Machine Learning-based Quantum Error Mitigation for Variational Algorithms

Daniil Rabinovich; Kirill Lakhmanskiy; Nikita Korolev

arxiv: 2606.02697 · v1 · pith:G4HJF4G3new · submitted 2026-06-01 · 🪐 quant-ph

Machine Learning-based Quantum Error Mitigation for Variational Algorithms

Nikita Korolev , Kirill Lakhmanskiy , Daniil Rabinovich This is my paper

Pith reviewed 2026-06-28 14:08 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum error mitigationmachine learningvariational quantum eigensolverNISQClifford circuitszero noise extrapolationSherrington-Kirkpatrick Hamiltonian

0 comments

The pith

Machine learning error mitigation trained on near-Clifford circuits achieves several-fold suppression in variational quantum eigensolvers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a machine learning-based quantum error mitigation method for variational algorithms that avoids the need for noiseless training data. Instead, it generates training examples by classically simulating circuits composed mostly of Clifford gates. The trained model then corrects the output of full variational circuits with any parameter values and applies to different but structurally similar Hamiltonians. When tested on the variational quantum eigensolver for the Sherrington-Kirkpatrick model with up to twelve qubits, the approach reduces errors by several times under various noise models and beats zero-noise extrapolation when noise levels are high.

Core claim

The proposed ML-QEM protocol generates training data by simulating (near-)Clifford circuits. This data is used for model selection and training, producing a mitigation model that can correct variational circuits with arbitrary parameters and transfer across different target Hamiltonians of similar structure. Benchmarks on VQE for the Sherrington-Kirkpatrick Hamiltonian show consistent several-fold error suppression and superior performance over ZNE in the high-noise regime.

What carries the argument

An ML-QEM protocol that trains on data from simulated near-Clifford circuits to produce a mitigation model for variational circuits.

If this is right

Several-fold error suppression across all tested settings
Superior performance to ZNE in high-noise regime
The model generalizes to variational circuits with arbitrary parameters
The model transfers across different target Hamiltonians of similar structure
Evidence for applicability to present-day NISQ processors

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This training strategy could reduce computational overhead for developing mitigation models.
The method might improve the trainability of larger variational algorithms on noisy hardware.
Combining this with other mitigation techniques could yield additional gains.
Generalization might hold for other quantum algorithms beyond VQE if the circuit structure is similar.

Load-bearing premise

The mitigation model trained on near-Clifford circuits generalizes to arbitrary-parameter variational circuits and transfers to different Hamiltonians of similar structure.

What would settle it

Failure to observe error suppression when the model is applied to a variational circuit whose parameters differ substantially from those used in training or to a Hamiltonian with different structure.

Figures

Figures reproduced from arXiv: 2606.02697 by Daniil Rabinovich, Kirill Lakhmanskiy, Nikita Korolev.

**Figure 3.** Figure 3: FIG. 3. Noiseless, noisy and mitigated cost landscapes with [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. VQE optimization dynamics for the depolarizing [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

read the original abstract

Machine Learning-based quantum error mitigation (ML-QEM) has emerged as a promising approach for improving the performance of noisy quantum algorithms. However, existing ML-QEM methods often have restricted applicability to variational circuits and rely on inaccessible noiseless training data. In this work, we propose a practical ML-QEM protocol tailored to variational quantum algorithms, which generates training data by simulating (near-)Clifford circuits. This data is used for model selection and training, producing a mitigation model that can correct variational circuits with arbitrary parameters and transfer across different target Hamiltonians of similar structure. We benchmark the proposed method on the Variational Quantum Eigensolver (VQE) task for the Sherrington-Kirkpatrick Hamiltonian of up to $n=12$ qubits under various noise models, analyzing its effect on trainability and comparing its performance against standard Zero-Noise Extrapolation (ZNE). The results demonstrate consistent several-fold error suppression across all tested settings and superior performance over ZNE in the high-noise regime, providing evidence for the applicability of the proposed protocol to present-day NISQ processors.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a concrete protocol for training ML error mitigators on simulated near-Clifford circuits so the model can handle arbitrary variational parameters and transfer across similar Hamiltonians, with benchmarks showing gains over ZNE.

read the letter

The main thing here is a training protocol that generates data from simulated near-Clifford circuits, then uses that to pick and fit an ML model meant to correct full variational circuits without needing noiseless targets. They apply it to VQE on the Sherrington-Kirkpatrick model up to 12 qubits under several noise models, track effects on trainability, and report several-fold error reduction that beats zero-noise extrapolation at higher noise levels.

The protocol itself is the clearest addition. Prior ML-QEM often needs ideal data or stays limited to fixed circuits; this one tries to make the training distribution accessible while claiming the resulting model stays useful when parameters vary freely and when the target Hamiltonian changes but keeps similar structure. The direct ZNE comparison on the same task is also useful for context.

The soft spot is exactly the generalization step the stress-test flags. Training happens on circuits whose angles sit near 0 or π/2, yet the claim is that the corrections work for optimized variational circuits whose angles range over [0, 2π). If the underlying noise model or the learned mapping is sensitive to that distribution shift, the reported suppression on the SK instances would not carry over to real runs. The abstract asserts the transfer works, but the paper needs explicit checks that model selection actually enforces parameter independence rather than fitting the Clifford-like ensemble. Cross-Hamiltonian transfer rests on the “similar structure” qualifier, which narrows the practical scope.

This is for people working on NISQ variational algorithms who want mitigation that can be trained without perfect simulators. A reader already running VQE or testing error mitigation would find the protocol and the ZNE numbers worth examining.

