Related papers: Implementation of analytic functions with quantum …
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow…
Quantum circuit synthesis and compilation are critical components in the quantum computing stack, both for contemporary quantum systems, where efficient use of limited resources is essential, as well as for large-scale fault-tolerant…
Realizing a conceptual quantum algorithm on an actual physical device necessitates the algorithm's quantum circuit description to undergo certain transformations in order to adhere to all constraints imposed by the hardware. In this regard,…
Quantum computing is an emerging technology, promising a paradigm shift in computing, and allowing for speedups in many different problems. However, quantum devices are still in their early stages, most with only a small number qubits. This…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…
In this Letter, we present two analytic expressions that most generally simulate $n$-qubit controlled-$U$ gates with standard one-qubit gates and CNOT gates using exponential and polynomial complexity respectively. Explicit circuits and…
Quantum circuit execution is the central task in quantum computation. Due to inherent quantum-mechanical constraints, quantum computing workflows often involve a considerable number of independent measurements over a large set of slightly…
Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…
Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum…
Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new…
There are quantum algorithms for finding a function $f$ satisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
Existing abstract models of quantum computation make reference to circuit elements, much in contrast to their classical counterparts. Circuits, as a model of computation, substantially limit algorithmic expression and obscure high-level…
Quantum logic gates must perform properly when operating on their standard input basis states, as well as when operating on complex superpositions of these states. Experiments using superconducting qubits have validated the truth table for…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
We describe a solid state implementation of a quantum computer using ballistic single electrons as flying qubits in 1D nanowires. We show how to implement all the steps required for universal quantum computation: preparation of the initial…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…