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We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
Quantum computers are expected to contribute more efficient and accurate ways of modeling economic processes. Quantum hardware is currently available at a relatively small scale, but effective algorithms are limited by the number of logic…
In 2005, H{\o}yer and \v{S}palek showed that constant-depth quantum circuits augmented with multi-qubit Fanout gates are quite powerful, able to compute a wide variety of Boolean functions as well as the quantum Fourier transform. They also…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
Feynman's circuit-to-Hamiltonian construction enables the mapping of a quantum circuit to a time-independent Hamiltonian. This model introduces a Hilbert space made from an ancillary clock register tracking the progress of the computation.…
In the noisy intermediate-scale quantum era, variational quantum algorithms (VQAs) have emerged as a promising avenue to obtain quantum advantage. However, the success of VQAs depends on the expressive power of parameterised quantum…
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…
Stabilizer simulation can efficiently simulate an important class of quantum circuits consisting exclusively of Clifford gates. However, all existing extensions of this simulation to arbitrary quantum circuits including non-Clifford gates…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
Hamiltonian encoding was introduced as a technique for revealing the mechanism of controlled quantum systems. It does so by decomposing the evolution into pathways between the computational basis states, where each pathway has an associated…
The "Sum-Over-Paths" formalism is a way to symbolically manipulate linear maps that describe quantum systems, and is a tool that is used in formal verification of such systems. We give here a new set of rewrite rules for the formalism, and…
Despite the continuous advancements in size and robustness of real quantum devices, reliable large-scale quantum computers are not yet available. Hence, classical simulation of quantum algorithms remains crucial for testing new methods and…
Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom and arbitrarily long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices, however, the…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
Motivated by recent studies of quantum computational complexity in quantum field theory and holography, we discuss how weighting certain classes of gates building up a quantum circuit more heavily than others does affect the complexity.…
Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and the vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a…
Power circuits are data structures which support efficient algorithms for highly compressed integers. Using this new data structure it has been shown recently by Myasnikov, Ushakov and Won that the Word Problem of the one-relator Baumslag…