It should go to peer review. The problem is current, the method is spelled out enough to test, and the benchmarks are on a standard instance even if the generalization claim needs tighter evidence.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a machine learning-based quantum error mitigation (ML-QEM) protocol for variational quantum algorithms. Training data is generated via simulation of (near-)Clifford circuits for model selection and training; the resulting model is claimed to correct variational circuits with arbitrary parameters and to transfer across different target Hamiltonians of similar structure. Benchmarks on the VQE task for the Sherrington-Kirkpatrick Hamiltonian (up to n=12 qubits) under various noise models report consistent several-fold error suppression and superior performance relative to zero-noise extrapolation (ZNE) in the high-noise regime.

Significance. If the generalization from near-Clifford training data to arbitrary variational parameters holds and is robustly validated, the protocol would address a key practical limitation of existing ML-QEM methods by eliminating the need for inaccessible noiseless training data, offering a potentially useful tool for improving the performance of NISQ variational algorithms.

major comments (2)

[Abstract] Abstract: the central claim that the mitigation model 'can correct variational circuits with arbitrary parameters' rests on training exclusively on (near-)Clifford circuits (parameters near 0 or π/2). No explicit ablation, hold-out test set, or comparison of performance on circuits whose rotation angles are sampled uniformly from [0,2π) versus the training distribution is reported; without this, the several-fold suppression observed on the SK-model instances does not establish transfer to optimized variational circuits.
[Abstract] Abstract and benchmark description: the reported results claim 'consistent several-fold error suppression' and superiority over ZNE, yet the manuscript provides no error bars, full methods details on the ML architecture/training procedure, or statistical verification of generalization across parameter regimes and Hamiltonians. This leaves the empirical support at the level of a high-level sketch rather than a load-bearing demonstration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments. Below we provide point-by-point responses to the major comments and outline the revisions we will make to address the concerns raised.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the mitigation model 'can correct variational circuits with arbitrary parameters' rests on training exclusively on (near-)Clifford circuits (parameters near 0 or π/2). No explicit ablation, hold-out test set, or comparison of performance on circuits whose rotation angles are sampled uniformly from [0,2π) versus the training distribution is reported; without this, the several-fold suppression observed on the SK-model instances does not establish transfer to optimized variational circuits.

Authors: The benchmarks presented involve VQE optimization on the Sherrington-Kirkpatrick Hamiltonian, during which the variational parameters are adjusted away from the near-Clifford values used in training. The consistent error suppression observed thus provides evidence of transfer to arbitrary parameters. Nevertheless, to more rigorously demonstrate this, we will include an explicit ablation study in the revised manuscript. This will feature a hold-out test set where rotation angles are sampled uniformly from [0, 2π) and compare performance against the near-Clifford training distribution. revision: yes
Referee: [Abstract] Abstract and benchmark description: the reported results claim 'consistent several-fold error suppression' and superiority over ZNE, yet the manuscript provides no error bars, full methods details on the ML architecture/training procedure, or statistical verification of generalization across parameter regimes and Hamiltonians. This leaves the empirical support at the level of a high-level sketch rather than a load-bearing demonstration.

Authors: We will enhance the manuscript by adding error bars to all quantitative results, providing more detailed descriptions of the ML architecture and training procedure (expanding on the existing Methods section), and including statistical verification such as multiple independent runs and tests across additional parameter regimes and Hamiltonians. These changes will ensure the empirical results meet the standards for a load-bearing demonstration. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical ML training and benchmarking are independent of target claims

full rationale

The paper's central results rest on training ML models exclusively on simulated (near-)Clifford data and then measuring error suppression on separate VQE instances for the Sherrington-Kirkpatrick model, with direct comparison to ZNE. No equations or procedures are shown to reduce by construction to their own fitted inputs, no uniqueness theorems are imported via self-citation, and no ansatz is smuggled through prior work. The generalization claim is presented as an empirical outcome rather than a definitional necessity, making the derivation chain self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no explicit free parameters, axioms, or invented entities are detailed beyond the general use of ML on Clifford-simulated data for error mitigation.

pith-pipeline@v0.9.1-grok · 5719 in / 1093 out tokens · 38434 ms · 2026-06-28T14:08:13.203366+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

66 extracted references · 1 canonical work pages · 1 internal anchor

[1]

For modeling two-qubit gate errors, we assume the noise affects only the specific qubits considered, i.e

Depolarizing noise [34], one of the most commonly used noise models in theoretical studies, with the 3 quantum channel E(ρ)depol = p d 1d + (1 − p)ρ, (5) where 1d is a d-dimensional identity. For modeling two-qubit gate errors, we assume the noise affects only the specific qubits considered, i.e. d = 4
[2]

Pauli noise [35], a more general, asymmetric version of the former model, with a single-qubit quantum channel of the form E(ρ)Pauli = (1 − px − py − pz)ρ + pxXρX +pyY ρY + pzZρZ, (6) where px, py, pz are the probabilities of applying the corresponding Pauli operators. In the scope of this work, we parametrize the single-qubit Pauli channel with a single s...
[3]

Composite noise model [36] consisting of three noise channels: depolarization (5), amplitude damping
[4]

black box

and phase damping [38] channels. A single- qubit amplitude damping channel with damping rate γ is described as Eamp(ρ) = E0ρE0 + E1ρE1, (7) where E0 = 1 0 0 √1 − γ , E 1 = 0 √γ 0 0 . (8) A single-qubit phase damping channel with a de- phasing rate λ is given by Eph(ρ) = K0ρK0 + K1ρK1, (9) K0 = 1 0 0 √ 1 − λ , K 1 = 0 0 0 √ λ . (10) To model realistic two-...
[5]

As this ansatz already uses Clifford entangling opera- tions (CNOTs) the circuit generation requires replacing only single qubit rotations with Clifford operations. It is important to note that the resulting circuits are not unique to the specific variational ansatz used; tailoring the consideration to any other ansatz with a similar en- tangling layer to...
[6]

