The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial optimization problems. We present a scheme to parallelize this approach for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest-neighbor interactions. The protocol consists of single qubit operations […]
In computing architectures, one important factor is the tradeoff between the need to couple bits of information (quantum or classical) to each other and to an external drive and the need to isolate them well enough in order to protect the information for an extended period of time. In the case of superconducting quantum circuits, […]
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, for example, the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). In this article, we present a decomposition-based approach to extend […]
This article addresses the question of implementing a maximum flow algorithm on directed graphs in a formulation suitable for a quantum annealing computer. Three distinct approaches are presented. In all three cases, the flow problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem amenable to quantum annealing. The first implementation augments a graph […]
Many challenging scheduling, planning, and resource allocation problems come with real-world input data and hard problem constraints, and reduce to optimizing a cost function over a combinatorially defined feasible set, such as colorings of a graph. Toward tackling such problems with quantum computers using quantum approximate optimization algorithms, we present novel efficient quantum alternating operator […]
This article outlines our point of view regarding the applicability, state-of-the-art, and potential of quantum computing for problems in finance. We provide an introduction to quantum computing as well as a survey on problem classes in finance that are computationally challenging classically and for which quantum computing algorithms are promising. In the main part, we […]
We consider the problem of optimizing the achievable EPR-pair distribution rate between multiple source-destination pairs in a quantum Internet, where the repeaters may perform a probabilistic Bell-state measurement and we may impose a minimum end-to-end fidelity as a requirement. We construct an efficient linear programming (LP) formulation that computes the maximum total achievable entanglement distribution […]
We provide a procedure to construct entanglement-assisted Calderbank-Shor-Steane (CSS) codes over qudits from the parity check matrices of two classical codes over F q , where q = p k , p is prime, and k is a positive integer. The construction procedure involves the proposed Euclidean Gram-Schmidt orthogonalization algorithm, followed by a procedure to extend the quantum operators […]
Due to several physical limitations in the realization of quantum hardware, today’s quantum computers are qualified as noisy intermediate-scale quantum (NISQ) hardware. NISQ hardware is characterized by a small number of qubits (50 to a few hundred) and noisy operations. Moreover, current realizations of superconducting quantum chips do not have the ideal all-to-all connectivity between […]
Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators to be translated into physical operators acting on physical quantum states. In this article, we propose a mathematical framework for synthesizing physical circuits that implement logical Clifford operators for stabilizer codes. Circuit synthesis is enabled by representing the […]