Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space

• URL: http://arxiv.org/abs/2601.00247v1
• Date: Thu, 01 Jan 2026 07:43:31 GMT
• Title: Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space
• Authors: Martin Plesch, Martin Friák, Ijaz Ahamed Mohammad,
• Abstract summary: Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements.<n>We introduce a logarithmic-qubit encoding that maps a system with $N$ physical sites onto only $lceil log N rceil$ qubits.<n>Within this reduced register, we construct a compatible variational circuit and a Gray-code-inspired measurement strategy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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