Quantum computing in the nisq era and beyond

John Preskill. Quantum computing in the nisq era and beyond. Quantum, 2:79, August 2018

2018
[7]

Valor, Julien Gacon, Caroline Tornow, Luciano Bello, Stefan Woerner, and Daniel J

Johannes Weidenfeller, Lucia C. Valor, Julien Gacon, Caroline Tornow, Luciano Bello, Stefan Woerner, and Daniel J. Egger. Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware. Quantum, 6:870, December 2022

2022
[8]

Scaling trapped ion quantum computers using fast gates and microtraps

Alexander K Ratcliffe, Richard L Taylor, Joseph J Hope, and Andr´ e RR Carvalho. Scaling trapped ion quantum computers using fast gates and microtraps. Physical Re- view Letters, 120(22):220501, 2018

2018
[9]

Numerical simula- tion of the performance of single qubit gates for trapped ions

LA Akopyan, O Lakhmanskaya, S Yu Zarutskiy, ND Ko- rolev, O Guseva, and K Lakhmanskiy. Numerical simula- tion of the performance of single qubit gates for trapped ions. JETP Letters, 116(8):580–585, 2022

2022
[10]

Hegde, Jingfu Zhang, and Dieter Suter

Swathi S. Hegde, Jingfu Zhang, and Dieter Suter. Toward the speed limit of high-fidelity two-qubit gates. Physical Review Letters, 128(23), June 2022

2022
[11]

Mills, Charles R

Adam R. Mills, Charles R. Guinn, Michael J. Gullans, Anthony J. Sigillito, Mayer M. Feldman, Erik Nielsen, and Jason R. Petta. Two-qubit silicon quantum processor with operation fidelity exceeding 99 Science Advances , 8(14), April 2022

2022
[12]

Theory of quantum error correction for general noise

Emanuel Knill, Raymond Laflamme, and Lorenza Viola. Theory of quantum error correction for general noise. Physical Review Letters , 84(11):2525, 2000

2000
[13]

Realization of quantum error correction

John Chiaverini, Dietrich Leibfried, Tobias Schaetz, Mur- ray D Barrett, RB Blakestad, Joseph Britton, Wayne M Itano, John D Jost, Emanuel Knill, Christopher Langer, et al. Realization of quantum error correction. Nature, 432(7017):602–605, 2004

2004
[14]

Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C

M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. Mc- Clean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles. Variational quantum algorithms. Na- ture Reviews Physics , 3(9):625–644, August 2021

2021
[15]

Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik

Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys., 94:015004, Feb 2022

2022
[16]

Near-term quantum computing techniques: Varia- tional quantum algorithms, error mitigation, circuit com- pilation, benchmarking and classical simulation

He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long. Near-term quantum computing techniques: Varia- tional quantum algorithms, error mitigation, circuit com- pilation, benchmarking and classical simulation. Science China Physics, Mechanics & Astronomy , 66(5):250302, 2023

2023
[17]

Measuring the capa- bilities of quantum computers

Timothy Proctor, Kenneth Rudinger, Kevin Young, Erik Nielsen, and Robin Blume-Kohout. Measuring the capa- bilities of quantum computers. Nature Physics, 18(1):75– 79, 2022

2022
[18]

Quantum error correction for beginners

Simon J Devitt, William J Munro, and Kae Nemoto. Quantum error correction for beginners. Reports on Progress in Physics , 76(7):076001, 2013

2013
[19]

Quantum error mitigation

Zhenyu Cai, Ryan Babbush, Simon C Benjamin, Suguru Endo, William J Huggins, Ying Li, Jarrod R McClean, and Thomas E O’Brien. Quantum error mitigation. Re- views of Modern Physics , 95(4):045005, 2023

2023
[20]

Gambetta

Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. Error mitigation for short-depth quantum circuits. Phys- ical Review Letters , 119(18), November 2017

2017
[21]

Gupta, Ewout van den Berg, Maika Takita, Diego Riste, Kristan Temme, and Abhinav Kandala

Riddhi S. Gupta, Ewout van den Berg, Maika Takita, Diego Riste, Kristan Temme, and Abhinav Kandala. Probabilistic error cancellation for dynamic quantum cir- cuits, 2023

2023
[22]

Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, An- drea Mari, and William J. Zeng. Digital zero noise ex- trapolation for quantum error mitigation. In 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), page 306–316. IEEE, October 2020

2020
[23]

Coles, and Lukasz Cincio

Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. Error mitigation with clifford quantum- circuit data. Quantum, 5:592, November 2021

2021
[24]

Adap- tive quantum error mitigation using pulse-based inverse 11 evolutions

Ivan Henao, Jader P Santos, and Raam Uzdin. Adap- tive quantum error mitigation using pulse-based inverse 11 evolutions. npj Quantum Information , 9(1):120, 2023

2023
[25]

Machine learning for practical quantum error mitigation

Haoran Liao, Derek S Wang, Iskandar Sitdikov, Ciro Sal- cedo, Alireza Seif, and Zlatko K Minev. Machine learning for practical quantum error mitigation. Nature Machine Intelligence, 6(12):1478–1486, 2024

2024
[26]

Learning-based quantum error mitigation

Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C Benjamin, and Ying Li. Learning-based quantum error mitigation. PRX Quantum , 2(4):040330, 2021

2021
[28]

A machine learning-based error mitigation approach for reliable software development on ibm’s quantum com- puters

Asmar Muqeet, Shaukat Ali, Tao Yue, and Paolo Arcaini. A machine learning-based error mitigation approach for reliable software development on ibm’s quantum com- puters. In Companion Proceedings of the 32nd ACM In- ternational Conference on the Foundations of Software Engineering, pages 80–91, 2024

