Related papers: A Decomposition Method for the Hybrid Quantum-Clas…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
To address the issue of excessive quantum resource requirements in Kuperberg's algorithm for the dihedral hidden subgroup problem, this paper proposes a distributed algorithm based on the function decomposition. By splitting the original…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
Interacting with a standard computer can enhance the capabilities of current quantum computers already today, particularly by offloading certain computations to the standard computer. Quantum computers that interact with standard computers…
Near-term large quantum computers are not able to operate as a single processing unit. It is therefore required to partition a quantum circuit into smaller parts, and then each part is executed on a small unit. This approach is known as…
We introduce a quantum decomposition algorithm (QDA) that decomposes the problem $\frac{\partial \rho}{\partial t}=\mathcal{L}\rho=\lambda \rho$ into a summation of eigenvalues times phase-space variables. One interesting feature of QDA…
Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
Proposals for scalable quantum computing devices suffer not only from decoherence due to the interaction with their environment, but also from severe engineering constraints. Here we introduce a practical solution to these major concerns,…
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to…
The rapid pace of recent advancements in numerical computation, notably the rise of GPU and TPU hardware accelerators, have allowed tensor network (TN) algorithms to scale to even larger quantum simulation problems, and to be employed more…
This paper presents an integer decomposition method. The method first writes an integer as a polynomial with 2 as variable that its coefficients are zero or one. Then, suppose that an integer is decomposed into product of such two…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…