Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space

Abstract

Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding that maps a system with $N$ physical sites onto only $\lceil {\log }_{2}N\rceil$ qubits while maintaining a clear correspondence with the underlying physical model. Within this reduced register, we construct a compatible variational circuit and a Gray-code-inspired measurement strategy whose number of global settings grows only logarithmically with system size. To quantify the overall hardware load, we introduce a volumetric efficiency metric that combines the number of qubit, circuit depth, and the number of measurement settings into a single measure, expressing the overall computation costs. Using this metric, we show that the total space-time-sampling volume required in a variational loop can be reduced dramatically from $N^2$ to $(logN{)}^3$ for hardware efficient ansatz, allowing an exponential reduction in time and size of the quantum hardware. These results demonstrate that large, structured solid-state Hamiltonians can be simulated on substantially smaller quantum registers with controlled sampling overhead and manageable circuit complexity, extending the reach of variational quantum algorithms on near-term devices.

21 pages, 6 figures

References in corpus (14)

• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum computational chemistry
• The Variational Quantum Eigensolver: a review of methods and best practices
• Variational Quantum Computation of Excited States
• Quantum-state preparation with universal gate decompositions
• Linear scaling Krylov subspace method for large scale {\it ab initio} electronic structure calculations of metals
• The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry
• A systematic variational approach to band theory in a quantum computer
• Efficient and Accurate Linear Algebraic Methods for Large-scale Electronic Structure Calculations with Non-orthogonal Atomic Orbitals
• Rise of conditionally clean ancillae for efficient quantum circuit constructions
• Resource-efficient utilization of quantum computers
• Combined tight-binding and configuration interaction study of unfolded electronic structure of G-color center in Si