A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians
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| Format: | Preprint |
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2024
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| _version_ | 1866915403233492992 |
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| author | Majsak, Joanna McNulty, Daniel Oszmaniec, Michał |
| author_facet | Majsak, Joanna McNulty, Daniel Oszmaniec, Michał |
| contents | We propose a simple scheme to estimate fermionic observables and Hamiltonians relevant in quantum chemistry and correlated fermionic systems. Our approach is based on implementing a measurement that jointly measures noisy versions of any product of two or four Majorana operators in an $N$ mode fermionic system. To realize our measurement we use: (i) a randomization over a set of unitaries that realize products of Majorana fermion operators; (ii) a unitary, sampled at random from a constant-size set of suitably chosen fermionic Gaussian unitaries; (iii) a measurement of fermionic occupation numbers; (iv) suitable post-processing. Our scheme can estimate expectation values of all quadratic and quartic Majorana monomials to $ε$ precision using $\mathcal{O}(N \log(N)/ε^2)$ and $\mathcal{O}(N^2 \log(N)/ε^2)$ measurement rounds respectively, matching the performance offered by fermionic classical shadows. In certain settings, such as a rectangular lattice of qubits which encode an $N$ mode fermionic system via the Jordan-Wigner transformation, our scheme can be implemented in circuit depth $\mathcal{O}(N^{1/2})$ with $\mathcal{O}(N^{3/2})$ two-qubit gates, offering an improvement over fermionic and matchgate classical shadows that require depth $\mathcal{O}(N)$ and $\mathcal{O}(N^2)$ two-qubit gates. By benchmarking our method on exemplary molecular Hamiltonians and observing performances comparable to fermionic classical shadows, we demonstrate a novel, competitive alternative to existing strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians Majsak, Joanna McNulty, Daniel Oszmaniec, Michał Quantum Physics Mathematical Physics We propose a simple scheme to estimate fermionic observables and Hamiltonians relevant in quantum chemistry and correlated fermionic systems. Our approach is based on implementing a measurement that jointly measures noisy versions of any product of two or four Majorana operators in an $N$ mode fermionic system. To realize our measurement we use: (i) a randomization over a set of unitaries that realize products of Majorana fermion operators; (ii) a unitary, sampled at random from a constant-size set of suitably chosen fermionic Gaussian unitaries; (iii) a measurement of fermionic occupation numbers; (iv) suitable post-processing. Our scheme can estimate expectation values of all quadratic and quartic Majorana monomials to $ε$ precision using $\mathcal{O}(N \log(N)/ε^2)$ and $\mathcal{O}(N^2 \log(N)/ε^2)$ measurement rounds respectively, matching the performance offered by fermionic classical shadows. In certain settings, such as a rectangular lattice of qubits which encode an $N$ mode fermionic system via the Jordan-Wigner transformation, our scheme can be implemented in circuit depth $\mathcal{O}(N^{1/2})$ with $\mathcal{O}(N^{3/2})$ two-qubit gates, offering an improvement over fermionic and matchgate classical shadows that require depth $\mathcal{O}(N)$ and $\mathcal{O}(N^2)$ two-qubit gates. By benchmarking our method on exemplary molecular Hamiltonians and observing performances comparable to fermionic classical shadows, we demonstrate a novel, competitive alternative to existing strategies. |
| title | A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2402.19230 |