Quantum error mitigations for quantum approximate optimization algorithms on IBM quantum processors
Explore the source record for details and available documents.
97 MATHEMATICS AND COMPUTING↗
SEARCH · Engineering Papers
Results for “Quantum Error Mitigation”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning
Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this work, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by 1.26x,1.29x,1.47x, and 2.65 x, respectively.
42 ENGINEERING↗
Uniformly decaying subspaces for error-mitigated quantum computation
Here, we present a general condition to obtain subspaces that decay uniformly in a system governed by the Lindblad master equation and use them to perform error-mitigated quantum computation. The expectation values of dynamics encoded in such subspaces are unbiased estimators of noise-free expectation values. In analogy to the decoherence free subspaces which are left invariant by the action of Lindblad operators, we show that the uniformly decaying subspaces are left invariant (up to orthogonal terms) by the action of the dissipative part of the Lindblad equation. We apply our theory to a system of qubits and qudits undergoing relaxation with varying decay rates and show that such subspaces can be used to eliminate bias up to first-order variations in the decay rates without requiring full knowledge of noise. Since such a bias cannot be corrected through standard symmetry verification, our method can improve error mitigation in dual-rail qubits and, given partial knowledge of noise, can perform better than probabilistic error cancellation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum error mitigation by layerwise Richardson extrapolation
A widely used method for mitigating errors in noisy quantum computers is Richardson extrapolation, a technique in which the overall effect of noise on the estimation of quantum expectation values is captured by a single parameter that, after being scaled to larger values, is eventually extrapolated to the zero-noise limit. We generalize this approach by introducing layerwise Richardson extrapolation (LRE), an error mitigation protocol in which the noise of different individual layers (or larger chunks of the circuit) is amplified and the associated expectation values are linearly combined to estimate the zero-noise limit. The coefficients of the linear combination are analytically obtained from the theory of multivariate Lagrange interpolation. LRE leverages the flexible configurational space of layerwise unitary folding, allowing for a more nuanced mitigation of errors by treating the noise level of each layer of the quantum circuit as an independent variable. Furthermore, we provide numerical simulations demonstrating scenarios where LRE achieves superior performance compared to traditional (single-variable) Richardson extrapolation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Robust Design Under Uncertainty in Quantum Error Mitigation
Error mitigation techniques are crucial to achieving near-term quantum advantage. Classical postprocessing of quantum computation outcomes is a popular approach for error mitigation, which includes methods, such as zero noise extrapolation, virtual distillation, and learning-based error mitigation. However, these techniques have limitations due to the propagation of uncertainty resulting from the finite shot number of a quantum measurement. In this work, we introduce general and unbiased methods for quantifying the uncertainty and error of error-mitigated observables based on the strategic sampling of error mitigation outcomes. We then extend our approach to demonstrate the optimization of performance and robustness of error mitigation under uncertainty. To illustrate our methods, we apply them to zero noise extrapolation and Clifford date regression in the ground state of the XY model simulated using depolarizing and International Business Machines Corporation (IBM) Toronto noise models, respectively. In particular, we optimize the choice of noise levels and the allocation of shots for zero noise extrapolation and the distribution of the training circuits for Clifford data regression. While our methods are readily applicable to any postprocessing-based error mitigation approach, in practice they must not be prohibitively expensive—even though they perform optimizations of the error mitigation hyperparameters requiring sampling of a statistical distribution of error mitigation outcomes. By leveraging surrogate-based optimization, we show that our methods can efficiently perform optimal design for a zero noise extrapolation implementation. We then further demonstrate the transferability of learned zero noise extrapolation hyperparameters to other similar circuits.
