Hardware errors are a major obstacle to demonstrating quantum advantage with the quantum approximate optimization algorithm (QAOA). Recently, symmetry verification has been proposed and empirically demonstrated to boost the quantum state fidelity, the expected solution quality, and the success probability of QAOA on a superconducting quantum processor. Symmetry verification uses parity checks that leverage the symmetries of the objective function to be optimized. We develop a theoretical framework for analyzing this approach under local noise and derive explicit formulas for fidelity improvements on problems with global ℤ2symmetry. We numerically investigate the symmetry verification on the MaxCut problem and identify the error regimes in which this approach improves the QAOA objective. We observe that these regimes correspond to the error rates present in near-term hardware. We further demonstrate the efficacy of symmetry verification on an IonQ trapped ion quantum processor where an improvement in the QAOA objective of up to 19.2% is observed.
Hardware errors are a major obstacle to demonstrating quantum advantage with the quantum approximate optimization algorithm (QAOA). Recently, symmetry verification has been proposed and empirically demonstrated to boost the quantum state fidelity, the expected solution quality, and the success probability of QAOA on a superconducting quantum processor. Symmetry verification uses parity checks that leverage the symmetries of the objective function to be optimized. We develop a theoretical framework for analyzing this approach under local noise and derive explicit formulas for fidelity improvements on problems with global ℤ2symmetry. We numerically investigate the symmetry verification on the MaxCut problem and identify the error regimes in which this approach improves the QAOA objective. We observe that these regimes correspond to the error rates present in near-term hardware. We further demonstrate the efficacy of symmetry verification on an IonQ trapped ion quantum processor where an improvement in the QAOA objective of up to 19.2% is observed.
High error rates and limited fidelity of quantum gates in near-term quantum devices are the central obstacles to successful execution of the Quantum Approximate Optimization Algorithm (QAOA). In this paper we introduce an application-specific approach for mitigating the errors in QAOA evolution by leveraging the symmetries present in the classical objective function to be optimized. Specifically, the QAOA state is projected into the symmetry-restricted subspace, with projection being performed either at the end of the circuit or throughout the evolution. Our approach improves the fidelity of the QAOA state, thereby increasing both the accuracy of the sample estimate of the QAOA objective and the probability of sampling the binary string corresponding to that objective value. We demonstrate the efficacy of the proposed methods on QAOA applied to the MaxCut problem, although our methods are general and apply to any objective function with symmetries, as well as to the generalization of QAOA with alternative mixers. We experimentally verify the proposed methods on an IBM Quantum processor, utilizing up to 5 qubits. When leveraging a global bit-flip symmetry, our approach leads to a 23% average improvement in quantum state fidelity.
Quantum error mitigation (QEM) is at the very heart of near-term quantum simulations and lattice gauge theories are no exceptions, rather their physical symmetries provide natural consistency checks on noise quantum states. In this work, we exploit the parity and fermion-number symmetries of a gauge theory, the (1+1)-dimensional Schwinger model, under depolarising noise and investigate symmetry verification under digital quantum simulation. We investigate two set-ups - symmetry- sector post-selection in adiabatic state preparation followed by real-time measurements of the chiral condensate and symmetry verification within a variational quantum eigensolver (VQE). In the first case, post-selection reduces the bias in the chiral condensate consistently removing up to 60% of the quantum noise induced error in our system. Motivated by the observed regularity of the residual bias (in the low-noise regime), we further introduce a global-noise calibration obtained from classically accessible smaller lattices and implemented on larger lattices recovering noiseless chiral condensate values within statistical uncertainty. However, in VQE, symmetry verification does not seem to generally improve the optimised parameters or the fidelity of the prepared states, although it reduces the bias in the estimated ground-state energy. This demonstates that improving a noisy cost-function estimator in variational algorithms does not necessarily improve the outcome of the algorithm. Our results show the strength of symmetry verification in different approaches while establishing that its usefulness critically depends on where it is applied in the computational workflow, and provide practical guidance for symmetry-assisted quantum error mitigation in quantum simulations of lattice gauge theories.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for solving combinatorial optimization problems on near-term quantum hardware. However, its practical deployment remains severely limited by hardware-induced noise and decoherence. In the absence of full fault tolerance, Quantum Error Mitigation (QEM) techniques offer a viable approach to enhance QAOA performance on noisy intermediate-scale quantum (NISQ) devices. In this work, we present a unified classification of QEM strategies specifically tailored for QAOA, systematically categorized into preprocessing, during execution, and post-processing phases. We further classify QAOA deployment settings—such as hardware-constrained devices, stochastic noise-dominated environments, and dense graphs problem—and recommend appropriate QEM techniques for each. A comparative analysis highlights the trade-offs among mitigation accuracy, resource overhead, and robustness to different noise types. By synthesizing recent advances and identifying open challenges, our paper provides both a comprehensive survey and a practical framework for designing robust, noise-resilient QAOA pipelines on near-term quantum platforms.
The Parity Architecture was originally introduced in the context of quantum optimization algorithms to overcome hardware connectivity constraints. Here, we show that its benefits extend beyond this role by identifying specific parity transformations that enhance the success probability of the Quantum Approximate Optimization Algorithm (QAOA) for optimization problems defined on hardware-native and sparse graphs. Numerical simulations suggest that this enhancement originates from the higher-order operators introduced by the Parity representation, which accelerate the propagation of correlations across the physical device. We investigate this mechanism for the Signed Max-Cut problem on 3-regular graph instances and demonstrate its practical relevance on IBM Heron quantum processors. QAOA parameters are first classically optimized on small training instances containing up to 14 vertices and subsequently transferred to larger instances executed on quantum hardware. We consider Signed Max-Cut instances of up to 40 vertices and find that, together with an error mitigation technique, the parity-based QAOA identifies the optimal solutions for all the considered 40-vertex instances, whereas the conventional QAOA fails under the same conditions.
The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.
This paper introduces a noise-aware distributed Quantum Approximate Optimization Algorithm (QAOA) tailored for execution on near-term quantum hardware. Leveraging a distributed framework, we address the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, which are hindered by limited qubit counts and high error rates. Our approach decomposes large QAOA problems into smaller subproblems, distributing them across multiple Quantum Processing Units (QPUs) to enhance scalability and performance. The noise-aware strategy incorporates error mitigation techniques to optimize qubit fidelity and gate operations, ensuring reliable quantum computations. We evaluate the efficacy of our framework using the HamilToniQ Benchmarking Toolkit, which quantifies the performance across various quantum hardware configurations. The results demonstrate that our distributed QAOA framework achieves significant improvements in computational speed and accuracy, showcasing its potential to solve complex optimization problems efficiently in the NISQ era. This work sets the stage for advanced algorithmic strategies and practical quantum system enhancements, contributing to the broader goal of achieving quantum advantage.