2024
[29]

Echo-evolution data generation for quantum error mitigation via neural networks: D

Danila Babukhin. Echo-evolution data generation for quantum error mitigation via neural networks: D. babukhin. Quantum Information Processing, 23(12):405, 2024

2024
[30]

Ridge regression

Gary C McDonald. Ridge regression. Wiley Interdisci- plinary Reviews: Computational Statistics , 1(1):93–100, 2009

2009
[31]

Xgboost: A scalable tree boosting system

Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting system. In Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining , pages 785–794, 2016

2016
[32]

Booth, and Jonathan Tennyson

Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Pi- cozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson. The variational quantum eigensolver: A re- view of methods and best practices. Physics Reports , 986:1–128, 2022. The Variational Quantum Eigensolver: a review of methods and best practices

2022
[33]

Variational quantum simulation for quantum chemistry

Yifan Li, Jiaqi Hu, Xiao-Ming Zhang, Zhigang Song, and Man-Hong Yung. Variational quantum simulation for quantum chemistry. Advanced Theory and Simulations , 2(4):1800182, 2019

2019
[34]

Overlap-adapt-vqe: practical quantum chemistry on quantum computers via overlap-guided compact ans¨ atze

C´ esar Feniou, Muhammad Hassan, Diata Traor´ e, Em- manuel Giner, Yvon Maday, and Jean-Philip Pique- mal. Overlap-adapt-vqe: practical quantum chemistry on quantum computers via overlap-guided compact ans¨ atze. Communications Physics, 6(1):192, 2023

2023
[35]

Quantum sim- ulations of materials on near-term quantum computers

He Ma, Marco Govoni, and Giulia Galli. Quantum sim- ulations of materials on near-term quantum computers. npj Computational Materials , 6(1):85, 2020

2020
[36]

Efficient variational quantum circuit structure for correlated topological phases

Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki. Efficient variational quantum circuit structure for correlated topological phases. Physical Review B , 108(7):075127, 2023

2023
[37]

Performance compari- son of optimization methods on variational quantum al- gorithms

Xavier Bonet-Monroig, Hao Wang, Diederick Vermetten, Bruno Senjean, Charles Moussa, Thomas B¨ ack, Vedran Dunjko, and Thomas E O’Brien. Performance compari- son of optimization methods on variational quantum al- gorithms. Physical Review A , 107(3):032407, 2023

2023
[38]

Tannu and Moinuddin K

Swamit S. Tannu and Moinuddin K. Qureshi. A case for variability-aware policies for nisq-era quantum comput- ers, 2018

2018
[39]

Standard forms of noisy quantum operations via depolarization

Wolfgang D¨ ur, Marc Hein, J Ignacio Cirac, and H-J Briegel. Standard forms of noisy quantum operations via depolarization. Physical Review A—Atomic, Molecular, and Optical Physics , 72(5):052326, 2005

2005
[40]

Efficient estima- tion of pauli channels

Steven T Flammia and Joel J Wallman. Efficient estima- tion of pauli channels. ACM Transactions on Quantum Computing, 1(1):1–32, 2020

2020
[41]

Modeling and simulating the noisy behavior of near-term quantum computers

Konstantinos Georgopoulos, Clive Emary, and Paolo Zuliani. Modeling and simulating the noisy behavior of near-term quantum computers. Physical Review A , 104(6), December 2021

2021
[42]

Information-theoretic aspects of the generalized amplitude-damping channel

Sumeet Khatri, Kunal Sharma, and Mark M Wilde. Information-theoretic aspects of the generalized amplitude-damping channel. Physical Review A , 102(1):012401, 2020

2020
[43]

Dynamic quantum tomography model for phase-damping channels

Artur Czerwi´ nski and Andrzej Jamio lkowski. Dynamic quantum tomography model for phase-damping channels. Open Systems & Information Dynamics , 23(04):1650019, 2016

2016
[44]

Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik

Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik. Noisy intermediate-scale quantum algorithms. Reviews of Mod- ern Physics , 94(1), February 2022

2022
[45]

Probabilistic error cancella- tion with sparse pauli–lindblad models on noisy quantum processors

Ewout Van Den Berg, Zlatko K Minev, Abhinav Kan- dala, and Kristan Temme. Probabilistic error cancella- tion with sparse pauli–lindblad models on noisy quantum processors. Nature physics, 19(8):1116–1121, 2023

2023
[46]

Sampling overhead analysis of quantum error mitigation: Uncoded vs

Yifeng Xiong, Daryus Chandra, Soon Xin Ng, and Lajos Hanzo. Sampling overhead analysis of quantum error mitigation: Uncoded vs. coded systems. IEEE Access, 8:228967–228991, 2020

2020
[47]

Best practices for quantum error mitigation with digital zero-noise extrapolation

Ritajit Majumdar, Pedro Rivero, Friedrike Metz, Areeq Hasan, and Derek S Wang. Best practices for quantum error mitigation with digital zero-noise extrapolation. In 2023 IEEE International Conference on Quantum Com- puting and Engineering (QCE) , volume 1, pages 881–887. IEEE, 2023

2023
[48]

Quantum error mitigation with artificial neural network

Changjun Kim, Kyungdeock Daniel Park, and June-Koo Rhee. Quantum error mitigation with artificial neural network. IEEE Access, 8:188853–188860, 2020

2020
[49]

Cerezo, Lukasz Cincio, and Patrick J

Samson Wang, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Lukasz Cincio, and Patrick J. Coles. Can error mitigation improve trainability of noisy variational quantum algorithms? Quantum, 8:1287, March 2024

2024
[50]

