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Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We discuss the realization of a universal set of ultrafast single- and two-qubit operations with superconducting quantum circuits and investigate the most relevant physical and technical limitations that arise when pushing for faster and…
Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on…
Quantum circuit optimization is a central task in Quantum Computing, as current Noisy Intermediate Scale Quantum devices suffer from error propagation that often scales with the number of operations. Among quantum operations, the CNOT gate…
Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…
With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum…
Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
Shor's algorithm is one of the most significant quantum algorithms. Shor's algorithm can factor large integers with a certain success probability in polynomial time. However, Shor's algorithm requires an unbearable amount of qubits in the…
We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage…
Quantum machine learning offers promising advantages for classification tasks, but noise, decoherence, and connectivity constraints in current devices continue to limit the efficient execution of feature map-based circuits. Gate Assessment…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
Shor's algorithm, which given appropriate hardware can factorise an integer $N$ in a time polynomial in its binary length $L$, has arguable spurred the race to build a practical quantum computer. Several different quantum circuits…
Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. To accommodate the diverse characteristics of quantum chemical systems,…
Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the…
We review the staircase algorithm to decompose the exponential of a generalized Pauli matrix and we propose two alternative recursive methods which offer more efficient quantum circuits. The first algorithm we propose, defined as the…
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. In QAOA, a quantum circuit is trained -- by repeatedly adjusting circuit parameters -- to solve a problem.…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…
We embed 1-layer QAOA circuits into the larger class of parameterized Instantaneous Quantum Polynomial circuits to produce an improved variational quantum algorithm for solving combinatorial optimization problems. The use of analytic…
The Quantum Approximate Optimization Algorithm (QAOA) is a well-known hybrid quantum-classical algorithm for combinatorial optimization problems. Improving QAOA involves enhancing its approximation ratio while addressing practical…