Related papers: Unitaria: Quantum Linear Algebra via Block Encodin…
This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
Discrete Laplacian operators arise ubiquitously in scientific computing and frequently appear in quantum algorithms for tasks such as linear algebra, Hamiltonian simulation, and partial differential equations. Block encoding provides the…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly…
The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when…
Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…
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…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
We introduce Quantum Index Algebra (QIA) as a finite, index-based algebraic framework for representing and manipulating quantum operators on Hilbert spaces of dimension $2^m$. In QIA, operators are expressed as structured combinations of…
The linear combination of unitaries (LCU) is a fundamental quantum algorithm primitive that embeds non-unitary operators via post-selection on an ancilla register. In standard LCU, only the $|0\dots0\rangle$ ancilla outcome is retained; the…
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.…
Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Quantum trajectory methods can be used for a wide range of open quantum systems to solve the master equation by unraveling the density operator evolution into individual stochastic trajectories in Hilbert space. This C++ class library…