Our study demonstrates successful error mitigation of indistinguishably-related noise in a quantum photonic processor through the application of the zero-noise extrapolation (ZNE) technique. By measuring observable values at different error levels, we were able to extrapolate toward a noise-free regime. We examined the impact of partial distinguishability of photons in a two-qubit processor implementing the variational quantum eigensolver for a Schwinger Hamiltonian. Our findings highlight the effectiveness of the extrapolation technique in mitigating indistinguishably-related noise and improving the accuracy of the Hamiltonian eigenvalue estimation.
Our study demonstrates successful error mitigation of indistinguishably-related noise in a quantum photonic processor through the application of the zero-noise extrapolation (ZNE) technique. By measuring observable values at different error levels, we were able to extrapolate toward a noise-free regime. We examined the impact of partial distinguishability of photons in a two-qubit processor implementing the variational quantum eigensolver for a Schwinger Hamiltonian. Our findings highlight the effectiveness of the extrapolation technique in mitigating indistinguishably-related noise and improving the accuracy of the Hamiltonian eigenvalue estimation.
Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm's sensitivity to these errors without increasing the number of required qubits. Here we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH+ molecule at 0.8A˚ in the presence of experimental noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time stretching the two-qubit gates, scaling the sideband detuning parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find that time stretching and sideband detuning scaling fail to scale the noise on our particular hardware in a way that can be extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve error suppression of 96.8, resulting in an energy estimate within $\ensuremath{-}0.004\ifmmode\pm\else\textpm\fi{}0.04$ hartree of the ground state energy. This is an improvement, but still outside the chemical accuracy threshold of 0.0016 hartree. Our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.
We propose a quantum error mitigation strategy for the variational quantum eigensolver (VQE) algorithm. We find, via numerical simulation, that very small amounts of coherent noise in VQE can cause substantially large errors that are difficult to suppress by conventional mitigation methods, and yet our proposed mitigation strategy is able to significantly reduce these errors. The proposed strategy is a combination of previously reported techniques, namely randomized compiling (RC) and zero-noise extrapolation (ZNE). Intuitively, randomized compiling turns coherent errors in the circuit into stochastic Pauli errors, which facilitates extrapolation to the zero-noise limit when evaluating the cost function. Our numerical simulation of VQE for small molecules shows that the proposed strategy can mitigate energy errors induced by various types of coherent noise by up to two orders of magnitude.
The indirect-control paradigm offers a scalable approach to quantum computation by restricting external operations to a small subset of qubits, whereas the entire system evolves under its intrinsic many-body Hamiltonian. This framework reduces hardware complexity and limits the noise introduced through control channels. Recently, Anan et al. proposed an implementation of the variational quantum eigensolver (VQE) within this indirect-control architecture. However, the impact and integration of quantum error mitigation techniques in such a setting remain largely unexplored. In particular, zero-noise extrapolation (ZNE), a widely used error mitigation strategy, has not yet been systematically adapted to indirect-control VQE. A key requirement of ZNE is the controlled amplification of noise, which is commonly achieved through circuit-level techniques such as unitary folding. In the indirect-control framework, however, quantum operations are largely governed by continuous time-evolution under the system Hamiltonian, making the construction of physically realizable inverse operations non-trivial. In this study, we investigate the feasibility of implementing ZNE within the indirect-controlVQEframework.We address the challenges associated with unitary folding in the presence of time-evolution operators and, with a minimal relaxation of the indirect-control constraint, we propose a ZNE-based error-mitigation strategy that exploits the symmetry of the one-dimensional XY spin chain.
Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline in performance due to the presence of stochastic errors and limited coherence time. In this work, we develop a recipe for mitigating quantum gate errors using zero-noise extrapolation. We introduce an experimentally amenable method to control error strength in the circuit. We utilize the fact that gate errors in a physical quantum device are distributed inhomogeneously over different qubits and qubit pairs. As a result, one can achieve different circuit error sums based on the manner in which abstract qubits in the circuit are mapped to a physical device. We apply the proposed protocol to variational quantum algorithms and find that the estimated energy is approximately linear with respect to the circuit error sum (CES). Consequently, a linear fit through the energy-CES data, when extrapolated to zero CES, can approximate the energy estimated by a noiseless variational algorithm. We demonstrate this numerically and investigate the applicability range of the technique.
Near term quantum processors operate in a noise dominated regime, motivating error mitigation techniques that recover accurate expectation values without full fault tolerance. Zero Noise Extrapolation (ZNE) is a widely used but biased error mitigation method that lacks rigorous error bounds. Its effective application requires nontrivial technical choices, most notably the selection of noise scaling factors and extrapolation models, making ZNE sensitive to user expertise and often necessitating costly trial and error procedures. Here, we introduce Folding Free Zero Noise Extrapolation (FF-ZNE), a method that removes the need for noise factor selection by achieving effective noise amplification without circuit folding. FF-ZNE exploits isomorphic hardware layouts with distinct native noise profiles, such that executing a fixed circuit across these layouts induces controllable variations in the effective noise strength. Under a depolarizing noise model, we analytically show that the resulting extrapolation admits a fixed linear form, eliminating extrapolator choice and enabling a seamless, user independent mitigation procedure. We further propose two algorithms that identify sets of isomorphic hardware layouts on which a given circuit yields sufficiently distinct expectation values to enable reliable zero noise extrapolation. Experiments on a 133 qubit IBM Quantum device demonstrate that FF-ZNE yields mitigated expectation values with average deviations of ~6% and 4.5% for up to 50 qubit EfficientSU2 (sparse) and Hamiltonian simulation (dense) circuits, respectively. The method is thus scalable and applicable to a broad range of circuits. By eliminating noise factor and extrapolator selection, FF-ZNE transforms zero noise extrapolation from a technique requiring expert tuning into a practical, scalable, and broadly accessible error mitigation method for current quantum hardware.
As quantum computing advances towards practical applications, reducing errors remains a crucial frontier for developing near-term devices. Errors in the quantum gates and quantum state readout could result in noisy circuits, which would prevent the acquisition of the exact expectation values of the observables. Although ultimate robustness to errors is known to be achievable by quantum error correction-based fault-tolerant quantum computing, its successful implementation demands large-scale quantum processors with low average error rates that are not yet widely available. In contrast, quantum error mitigation (QEM) offers more immediate and practical techniques, which do not require extensive resources and can be readily applied to existing quantum devices to improve the accuracy of the expectation values. Here, we report the implementation of a zero-noise extrapolation-based error mitigation technique on a silicon spin qubit platform. This technique has recently been successfully demonstrated for other platforms such as superconducting qubits, trapped-ion qubits, and photonic processors. We first explore three methods for amplifying noise on a silicon spin qubit: global folding, local folding, and pulse stretching, using a standard randomized benchmarking protocol. We then apply global folding-based zero-noise extrapolation to the state tomography and achieve a state fidelity of 99.96% (98.52%), compared to the unmitigated fidelity of 75.82% (82.16%) for different preparation states. The results show that the zero-noise extrapolation technique is a versatile approach that is generally adaptable to quantum computing platforms with different noise characteristics through appropriate noise amplification methods.