Related papers: Randomized Subsystem Descent for Fermion-to-Qubit …

We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

The Fermi-Hubbard model (FHM) on a two dimensional square lattice has long been an important testbed and target for simulating fermionic Hamiltonians on quantum hardware. We present an alternative for quantum simulation of FHMs based on an…

We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…

In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms onto specific quantum hardware. Our approach decomposes the…

We introduce a framework which allows to systematically and arbitrarily scale the code distance of local fermion-to-qubit encodings in one and two dimensions without growing the weights of stabilizers. This is achieved by embedding…

In this work we present a method for generating a fermionic encoding tailored to a set of target fermionic operators and to a target hardware connectivity. Our method uses brute force search, over the space of all encodings which map from…

We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…

Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…

A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…

We present a quantum-inspired algorithm that utilizes Quantum Hamiltonian Descent (QHD) for efficient community detection. Our approach reformulates the community detection task as a Quadratic Unconstrained Binary Optimization (QUBO)…

We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

The natural gradient descent optimisation technique is an efficient optimising protocol for broad classes of classical and quantum systems that takes the underlying geometry of the parameter manifold into account by means of using either…

With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…

We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization in Ref. [1], whose gauge constraints project onto the subspace of the…

We present a new framework for the analysis and design of randomized algorithms for solving various types of linear systems, including consistent or inconsistent, full rank or rank-deficient. Our method is formulated with four randomized…

A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…