We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra, supported by an analytic proof of its inherent resilience to state preparation and measurement errors, as well as midcircuit multiqubit depolarizing noise. Our analysis extends to a broader class of Markovian noise, employing error mitigation strategies that optimize the utilization of quantum resources. By integrating trial-state optimization and classical signal processing into the algorithm, we amplify the signal peak corresponding to the exact target gap beyond the error threshold, thereby significantly reducing gap estimate errors. The algorithm's robustness is demonstrated through noisy simulations on the Qiskit Aer simulator and demonstrations on IBM Quantum processors. These results underscore the potential to enable accurate quantum simulations on near-term noisy quantum devices without resource-intensive error correction.
We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra, supported by an analytic proof of its inherent resilience to state preparation and measurement errors, as well as midcircuit multiqubit depolarizing noise. Our analysis extends to a broader class of Markovian noise, employing error mitigation strategies that optimize the utilization of quantum resources. By integrating trial-state optimization and classical signal processing into the algorithm, we amplify the signal peak corresponding to the exact target gap beyond the error threshold, thereby significantly reducing gap estimate errors. The algorithm's robustness is demonstrated through noisy simulations on the Qiskit Aer simulator and demonstrations on IBM Quantum processors. These results underscore the potential to enable accurate quantum simulations on near-term noisy quantum devices without resource-intensive error correction.
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.
Analog quantum simulation has been proposed as an efficient approach for
probing classically intractable many-body physics. In contrast to digital,
gate-based quantum simulation, the analog approach involves configuring the
quantum hardware to directly mimic the physics of the target system. This
reduces the level of control required and can offer a degree of inherent
robustness, but it comes at the cost that known error-handling techniques may
be inapplicable. Accumulation of error is thus a major challenge facing
medium-scale and large-scale analog quantum simulation with current and
near-term noisy quantum (NISQ) devices. Here we propose a hybrid error
mitigation scheme that can suppress general local Markovian noise in analog
quantum simulators. We employ stochastic error mitigation for physical noise
and use Richardson extrapolation to compensate for model estimation error. We
numerically test the error mitigation scheme for an Ising-type Hamiltonian with
energy relaxation and dephasing noise, and show an improvement of simulation
accuracy by two orders. We assess the resource cost of our error mitigation
scheme and conclude that analog quantum simulation at scale is feasible with
NISQ hardware.
Estimating the energy spectra of quantum many-body systems is a fundamental task in quantum physics, with applications ranging from chemistry to condensed matter. Algorithmic shadow spectroscopy is a recent method that leverages randomized measurements on time-evolved quantum states to extract spectral information. However, implementing accurate time evolution with low-depth circuits remains a key challenge for near-term quantum hardware. In this work, we propose a hybrid quantum-classical protocol that integrates Time Evolution via Probabilistic Angle Interpolation (TE-PAI) into the shadow spectroscopy framework. TE-PAI enables the simulation of time evolution using shallow stochastic circuits while preserving unbiased estimates through quasiprobability sampling. We construct the combined estimator and derive its theoretical properties. Through numerical simulations, we demonstrate that our method accurately resolves energy gaps and exhibits enhanced robustness to gate noise compared to first-order Trotter-based shadow spectroscopy. We further validate the protocol experimentally on up to 20 qubits using IBM quantum hardware. This makes TE-PAI shadow spectroscopy a promising tool for spectral analysis on noisy intermediate-scale quantum (NISQ) devices.
As quantum processors move into the noisy intermediate-scale quantum (NISQ) era, the central question is no longer whether a quantum algorithm is asymptotically faster than its classical counterpart, but whether it can retain a meaningful speedup under realistic noise, compilation, and measurement constraints. This work develops a quantitative framework for characterizing the noise resilience of quantum advantage. We introduce the advantage robustness function RA(ε), which measures how the asymptotic and concrete performance of an algorithm A degrades with physical error rate ε, and we compute it analytically or numerically for twelve representative algorithm families, including Grover search, amplitude estimation, phase estimation, HHL, VQE/QAOA, Hamiltonian simulation, and sampling algorithms. For each class, we derive critical noise thresholds and depth limits beyond which classical algorithms regain supremacy, explicitly incorporating realistic connectivity and compilation overheads. We show that algorithms based on coherent amplitude amplification are more fragile to coherent errors than depolarizing noise, while variational algorithms display a tradeoff between expressivity and robustness. By combining these algorithm-specific robustness curves with current and projected hardware error rates for superconducting, trapped-ion, neutralatom, and photonic platforms, we map out a phase diagram of practical quantum advantage that links problem size, noise rate, and algorithm type. Our analysis identifies promising near-term application windows in risk analytics, small-molecule chemistry, and structured optimization, and also delineates regions where no advantage is realistic, providing valuable guidance for both algorithm designers and hardware architects.
Abstract We present a novel ground-state energy estimation algorithm that is robust under global depolarizing error channels. Building upon the recently developed Quantum Exponential Least Squares (QCELS) algorithm [Ding, Lin, PRX Quantum, 4, 020331, 2023], our new approach incorporates significant advancements to ensure robust estimation while maintaining a polynomial cost in precision. By leveraging the spectral gap of the Hamiltonian effectively, our algorithm overcomes limitations observed in previous methods like quantum phase estimation (QPE) and robust phase estimation (RPE). Going beyond global depolarizing error channels, our work underscores the significance and practical advantages of utilizing randomized compiling techniques to tailor quantum noise towards depolarizing error channels. Our research demonstrates the feasibility of ground-state energy estimation in the presence of depolarizing noise, offering potential advancements in error correction and algorithmic-level error mitigation for quantum algorithms.
Extracting energy spectra from quantum Hamiltonians is a fundamental task for quantum simulation, yet remains challenging on noisy intermediate-scale quantum (NISQ) devices. We propose Measured Quantum Time Evolution (MQTE), an ancilla-free algorithm that estimates energy gaps by applying real-time evolution to a reference state and measuring time-resolved probabilities via repeated projective measurements. Spectral analysis of these signals reveals oscillation frequencies corresponding to eigenvalue differences. Crucially, MQTE exhibits inherent robustness to quantum hardware noise and sampling errors: these disturbances manifest as a white-noise background, which does not distort the underlying spectral structure but rather obscures the frequency information. By increasing the number of measurement samples, the intensity of the background white noise can be suppressed, thereby recovering the original spectral content. We validate the algorithm's performance via numerical simulations on one- and two-dimensional Heisenberg models, demonstrating accurate extraction of energy gaps and resilience against both sampling and circuit-level noise. Experimental implementation on the superconducting quantum processor Tianyan-176-II further confirms the practical feasibility and noise tolerance of MQTE under real hardware conditions. This work provides a robust and scalable framework for quantum spectral estimation in the NISQ era.