A generalized framework for quantum subspace diagonalization

TL;DR

This paper introduces a flexible, memory-efficient framework for quantum subspace diagonalization that improves computational performance for Hamiltonian eigenproblems in quantum chemistry and condensed matter physics.

Contribution

It presents a unified, operator-extended approach with optimized data structures enabling scalable, sparse, and matrix-free solutions adaptable to various eigensolvers.

Findings

Achieves up to an order of magnitude reduction in memory and runtime.

Supports both sparse matrix construction and matrix-free solutions.

Demonstrates effectiveness on quantum chemistry and condensed matter examples.

Abstract

We present a framework for computing the solution to Hamiltonian eigenproblems in a subspace defined by bit-strings sampled from a quantum computer. Hamiltonians are represented using an extended alphabet that includes projection and ladder operators, yielding a unified solution method for qubit and fermionic systems. Operators are grouped and sorted so that only non-zero terms are evaluated and a minimal number of subspace lookup operations are performed. Bit-strings are expressed using bit-sets to reduce memory consumption and allow for evaluating operators with no intrinsic limitation on the number of qubits. Subspaces defined over bit-sets are stored in a hash map format that allows for efficient indexing and lookup operations. Our method can be used to directly construct sparse matrix representations or obtain matrix-free solutions. Users are free to utilize these in their eigensolver of choice. We show the benefits of our framework by computing the ground-state solution to examples from condensed matter physics and quantum chemistry with less memory and runtime compared to existing techniques, in some cases by an order of magnitude or more. This work provides a flexible interface for performant quantum-classical eigensolutions for candidate quantum advantage applications.