2024/02/29 by Joanna Majsak, Daniel McNulty, Majsak, Joanna +3 · 3 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear physics research studies #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2402.19230
openalex publication_date 2024/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 O(N log(N)/ε2) and O(N2 log(N)/ε2) 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 O(N1/2) with O(N3/2) two-qubit gates, offering an improvement over fermionic and matchgate classical shadows that require depth O(N) and O(N2) 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.