97 MATHEMATICS AND COMPUTING↗
Quantum utility-scale error mitigation for quantum quench dynamics in Heisenberg spin chains
Here, we implement a quantum error mitigation method termed self-mitigation, which is comparable to zero-noise extrapolation, at large scales to achieve quantum utility on near-term, noisy quantum computers. We investigate the effectiveness of several quantum error mitigation strategies, including self-mitigation, by simulating quantum quench dynamics for Heisenberg spin chains with system sizes up to 104 qubits using IBM quantum processors. In particular, we discuss the limitations of zero-noise extrapolation and the advantages offered by self-mitigation at large scales. The self-mitigation method demonstrates stable accuracy with large systems of 104 qubits comprising more than 3,000 CNOT gates. Also, we combine the discussed quantum error mitigation methods with practical entanglement entropy measuring methods, and it shows a good agreement with the theoretical estimation. Our study illustrates the usefulness of near-term noisy quantum hardware in examining the quantum quench dynamics of many-body systems at large scales and lays the groundwork for surpassing classical simulations with quantum methods prior to the development of fault-tolerant quantum computers.
97 MATHEMATICS AND COMPUTING↗
Quantum error mitigation for Fourier moment computation
Hamiltonian moments in Fourier space—expectation values of the unitary evolution operator under a Hamiltonian at different times—provide a convenient framework to understand quantum systems. They offer insights into the energy distribution, higher-order dynamics, response functions, correlation information, and physical properties. This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices. Published by the American Physical Society 2025
Kiss, Oriel (ORCID:0000000174613342)↗
scientific ML, AI, and UQ, with applications to quantum error mitigation
Explore the source record for details and available documents.
McKerns, Michael↗
Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning
Quantum computing technology has the potential to revolutionize the simulation of materials and molecules in the near future. A primary challenge in achieving near-term quantum advantage is effectively mitigating the noise effects inherent in current quantum processing units (QPUs). This challenge is also decisive in the context of quantum-classical hybrid schemes employing variational quantum eigensolvers (VQEs) that have attracted significant interest in recent years. In this paper, we present a method that employs parametric Gaussian process regression (GPR) within an active learning framework to mitigate noise in quantum computations, focusing on VQEs. Our approach, grounded in probabilistic machine learning, exploits a custom prior based on the VQE ansatz to capture the underlying correlations between VQE outputs for different variational parameters, thereby enhancing both accuracy and efficiency. We demonstrate the effectiveness of our method on a two-site Anderson impurity model and a eight-site Heisenberg model, using the IBM open-source quantum computing framework, Qiskit, showcasing substantial improvements in the accuracy of VQE outputs while reducing the number of direct QPU energy evaluations. This paper contributes to the ongoing efforts in quantum-error mitigation and optimization, bringing us a step closer to realizing the potential of quantum computing in quantum matter simulations. Published by the American Physical Society 2024
97 MATHEMATICS AND COMPUTING↗
Quantum Time Dynamics Mediated by the Yang–Baxter Equation and Artificial Neural Networks
Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANNs) and the Yang–Baxter equation (YBE). Unlike traditional error mitigation methods, which are computationally intensive, we investigate artificial error mitigation. We developed a novel method that combines ANNs for noise mitigation combined with the YBE to generate noisy data. This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results. The YBE rigorously preserves quantum correlations and symmetries in spin chain simulations in certain classes of integrable lattice models, enabling effective compression of quantum circuits while retaining linear scalability with the number of qubits. This compression facilitates both full and partial implementations, allowing the generation of noisy quantum data on hardware alongside noiseless simulations using classical platforms. By introducing controlled noise through the YBE, we enhance the data set for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in mitigating errors in time-evolving quantum states, providing a scalable framework to enhance quantum computation fidelity, particularly in noisy intermediate-scale quantum (NISQ) systems. We demonstrate the efficacy of this approach by performing quantum time dynamics simulations using the Heisenberg XY Hamiltonian on real quantum devices.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Enhancing quantum annealing accuracy through replication-based error mitigation *
Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.
Djidjev, Hristo N. (ORCID:0000000192868824)↗
Tough Errors Are no Match (TEAM): Optimizing the quantum compiler for noise resilience
This report summarizes Unitary Fund’s contributions to the Department of Energy’s TEAM project (DE-SC0020266) under Thrust 2: Quantum Programming and Compilation. The central outcomes of this work have been the development of Mitiq, an open-source Python toolkit for applying quantum error mitigation (QEM) techniques to noisy quantum programs, and the invention, benchmarking and theoretical investigation of novel QEM techniques. Additional outcomes include the development of other open source software packages for the usage, simulation and control of quantum computers.