Quantum computing with Qiskit

Ali Javadi-Abhari, Matthew Treinish, Kevin Krsulich, Christopher J Wood, Jake Lishman, Julien Gacon, Si- mon Martiel, Paul D Nation, Lev S Bishop, Andrew W Cross, et al. Quantum computing with qiskit. arXiv preprint arXiv:2405.08810, 2024

work page internal anchor Pith review Pith/arXiv arXiv 2024
[51]

Package ‘xgboost’

Tianqi Chen, Tong He, Michael Benesty, and Vadim Khotilovich. Package ‘xgboost’. R version , 90(1-66):40, 2019

2019
[52]

Scikit-learn: Machine learning in python

Fabian Pedregosa, Ga¨ el Varoquaux, Alexandre Gram- fort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vin- cent Dubourg, et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research , 12:2825–2830, 2011

2011
[53]

64-qubit quantum circuit simulation

Zhao-Yun Chen, Qi Zhou, Cheng Xue, Xia Yang, Guang- Can Guo, and Guo-Ping Guo. 64-qubit quantum circuit simulation. Science Bulletin , 63(15):964–971, 2018

2018
[54]

Improved sim- ulation of stabilizer circuits

Scott Aaronson and Daniel Gottesman. Improved sim- ulation of stabilizer circuits. Physical Review A , 70(5), November 2004. 12

2004
[55]

Uni- fied approach to data-driven quantum error mitigation

Angus Lowe, Max Hunter Gordon, Piotr Czarnik, An- drew Arrasmith, Patrick J Coles, and Lukasz Cincio. Uni- fied approach to data-driven quantum error mitigation. Physical Review Research, 3(3):033098, 2021

2021
[56]

Generating haar-uniform randomness using stochastic quantum walks on a pho- tonic chip

Hao Tang, Leonardo Banchi, Tian-Yu Wang, Xiao-Wen Shang, Xi Tan, Wen-Hao Zhou, Zhen Feng, Anurag Pal, Hang Li, Cheng-Qiu Hu, et al. Generating haar-uniform randomness using stochastic quantum walks on a pho- tonic chip. Physical Review Letters, 128(5):050503, 2022

2022
[57]

The sherrington-kirkpatrick model: an overview

Dmitry Panchenko. The sherrington-kirkpatrick model: an overview. Journal of Statistical Physics , 149(2):362– 383, 2012

2012
[58]

Solvable model of a spin-glass

David Sherrington and Scott Kirkpatrick. Solvable model of a spin-glass. Physical review letters, 35(26):1792, 1975

1975
[59]

Dahlhauser and Travis S

Megan L. Dahlhauser and Travis S. Humble. Modeling noisy quantum circuits using experimental characteriza- tion. Physical Review A , 103(4), April 2021

2021
[60]

Linear regression

Xiaogang Su, Xin Yan, and Chih-Ling Tsai. Linear regression. Wiley Interdisciplinary Reviews: Computa- tional Statistics , 4(3):275–294, 2012

2012
[61]

Lasso regression

Jonas Ranstam and Jonathan A Cook. Lasso regression. Journal of British Surgery , 105(10):1348–1348, 2018

2018
[62]

Elastic net regression modeling with the orthant normal prior

Chris Hans. Elastic net regression modeling with the orthant normal prior. Journal of the American Statistical Association, 106(496):1383–1393, 2011

2011
[63]

Random forest

Steven J Rigatti. Random forest. Journal of insurance medicine, 47(1):31–39, 2017

2017
[64]

Tutorial on support vector ma- chine (svm)

Vikramaditya Jakkula. Tutorial on support vector ma- chine (svm). School of EECS, Washington State Univer- sity, 37(2.5):3, 2006

2006
[65]

An efficient instance selection algorithm for k nearest neighbor regression

Yunsheng Song, Jiye Liang, Jing Lu, and Xingwang Zhao. An efficient instance selection algorithm for k nearest neighbor regression. Neurocomputing, 251:26–34, 2017

2017
[66]

Multilayer percep- tron (mlp)

Hind Taud and Jean-Franccois Mas. Multilayer percep- tron (mlp). In Geomatic approaches for modeling land change scenarios, pages 451–455. Springer, 2017

2017
[67]

On the limited memory bfgs method for large scale optimization

Dong C Liu and Jorge Nocedal. On the limited memory bfgs method for large scale optimization. Mathematical programming, 45(1):503–528, 1989. Appendix A: RMSE for ML-QEM benchmark in VQE The results of benchmarking the proposed protocol un- der different noise models and comparing it to ZNE, given in the table II are represented here in the RMSE format, i....

1989

[1] [1]

For modeling two-qubit gate errors, we assume the noise affects only the specific qubits considered, i.e

Depolarizing noise [34], one of the most commonly used noise models in theoretical studies, with the 3 quantum channel E(ρ)depol = p d 1d + (1 − p)ρ, (5) where 1d is a d-dimensional identity. For modeling two-qubit gate errors, we assume the noise affects only the specific qubits considered, i.e. d = 4

[2] [2]

Pauli noise [35], a more general, asymmetric version of the former model, with a single-qubit quantum channel of the form E(ρ)Pauli = (1 − px − py − pz)ρ + pxXρX +pyY ρY + pzZρZ, (6) where px, py, pz are the probabilities of applying the corresponding Pauli operators. In the scope of this work, we parametrize the single-qubit Pauli channel with a single s...

