Quantum Energy Gap Estimation Achieves Accuracy with 20 Qubits and Randomization

Scientists are tackling the crucial problem of accurately estimating energy gaps , vital for fields spanning chemistry and materials science! Hugo Pages (Graduate School of Engineering Science, The University of Osaka), Chusei Kiumi (Strasbourg University), and Yuto Morohoshi (Graduate School of Engineering Science, The University of Osaka) et al. present a novel approach integrating Time Evolution via Probabilistic Angle Interpolation (TE-PAI) with shadow spectroscopy. This research is significant because it offers a pathway to spectral analysis on near-term quantum computers, overcoming limitations imposed by the difficulty of creating complex quantum circuits , their hybrid classical-quantum protocol uses shallow, randomised circuits to achieve unbiased estimates and demonstrably improves robustness against gate noise, validated through simulations and experiments on up to 20 qubits using IBM hardware.

A key innovation lies in the formulation of a combined estimator that accounts for the nested quasiprobability sampling structure inherent in the protocol. Through rigorous analysis, scientists prove that the method yields unbiased estimators, providing confidence in the accuracy of the spectral analysis. This work opens new avenues for spectral analysis on noisy intermediate-scale quantum (NISQ) devices, potentially enabling more efficient and reliable quantum simulations.

Furthermore, the protocol’s simplicity, requiring only Pauli rotation gates with fixed angles, and avoidance of ancillary qubits or controlled time evolution make it particularly well-suited for current hardware limitations. Numerical simulations then demonstrated the method’s ability to accurately resolve energy gaps, showcasing its precision in spectral analysis. This technique requires only straightforward time evolution of the Hamiltonian, avoiding the need for ancillary qubits or complex controlled time evolution, a simplification that improves compatibility with NISQ devices. By integrating TE-PAI, the study pioneers a pathway towards spectral analysis on noisy intermediate-scale quantum (NISQ) devices, promising a valuable tool for future quantum simulations and analyses.

TE-PAI improves energy spectra estimation with noise

Scientists achieved a breakthrough in estimating energy spectra, a fundamental task with applications spanning chemistry to condensed matter physics, by developing a hybrid quantum-classical protocol. Through numerical simulations, the team demonstrated that their method accurately resolves energy gaps and exhibits enhanced robustness to gate noise when compared to standard Trotter-based shadow spectroscopy. Researchers benchmarked the performance of their approach against conventional algorithmic shadow spectroscopy on a 20-qubit system, confirming the practical viability of the method on contemporary noisy quantum devices. This highlights its potential for simulating many-body quantum systems within the current NISQ era. Measurements confirm that the TE-PAI method significantly reduces the circuit depth required for time evolution, employing a decomposition of Pauli rotation gates represented as RP,θ = a1(θ)RP,1 + a2(θ)RP,2 + a3(θ)RP,3. Future research will focus on optimising this trade-off and exploring applications on quantum devices with varying error rates.