Measurement reduction for expectation values via fine-grained commutativity
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914047583059968 |
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| author | DalFavero, Ben Sarkar, Rahul Rowland, Jeremiah Camps, Daan Sawaya, Nicolas LaRose, Ryan |
| author_facet | DalFavero, Ben Sarkar, Rahul Rowland, Jeremiah Camps, Daan Sawaya, Nicolas LaRose, Ryan |
| contents | We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubit-wise commutativity and (full) commutativity. We apply this notion, which we call $k$-commutativity, to measuring expectation values of observables in quantum circuits and show a reduction in the number measurements at the cost of increased circuit depth. Last, we discuss the asymptotic measurement complexity of $k$-commutativity for several families of $n$-qubit Hamiltonians, showing examples with $O(1)$, $O(\sqrt{n})$, and $O(n)$ scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11840 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Measurement reduction for expectation values via fine-grained commutativity DalFavero, Ben Sarkar, Rahul Rowland, Jeremiah Camps, Daan Sawaya, Nicolas LaRose, Ryan Quantum Physics We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubit-wise commutativity and (full) commutativity. We apply this notion, which we call $k$-commutativity, to measuring expectation values of observables in quantum circuits and show a reduction in the number measurements at the cost of increased circuit depth. Last, we discuss the asymptotic measurement complexity of $k$-commutativity for several families of $n$-qubit Hamiltonians, showing examples with $O(1)$, $O(\sqrt{n})$, and $O(n)$ scaling. |
| title | Measurement reduction for expectation values via fine-grained commutativity |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.11840 |