[3] [3]

Composite noise model [36] consisting of three noise channels: depolarization (5), amplitude damping

[4] [4]

black box

and phase damping [38] channels. A single- qubit amplitude damping channel with damping rate γ is described as Eamp(ρ) = E0ρE0 + E1ρE1, (7) where E0 = 1 0 0 √1 − γ , E 1 = 0 √γ 0 0 . (8) A single-qubit phase damping channel with a de- phasing rate λ is given by Eph(ρ) = K0ρK0 + K1ρK1, (9) K0 = 1 0 0 √ 1 − λ , K 1 = 0 0 0 √ λ . (10) To model realistic two-...

[5] [5]

As this ansatz already uses Clifford entangling opera- tions (CNOTs) the circuit generation requires replacing only single qubit rotations with Clifford operations. It is important to note that the resulting circuits are not unique to the specific variational ansatz used; tailoring the consideration to any other ansatz with a similar en- tangling layer to...

[6] [6]

Quantum computing in the nisq era and beyond

John Preskill. Quantum computing in the nisq era and beyond. Quantum, 2:79, August 2018

2018

[7] [7]

Valor, Julien Gacon, Caroline Tornow, Luciano Bello, Stefan Woerner, and Daniel J

Johannes Weidenfeller, Lucia C. Valor, Julien Gacon, Caroline Tornow, Luciano Bello, Stefan Woerner, and Daniel J. Egger. Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware. Quantum, 6:870, December 2022

2022

[8] [8]

Scaling trapped ion quantum computers using fast gates and microtraps

Alexander K Ratcliffe, Richard L Taylor, Joseph J Hope, and Andr´ e RR Carvalho. Scaling trapped ion quantum computers using fast gates and microtraps. Physical Re- view Letters, 120(22):220501, 2018

2018

[9] [9]

Numerical simula- tion of the performance of single qubit gates for trapped ions

LA Akopyan, O Lakhmanskaya, S Yu Zarutskiy, ND Ko- rolev, O Guseva, and K Lakhmanskiy. Numerical simula- tion of the performance of single qubit gates for trapped ions. JETP Letters, 116(8):580–585, 2022

2022

[10] [10]

Hegde, Jingfu Zhang, and Dieter Suter

Swathi S. Hegde, Jingfu Zhang, and Dieter Suter. Toward the speed limit of high-fidelity two-qubit gates. Physical Review Letters, 128(23), June 2022

2022

[11] [11]

Mills, Charles R

Adam R. Mills, Charles R. Guinn, Michael J. Gullans, Anthony J. Sigillito, Mayer M. Feldman, Erik Nielsen, and Jason R. Petta. Two-qubit silicon quantum processor with operation fidelity exceeding 99 Science Advances , 8(14), April 2022

2022

[12] [12]

Theory of quantum error correction for general noise

Emanuel Knill, Raymond Laflamme, and Lorenza Viola. Theory of quantum error correction for general noise. Physical Review Letters , 84(11):2525, 2000

2000

[13] [13]

Realization of quantum error correction

John Chiaverini, Dietrich Leibfried, Tobias Schaetz, Mur- ray D Barrett, RB Blakestad, Joseph Britton, Wayne M Itano, John D Jost, Emanuel Knill, Christopher Langer, et al. Realization of quantum error correction. Nature, 432(7017):602–605, 2004

2004

[14] [14]

Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C

M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. Mc- Clean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles. Variational quantum algorithms. Na- ture Reviews Physics , 3(9):625–644, August 2021

2021

[15] [15]

Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik

Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys., 94:015004, Feb 2022

2022

[16] [16]

Near-term quantum computing techniques: Varia- tional quantum algorithms, error mitigation, circuit com- pilation, benchmarking and classical simulation

He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long. Near-term quantum computing techniques: Varia- tional quantum algorithms, error mitigation, circuit com- pilation, benchmarking and classical simulation. Science China Physics, Mechanics & Astronomy , 66(5):250302, 2023

2023

[17] [17]

Measuring the capa- bilities of quantum computers

Timothy Proctor, Kenneth Rudinger, Kevin Young, Erik Nielsen, and Robin Blume-Kohout. Measuring the capa- bilities of quantum computers. Nature Physics, 18(1):75– 79, 2022

2022

[18] [18]

Quantum error correction for beginners

Simon J Devitt, William J Munro, and Kae Nemoto. Quantum error correction for beginners. Reports on Progress in Physics , 76(7):076001, 2013

2013

[19] [19]

Quantum error mitigation

Zhenyu Cai, Ryan Babbush, Simon C Benjamin, Suguru Endo, William J Huggins, Ying Li, Jarrod R McClean, and Thomas E O’Brien. Quantum error mitigation. Re- views of Modern Physics , 95(4):045005, 2023

2023

[20] [20]

Gambetta

Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. Error mitigation for short-depth quantum circuits. Phys- ical Review Letters , 119(18), November 2017

2017

[21] [21]

Gupta, Ewout van den Berg, Maika Takita, Diego Riste, Kristan Temme, and Abhinav Kandala

Riddhi S. Gupta, Ewout van den Berg, Maika Takita, Diego Riste, Kristan Temme, and Abhinav Kandala. Probabilistic error cancellation for dynamic quantum cir- cuits, 2023

2023

[22] [22]

Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, An- drea Mari, and William J. Zeng. Digital zero noise ex- trapolation for quantum error mitigation. In 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), page 306–316. IEEE, October 2020

2020

[23] [23]

Coles, and Lukasz Cincio

Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. Error mitigation with clifford quantum- circuit data. Quantum, 5:592, November 2021

2021

[24] [24]

Adap- tive quantum error mitigation using pulse-based inverse 11 evolutions

Ivan Henao, Jader P Santos, and Raam Uzdin. Adap- tive quantum error mitigation using pulse-based inverse 11 evolutions. npj Quantum Information , 9(1):120, 2023

2023

[25] [25]

