Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910212631298048 |
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| author | Plesch, Martin Friák, Martin Mohammad, Ijaz Ahamed |
| author_facet | Plesch, Martin Friák, Martin Mohammad, Ijaz Ahamed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space Plesch, Martin Friák, Martin Mohammad, Ijaz Ahamed Quantum Physics 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. |
| title | Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.00247 |