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arXiv:2404.01412 · Quantum

Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping

Filip B. Maciejewski, Jacob Biamonte, Stuart Hadfield, Davide Venturelli

Published Nov 6, 2025• 10 citations
arXivHTMLPDF

Abstract

We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that features a global attractor state. In a standard setting, such noise can be detrimental to the quantum optimization performance. Our algorithm bootstraps the noise attractor state by iteratively gauge-transforming the cost-function Hamiltonian in a way that transforms the noise attractor into higher-quality solutions. The transformation effectively changes the attractor into a higher-quality solution of the Hamiltonian based on the results of the previous step. The end result is that noise aids variational optimization, as opposed to hindering it. We present an improved Quantum Approximate Optimization Algorithm (QAOA) runs in experiments on Rigetti's quantum device. We report approximation ratios 0.9 - 0.96 for random, fully connected graphs on n = 82 qubits, using only depth p = 1 QAOA with NDAR. This compares to 0.34 - 0.51 for standard p = 1 QAOA with the same number of function calls.

DOI
10.22331/q-2025-11-06-1906

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We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that features a global attractor state. In a standard setting, such noise can be detrimental to the quantum optimization performance. Our algorithm bootstraps the noise attractor state by iteratively gauge-transforming the cost-function Hamiltonian in a way that transforms the noise attractor into higher-quality solutions. The transformation effectively changes the attractor into a higher-quality solution of the Hamiltonian based on the results of the previous step. The end result is that noise aids variational optimization, as opposed to hindering it. We present an improved Quantum Approximate Optimization Algorithm (QAOA) runs in experiments on Rigetti's quantum device. We report approximation ratios 0.9 - 0.96 for random, fully connected graphs on n = 82 qubits, using only depth p = 1 QAOA with NDAR. This compares to 0.34 - 0.51 for standard p = 1 QAOA with the same number of function calls.
Progress towards a quantum advantage using known heuristic methods for combinatorial optimization is impeded by hardware noise and limited qubit count. Here, we propose a noise-aware adaptive approach to quantum approximate optimization, Noise-Directed Adaptive Warm-Starting (ND-AWS), that builds on recent concepts such as Warm-Start QAOA and Noise-Directed Adaptive Remapping. By leveraging bitflip gauge transformations, our algorithm exploits amplitude-damping-like noise components. We experimentally implement high-performance quantum optimization ansätze on 100-qubit Ising Hamiltonians, showing that ND-AWS generally improves the performance over a non-gauge-transformed iterative Warm-Starting variant, at no additional circuit cost. This places our results among the highest-quality demonstrations of quantum optimization with similar ansätze at this scale. Crucially, the simplicity of the framework opens the door for future enhancements such as adaptive bias schedules, and integration with classical solvers.
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the existing quantum processing units (QPUs) are of relatively small size, and canonical mappings of QUBO via the Ising model require one qubit per variable, rendering direct large-scale optimization infeasible. In classical optimization, a general strategy for addressing many large-scale problems is via multilevel/multigrid methods, where the large target problem is iteratively coarsened and the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentally test how existing QPUs perform when used as a sub-solver within such a multilevel strategy. To this aim, we combine and extend (via additional classical processing steps) the recently proposed Noise-Directed Adaptive Remapping (NDAR) and Quantum Relax & Round (QRR) algorithms. We first demonstrate the effectiveness of our heuristic extensions on Rigetti's superconducting transmon device Ankaa-2. We find approximate solutions to 10 instances of fully connected 82-qubit Sherrington-Kirkpatrick graphs with random integer-valued coefficients obtaining normalized approximation ratios (ARs) in the range∼0.98−1.0\sim 0.98-1.0∼0.98−1.0, and the same class with real-valued coefficients (ARs∼0.94−1.0)\sim 0.94-1.0)∼0.94−1.0). Then, we implement the extended NDAR and QRR algorithms as subsolvers in the multilevel algorithm for 6 large-scale graphs with at most∼27,000\sim 27,000∼27,000variables. In practice, the QPU (with classical post-processing steps) is used to find approximate solutions to dozens of at most 82-qubit problems, which are iteratively used to construct the global solution. We observe that quantum optimization results are competitive in terms of the quality of solutions when compared to classical heuristics used as subsolvers within the multilevel approach. Reproducibility: source code and data will be available at [1].
Quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve NP-hard problems in near-term gate-based noisy quantum devices. In QAOA, the gate parameters of a parameterized quantum circuit (PQC) are varied by a classical optimizer to generate a quantum state with a significant support to the optimal solution. The existing analysis fails to consider nonidealities in the qubit quality i.e., short lifetime and imperfect gate operations in a realistic quantum hardware. In this article, we study the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analysis indicates that QAOA performance is noise-sensitive (especially higher-depth QAOA instances). Therefore, the optimal number of stages (p-value) for any QAOA instance is limited by the noise in the target hardware as opposed to the current perception that QAOA will provide monotonically better performance with higher-depth. We show that the two-qubit gate error has to be decreased by more than 75% of the current state-of-the-art levels to attain a performance within 10% of the maximum value for the lowest-depth QAOA.
Molecular docking, a critical task in drug discovery, represents a highly promising application domain for quantum computing. While the Quantum Approximate Optimization Algorithm (QAOA) shows potential, its performance on near-term quantum devices is limited by noise susceptibility and optimization challenges such as barren plateaus. To address these limitations, we apply Adaptive Bias Fields QAOA (ABF-QAOA) to solve molecular docking problems mapped to Ising Hamiltonians. Our results demonstrate that ABF-QAOA achieves accelerated convergence and higher solution accuracy compared to standard QAOA. In addition, under simulated quantum noise conditions, ABF-QAOA maintains higher solution quality, showcasing significantly enhanced noise resilience. This work establishes ABF-QAOA as a robust quantum approach for molecular docking on noisy intermediate-scale quantum (NISQ) hardware.
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.
The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wave function into one that encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wave function at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MaxCut problems that, for a fixed accuracy, this procedure decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA, and no additional measurements. This modified algorithm enhances the prospects for quantum advantage for certain optimization problems.