Machine learning for practical quantum error mitigation

Haoran Liao, Derek S Wang, Iskandar Sitdikov, Ciro Sal- cedo, Alireza Seif, and Zlatko K Minev. Machine learning for practical quantum error mitigation. Nature Machine Intelligence, 6(12):1478–1486, 2024

2024

[26] [26]

Learning-based quantum error mitigation

Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C Benjamin, and Ying Li. Learning-based quantum error mitigation. PRX Quantum , 2(4):040330, 2021

2021

[27] [28]

A machine learning-based error mitigation approach for reliable software development on ibm’s quantum com- puters

Asmar Muqeet, Shaukat Ali, Tao Yue, and Paolo Arcaini. A machine learning-based error mitigation approach for reliable software development on ibm’s quantum com- puters. In Companion Proceedings of the 32nd ACM In- ternational Conference on the Foundations of Software Engineering, pages 80–91, 2024

2024

[28] [29]

Echo-evolution data generation for quantum error mitigation via neural networks: D

Danila Babukhin. Echo-evolution data generation for quantum error mitigation via neural networks: D. babukhin. Quantum Information Processing, 23(12):405, 2024

2024

[29] [30]

Ridge regression

Gary C McDonald. Ridge regression. Wiley Interdisci- plinary Reviews: Computational Statistics , 1(1):93–100, 2009

2009

[30] [31]

Xgboost: A scalable tree boosting system

Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting system. In Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining , pages 785–794, 2016

2016

[31] [32]

Booth, and Jonathan Tennyson

Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Pi- cozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson. The variational quantum eigensolver: A re- view of methods and best practices. Physics Reports , 986:1–128, 2022. The Variational Quantum Eigensolver: a review of methods and best practices

2022

[32] [33]

Variational quantum simulation for quantum chemistry

Yifan Li, Jiaqi Hu, Xiao-Ming Zhang, Zhigang Song, and Man-Hong Yung. Variational quantum simulation for quantum chemistry. Advanced Theory and Simulations , 2(4):1800182, 2019

2019

[33] [34]

Overlap-adapt-vqe: practical quantum chemistry on quantum computers via overlap-guided compact ans¨ atze

C´ esar Feniou, Muhammad Hassan, Diata Traor´ e, Em- manuel Giner, Yvon Maday, and Jean-Philip Pique- mal. Overlap-adapt-vqe: practical quantum chemistry on quantum computers via overlap-guided compact ans¨ atze. Communications Physics, 6(1):192, 2023

2023

[34] [35]

Quantum sim- ulations of materials on near-term quantum computers

He Ma, Marco Govoni, and Giulia Galli. Quantum sim- ulations of materials on near-term quantum computers. npj Computational Materials , 6(1):85, 2020

2020

[35] [36]

Efficient variational quantum circuit structure for correlated topological phases

Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki. Efficient variational quantum circuit structure for correlated topological phases. Physical Review B , 108(7):075127, 2023

2023

[36] [37]

Performance compari- son of optimization methods on variational quantum al- gorithms

Xavier Bonet-Monroig, Hao Wang, Diederick Vermetten, Bruno Senjean, Charles Moussa, Thomas B¨ ack, Vedran Dunjko, and Thomas E O’Brien. Performance compari- son of optimization methods on variational quantum al- gorithms. Physical Review A , 107(3):032407, 2023

2023

[37] [38]

Tannu and Moinuddin K

Swamit S. Tannu and Moinuddin K. Qureshi. A case for variability-aware policies for nisq-era quantum comput- ers, 2018

2018

[38] [39]

Standard forms of noisy quantum operations via depolarization

Wolfgang D¨ ur, Marc Hein, J Ignacio Cirac, and H-J Briegel. Standard forms of noisy quantum operations via depolarization. Physical Review A—Atomic, Molecular, and Optical Physics , 72(5):052326, 2005

2005

[39] [40]

Efficient estima- tion of pauli channels

Steven T Flammia and Joel J Wallman. Efficient estima- tion of pauli channels. ACM Transactions on Quantum Computing, 1(1):1–32, 2020

2020

[40] [41]

Modeling and simulating the noisy behavior of near-term quantum computers

Konstantinos Georgopoulos, Clive Emary, and Paolo Zuliani. Modeling and simulating the noisy behavior of near-term quantum computers. Physical Review A , 104(6), December 2021

2021

[41] [42]

Information-theoretic aspects of the generalized amplitude-damping channel

Sumeet Khatri, Kunal Sharma, and Mark M Wilde. Information-theoretic aspects of the generalized amplitude-damping channel. Physical Review A , 102(1):012401, 2020

2020

[42] [43]

Dynamic quantum tomography model for phase-damping channels

Artur Czerwi´ nski and Andrzej Jamio lkowski. Dynamic quantum tomography model for phase-damping channels. Open Systems & Information Dynamics , 23(04):1650019, 2016

2016

[43] [44]

Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik

Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Al´ an Aspuru-Guzik. Noisy intermediate-scale quantum algorithms. Reviews of Mod- ern Physics , 94(1), February 2022

2022

[44] [45]

Probabilistic error cancella- tion with sparse pauli–lindblad models on noisy quantum processors

Ewout Van Den Berg, Zlatko K Minev, Abhinav Kan- dala, and Kristan Temme. Probabilistic error cancella- tion with sparse pauli–lindblad models on noisy quantum processors. Nature physics, 19(8):1116–1121, 2023

2023

[45] [46]

Sampling overhead analysis of quantum error mitigation: Uncoded vs

Yifeng Xiong, Daryus Chandra, Soon Xin Ng, and Lajos Hanzo. Sampling overhead analysis of quantum error mitigation: Uncoded vs. coded systems. IEEE Access, 8:228967–228991, 2020

2020

[46] [47]

Best practices for quantum error mitigation with digital zero-noise extrapolation

