Curator's Take
This work represents a significant step toward using near-term quantum computers for complex many-body physics problems that are classically intractable in the thermodynamic limit. The researchers cleverly combine quantum algorithms with numerical linked-cluster expansion techniques to extract infinite-system properties from small quantum calculations, demonstrating the approach on IonQ's 20-qubit trapped-ion system across multiple challenging models including the transverse-field Ising model. What makes this particularly noteworthy is their development of the "CX-test" as an alternative to traditional measurement schemes, and their honest assessment of current hardware limitations when dealing with the noise amplification that comes from classical post-processing steps like matrix inversions. This hybrid quantum-classical framework could become a powerful tool for studying quantum many-body systems once quantum hardware improves enough to provide the requisite measurement precision.
— Mark Eatherly
Summary
We run a numerical linked-cluster expansion with a quantum algorithm (NLCE+QA), computing ground-state energies and one quasi-particle dispersions in the thermodynamic limit using a 20-qubit trapped-ion quantum processing unit (QPU). The NLCE+QA framework extracts thermodynamic-limit properties from small-cluster calculations, making it naturally suited for near-term quantum devices. Projector-based block-diagonalization schemes such as projective cluster-additive transformation (PCAT) are essential to NLCE+QA, and they involve matrix inversion and square root operations that amplify measurement noise. A central question is therefore whether current hardware can provide expectation values that are accurate enough to withstand non-linear classical post-processing. We explore this challenge for the transverse-field Ising model (TFIM) in one dimension, on a ladder geometry, as well as in a longitudinal field in one dimension. For the quantum algorithm, we consider adiabatic state preparation (ASP), as well as a variational quantum eigensolver (VQE) trained on a classical device. The final expectation values are obtained from the QPU, using a novel alternative to the Hadamard test that we name the CX-test. We explore the regimes currently attainable on quantum devices and comment on the improvements needed for quantum computers to achieve results beyond classical reach.