Related papers: Operating with Quantum Integers: an Efficient 'Mul…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
Efficient encoding of classical data into quantum state -- currently referred to as quantum encoding -- holds crucial significance in quantum computation. For finite-size databases and qubit registers, a common strategy of the quantum…
The encoding of classical to quantum data mapping through trigonometric functions within arithmetic-based quantum computation algorithms leads to the exploitation of multivariate distributions. The studied variational quantum gate learning…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
Quantum algorithms often apply classical operations, such as arithmetic or predicate checks, over a quantum superposition of classical data; these so-called oracles are often the largest components of a quantum program. To ease the…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a…
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity.…
Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt…
Quantum computing has the potential to surpass the capabilities of current classical computers when solving complex problems. Combinatorial optimization has emerged as one of the key target areas for quantum computers as problems found in…
The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
A perturbative approach to quantum field theory involves the computation of loop integrals, as soon as one goes beyond the leading term in the perturbative expansion. First I review standard techniques for the computation of loop integrals.…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…