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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.04222 |
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| _version_ | 1866912142611972096 |
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| author | Mari, Andrea |
| author_facet | Mari, Andrea |
| contents | We show that counting the number of collisions (re-sampled bitstrings) when measuring a random quantum circuit provides a practical benchmark for the quality of a quantum computer and a quantitative noise characterization method. We analytically estimate the difference in the expected number of collisions when sampling bitstrings from a pure random state and when sampling from the classical uniform distribution. We show that this quantity, if properly normalized, can be used as a "collision anomaly" benchmark or as a "collision volume" test which is similar to the well-known quantum volume test, with advantages (no classical computing cost) and disadvantages (high sampling cost). We also propose to count the number of cross-collisions between two independent quantum computers running the same random circuit in order to obtain a cross-validation test of the two devices. Finally, we quantify the sampling cost of quantum collision experiments. We find that the sampling cost for running a collision volume test on state-of-the-art processors (e.g.~20 effective clean qubits) is quite small: less than $10^5$ shots. For large-scale experiments in the quantum supremacy regime the required number of shots for observing a quantum signal in the observed number of collisions is currently infeasible ($>10^{12}$), but not completely out of reach for near-future technology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04222 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting collisions in random circuit sampling for benchmarking quantum computers Mari, Andrea Quantum Physics We show that counting the number of collisions (re-sampled bitstrings) when measuring a random quantum circuit provides a practical benchmark for the quality of a quantum computer and a quantitative noise characterization method. We analytically estimate the difference in the expected number of collisions when sampling bitstrings from a pure random state and when sampling from the classical uniform distribution. We show that this quantity, if properly normalized, can be used as a "collision anomaly" benchmark or as a "collision volume" test which is similar to the well-known quantum volume test, with advantages (no classical computing cost) and disadvantages (high sampling cost). We also propose to count the number of cross-collisions between two independent quantum computers running the same random circuit in order to obtain a cross-validation test of the two devices. Finally, we quantify the sampling cost of quantum collision experiments. We find that the sampling cost for running a collision volume test on state-of-the-art processors (e.g.~20 effective clean qubits) is quite small: less than $10^5$ shots. For large-scale experiments in the quantum supremacy regime the required number of shots for observing a quantum signal in the observed number of collisions is currently infeasible ($>10^{12}$), but not completely out of reach for near-future technology. |
| title | Counting collisions in random circuit sampling for benchmarking quantum computers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.04222 |