Ritajit Majumdar, Pedro Rivero, Friedrike Metz, Areeq Hasan, and Derek S Wang. Best practices for quantum error mitigation with digital zero-noise extrapolation. In 2023 IEEE International Conference on Quantum Com- puting and Engineering (QCE) , volume 1, pages 881–887. IEEE, 2023

2023

[47] [48]

Quantum error mitigation with artificial neural network

Changjun Kim, Kyungdeock Daniel Park, and June-Koo Rhee. Quantum error mitigation with artificial neural network. IEEE Access, 8:188853–188860, 2020

2020

[48] [49]

Cerezo, Lukasz Cincio, and Patrick J

Samson Wang, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Lukasz Cincio, and Patrick J. Coles. Can error mitigation improve trainability of noisy variational quantum algorithms? Quantum, 8:1287, March 2024

2024

[49] [50]

Quantum computing with Qiskit

Ali Javadi-Abhari, Matthew Treinish, Kevin Krsulich, Christopher J Wood, Jake Lishman, Julien Gacon, Si- mon Martiel, Paul D Nation, Lev S Bishop, Andrew W Cross, et al. Quantum computing with qiskit. arXiv preprint arXiv:2405.08810, 2024

work page internal anchor Pith review Pith/arXiv arXiv 2024

[50] [51]

Package ‘xgboost’

Tianqi Chen, Tong He, Michael Benesty, and Vadim Khotilovich. Package ‘xgboost’. R version , 90(1-66):40, 2019

2019

[51] [52]

Scikit-learn: Machine learning in python

Fabian Pedregosa, Ga¨ el Varoquaux, Alexandre Gram- fort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Peter Prettenhofer, Ron Weiss, Vin- cent Dubourg, et al. Scikit-learn: Machine learning in python. the Journal of machine Learning research , 12:2825–2830, 2011

2011

[52] [53]

64-qubit quantum circuit simulation

Zhao-Yun Chen, Qi Zhou, Cheng Xue, Xia Yang, Guang- Can Guo, and Guo-Ping Guo. 64-qubit quantum circuit simulation. Science Bulletin , 63(15):964–971, 2018

2018

[53] [54]

Improved sim- ulation of stabilizer circuits

Scott Aaronson and Daniel Gottesman. Improved sim- ulation of stabilizer circuits. Physical Review A , 70(5), November 2004. 12

2004

[54] [55]

Uni- fied approach to data-driven quantum error mitigation

Angus Lowe, Max Hunter Gordon, Piotr Czarnik, An- drew Arrasmith, Patrick J Coles, and Lukasz Cincio. Uni- fied approach to data-driven quantum error mitigation. Physical Review Research, 3(3):033098, 2021

2021

[55] [56]

Generating haar-uniform randomness using stochastic quantum walks on a pho- tonic chip

Hao Tang, Leonardo Banchi, Tian-Yu Wang, Xiao-Wen Shang, Xi Tan, Wen-Hao Zhou, Zhen Feng, Anurag Pal, Hang Li, Cheng-Qiu Hu, et al. Generating haar-uniform randomness using stochastic quantum walks on a pho- tonic chip. Physical Review Letters, 128(5):050503, 2022

2022

[56] [57]

The sherrington-kirkpatrick model: an overview

Dmitry Panchenko. The sherrington-kirkpatrick model: an overview. Journal of Statistical Physics , 149(2):362– 383, 2012

2012

[57] [58]

Solvable model of a spin-glass

David Sherrington and Scott Kirkpatrick. Solvable model of a spin-glass. Physical review letters, 35(26):1792, 1975

1975

[58] [59]

Dahlhauser and Travis S

Megan L. Dahlhauser and Travis S. Humble. Modeling noisy quantum circuits using experimental characteriza- tion. Physical Review A , 103(4), April 2021

2021

[59] [60]

Linear regression

Xiaogang Su, Xin Yan, and Chih-Ling Tsai. Linear regression. Wiley Interdisciplinary Reviews: Computa- tional Statistics , 4(3):275–294, 2012

2012

[60] [61]

Lasso regression

Jonas Ranstam and Jonathan A Cook. Lasso regression. Journal of British Surgery , 105(10):1348–1348, 2018

2018

[61] [62]

Elastic net regression modeling with the orthant normal prior

Chris Hans. Elastic net regression modeling with the orthant normal prior. Journal of the American Statistical Association, 106(496):1383–1393, 2011

2011

[62] [63]

Random forest

Steven J Rigatti. Random forest. Journal of insurance medicine, 47(1):31–39, 2017

2017

[63] [64]

Tutorial on support vector ma- chine (svm)

Vikramaditya Jakkula. Tutorial on support vector ma- chine (svm). School of EECS, Washington State Univer- sity, 37(2.5):3, 2006

2006

[64] [65]

An efficient instance selection algorithm for k nearest neighbor regression

Yunsheng Song, Jiye Liang, Jing Lu, and Xingwang Zhao. An efficient instance selection algorithm for k nearest neighbor regression. Neurocomputing, 251:26–34, 2017

2017

[65] [66]

Multilayer percep- tron (mlp)

Hind Taud and Jean-Franccois Mas. Multilayer percep- tron (mlp). In Geomatic approaches for modeling land change scenarios, pages 451–455. Springer, 2017

2017

[66] [67]

On the limited memory bfgs method for large scale optimization

Dong C Liu and Jorge Nocedal. On the limited memory bfgs method for large scale optimization. Mathematical programming, 45(1):503–528, 1989. Appendix A: RMSE for ML-QEM benchmark in VQE The results of benchmarking the proposed protocol un- der different noise models and comparing it to ZNE, given in the table II are represented here in the RMSE format, i....

1989