Related papers: Quantum algorithms for solving a drift-diffusion e…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
We present a variational quantum algorithm that solves the one-dimensional diffusion problem with a space-dependent diffusion constant $D(x)$. This problem is relevant for the exchange of hydroxide ions across a multi-layer membrane in an…
We present two experimental schemes that can be used to implement the Factorized Quantum Lattice-Gas Algorithm for the 1D Diffusion Equation with Persistent-Current Qubits. One scheme involves biasing the PC Qubit at multiple flux bias…
Simulating differential equations on classical computers becomes an intractable problem if the grid size is extremely large. Quantum computers are believed to achieve a possibly exponential speedup in the matrix operation. In this paper, we…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
When using unitary gate sequences, the growth in depth of many quantum circuits with output size poses significant obstacles to practical quantum computation. The quantum fan-out operation, which reduces the circuit depth of quantum…
Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared…
Scalability is currently one of the most sought-after objectives in the field of quantum computing. Distributing a quantum circuit across a quantum network is one way to facilitate large computations using current quantum computers. In this…
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
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…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
We introduce crosstalk-robust gate sets, which are obtained using a novel, scalable optimal control problem exploiting locality. Through the suppression of pairwise quantum crosstalk, the gate sets enable robustness that extends to…
This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a…