97 MATHEMATICS AND COMPUTING↗
Error-mitigated nonorthogonal quantum eigensolver via shadow tomography
We present a shadow-tomography-enhanced nonorthogonal quantum eigensolver (NOQE) for more efficient and accurate electronic structure calculations on near-term quantum devices. By integrating shadow tomography into the NOQE, the measurement cost scales linearly rather than quadratically with the number of reference states, while also reducing the required qubits and circuit depth by half. This approach enables extraction of all matrix elements via randomized measurements and classical postprocessing. We analyze its sample complexity and show that, for small systems, it remains constant in the high-precision regime, while for larger systems, it scales linearly with the system size. We further apply shadow-based error mitigation to suppress noise-induced bias without increasing quantum resources. Demonstrations on the hydrogen molecule in the strongly correlated regime achieve chemical accuracy under realistic noise, showing that our method is both resource-efficient and noise-resilient for practical quantum chemistry simulations in the near term.
quantum algorithms & computation↗
Group-theoretic error mitigation enabled by classical shadows and symmetries
Abstract Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy called symmetry-adjusted classical shadows , by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global U(1) symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry.
Zhao, Andrew (ORCID:0000000202990277)↗
Capturing the Page curve and entanglement dynamics of black holes in quantum computers
Quantum computers are emerging technologies expected to become important tools for exploring various aspects of fundamental physics in the future. Therefore, we pose the question of whether quantum computers can help us to study the Page curve and the black hole information dynamics, which has been a key focus in fundamental physics. In this regard, we rigorously examine the qubit transport model, a toy qubit model of black hole evaporation on IBM’s superconducting quantum computers, to shed light on this question. Specifically, we implement the quantum simulation of the scrambling dynamics in black holes using an efficient random unitary circuit. Furthermore, we employ the swap-based many-body interference protocol and the randomized measurement protocol to measure the entanglement entropy of Hawking radiation qubits in this model. Finally, by incorporating quantum error mitigation techniques into our challenging implementation of entanglement entropy measurement protocols on the IBM quantum hardware, we accurately determine the Rényi entropy in the qubit transport model, thus showcasing the utility of quantum computers for future investigations of complex quantum systems.
97 MATHEMATICS AND COMPUTING↗
Quantum subspace expansion in the presence of hardware noise
Finding ground state energies on current quantum processing units (QPUs) using algorithms such as the variational quantum eigensolver (VQE) continues to pose challenges. Hardware noise severely affects both the expressivity and trainability of parameterized quantum circuits, limiting them to shallow depths in practice. Here, we demonstrate that both issues can be addressed by synergistically integrating VQE with a quantum subspace expansion, allowing for an optimal balance between quantum and classical computing capabilities and costs. We perform a systematic benchmark analysis of the iterative quantum-assisted eigensolver in the presence of hardware noise. We determine ground state energies of 1D and 2D mixed-field Ising spin models on noisy simulators and the IBM QPUs ibmq_quito (5 qubits) and ibmq_guadalupe (16 qubits). To maximize accuracy, we propose a suitable criterion to select the subspace basis vectors according to the trace of the noisy overlap matrix. Finally, we show how to systematically approach the exact solution by performing controlled quantum error mitigation based on probabilistic error reduction on the noisy backend fake_guadalupe.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum Computing for High-Energy Physics: State of the Art and Challenges
Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage—namely, a significant (in some cases exponential) speedup of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small-scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models that are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this Roadmap paper, led by CERN, DESY, and IBM, we provide the status of high-energy physics quantum computations and give examples of theoretical and experimental target benchmark applications, which can be addressed in the near future. Having in mind hardware with about 100 qubits capable of executing several thousand two-qubit gates, where possible, we also provide resource estimates for the examples given using error-mitigated quantum computing. The ultimate declared goal of this task force is therefore to trigger further research in the high-energy physics community to develop interesting use cases for demonstrations on near-term quantum computers.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Final Report for Zero-noise Extrapolation for Quantum Sensing
Final Report for the DOE EXPRESS 2022 project "Zero-noise Extrapolation for Quantum Sensing." Contains a description of the motivation, accomplishments, and implications of the technical work performed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