quantum computation, which is the basis of the aforementioned QAOA. Much larger numbers have been factorized in this way (the largest so far is 1099551473989). Still, the success of these factorizations has depended heavily on classical calculations to reduce the number of qubits needed. As part of solving optimization problems using QAOA, we also deal with this method of factorization.

Quantum Circuits Optimization