Error-mitigated fermionic classical shadows on noisy quantum devices

Abstract

Abstract Efficiently estimating fermionic Hamiltonian expectation values is vital for simulating various physical systems. Classical shadow (CS) algorithms offer a solution by reducing the number of quantum state copies needed, but noise in quantum devices poses challenges. We propose an error-mitigated CS algorithm assuming gate-independent, time-stationary, and Markovian (GTM) noise. For n -qubit systems, our algorithm, which employs the easily prepared initial state $$\left\vert {0}^{n}\right\rangle \,\left\langle {0}^{n}\right\vert$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfenced> <mml:mspace/> <mml:mfenced> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> assumed to be noiseless, efficiently estimates k -RDMs with $$\widetilde{{{{\mathcal{O}}}}}(k{n}^{k})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mo>̃</mml:mo> </mml:mover> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mi>k</mml:mi> <mml:msup> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> state copies and $$\widetilde{{{{\mathcal{O}}}}}(\sqrt{n})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mo>̃</mml:mo> </mml:mover> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msqrt> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> calibration measurements for GTM noise with constant fidelities. We show that our algorithm is robust against noise types like depolarizing, damping, and X -rotation noise with constant strengths, showing scalings akin to prior CS algorithms for fermions but with better noise resilience. Numerical simulations confirm our algorithm’s efficacy in noisy settings, suggesting its viability for near-term quantum devices.

Topics & Concepts