Work

Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space

Year: 2026

Type: article

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 ⌈ log 2 ⁡ N ⌉ 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 qubits, 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 ( log ⁡ N ) 3 for a 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.

Source: Quantum

DOI: 10.22331/q-2026-05-08-2099

Authors: Martin Plesch, Martin Friák, Ijaz Ahamed Mohammad