Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices

Noisy intermediate-scale quantum (NISQ) devices are restricted by their limited number of qubits and their short decoherence times. An approach addressing these problems is quantum circuit cutting. It decomposes the execution of a large quantum circuit into the execution of multiple smaller quantum circuits with additional classical postprocessing. Since these smaller quantum circuits require fewer qubits and gates, they are more suitable for NISQ devices. To investigate the effect of quantum circuit cutting in a quantum algorithm targeting NISQ devices, we design two experiments using the quantum approximate optimization algorithm (QAOA) for the Maximum Cut (MaxCut) problem and conduct them on state-of-the-art superconducting devices. Our first experiment studies the influence of circuit cutting on the objective function of QAOA, and the second evaluates the quality of results obtained by the whole algorithm with circuit cutting. The results show that circuit cutting can reduce the effects of noise in QAOA, and therefore, the algorithm yields better solutions on NISQ devices.

[1]  Moinuddin K. Qureshi,et al.  FrozenQubits: Boosting Fidelity of QAOA by Skipping Hotspot Nodes , 2022, ASPLOS.

[2]  F. Leymann,et al.  Configurable Readout Error Mitigation in Quantum Workflows , 2022, Electronics.

[3]  J. Gambetta,et al.  The future of quantum computing with superconducting qubits , 2022, Journal of Applied Physics.

[4]  B. Montrucchio,et al.  Understanding the Impact of Cutting in Quantum Circuits Reliability to Transient Faults , 2022, 2022 IEEE 28th International Symposium on On-Line Testing and Robust System Design (IOLTS).

[5]  N. Killoran,et al.  Fast quantum circuit cutting with randomized measurements , 2022, Quantum.

[6]  Jian-Wei Pan,et al.  Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits. , 2022, Physical review letters.

[7]  M. Martonosi,et al.  ScaleQC: A Scalable Framework for Hybrid Computation on Quantum and Classical Processors , 2022, ArXiv.

[8]  Cenk Tuysuz,et al.  Classical splitting of parametrized quantum circuits , 2022, Quantum Machine Intelligence.

[9]  Xinmei Tian,et al.  QAOA-in-QAOA: Solving Large-Scale MaxCut Problems on Small Quantum Machines , 2022, Physical Review Applied.

[10]  G. Carleo,et al.  Entanglement Forging with generative neural network models , 2022, 2205.00933.

[11]  David Sutter,et al.  Circuit knitting with classical communication , 2022, IEEE Transactions on Information Theory.

[12]  V. Dunjko,et al.  High Dimensional Quantum Machine Learning With Small Quantum Computers , 2022, Quantum.

[13]  F. Leymann,et al.  Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem , 2022, Electronics.

[14]  Phillip C. Lotshaw,et al.  Multi-angle quantum approximate optimization algorithm , 2021, Scientific Reports.

[15]  M. Cerezo,et al.  Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms? , 2021, ArXiv.

[16]  M. Martonosi,et al.  Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation , 2021, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE).

[17]  Martin Suchara,et al.  Quantum Local Search with the Quantum Alternating Operator Ansatz , 2021, Quantum.

[18]  James C. Osborn,et al.  Quantum circuit cutting with maximum-likelihood tomography , 2021 .

[19]  Tanvi P. Gujarati,et al.  Doubling the Size of Quantum Simulators by Entanglement Forging , 2021, PRX Quantum.

[20]  Patrick J. Coles,et al.  Cost function dependent barren plateaus in shallow parametrized quantum circuits , 2021, Nature Communications.

[21]  Swaroop Ghosh,et al.  Large-Scale Quantum Approximate Optimization via Divide-and-Conquer , 2021, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[22]  Yuri Alexeev,et al.  Quantum Divide and Compute: Exploring the Effect of Different Noise Sources , 2021, SN Computer Science.

[23]  Stefan Woerner,et al.  Quasiprobability decompositions with reduced sampling overhead , 2021, npj Quantum Information.

[24]  S. Bravyi,et al.  Obstacles to Variational Quantum Optimization from Symmetry Protection. , 2020, Physical review letters.

[25]  M. Cerezo,et al.  Variational quantum algorithms , 2020, Nature Reviews Physics.

[26]  Wei Tang,et al.  CutQC: using small Quantum computers for large Quantum circuit evaluations , 2020, ASPLOS.

[27]  M. Cerezo,et al.  Effect of barren plateaus on gradient-free optimization , 2020, Quantum.

[28]  Frank Leymann,et al.  About a criterion of successfully executing a circuit in the NISQ era: what wd ≪ 1/𝜖 eff really means , 2020, APEQES@ESEC/SIGSOFT FSE.

[29]  Christopher J. Wood,et al.  Measurement Error Mitigation for Variational Quantum Algorithms , 2020, 2010.08520.

[30]  R. Wille,et al.  NISQ circuit compilation is the travelling salesman problem on a torus , 2020 .

[31]  Jakub Marecek,et al.  Warm-starting quantum optimization , 2020, Quantum.

[32]  Raul Garcia-Patron,et al.  Limitations of optimization algorithms on noisy quantum devices , 2020, Nature Physics.

[33]  Swaroop Ghosh,et al.  Analysis of crosstalk in NISQ devices and security implications in multi-programming regime , 2020, ISLPED.

[34]  Patrick J. Coles,et al.  Noise-induced barren plateaus in variational quantum algorithms , 2020, Nature Communications.

[35]  Keisuke Fujii,et al.  Overhead for simulating a non-local channel with local channels by quasiprobability sampling , 2020, Quantum.

[36]  F. Leymann,et al.  The bitter truth about gate-based quantum algorithms in the NISQ era , 2020, Quantum Science and Technology.

[37]  S. Eidenbenz,et al.  Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation , 2020, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE).

[38]  François-Marie Le Régent,et al.  Quantum Divide and Compute: Hardware Demonstrations and Noisy Simulations , 2020, 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI).

[39]  David Gamarnik,et al.  The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: A Typical Case , 2020, ArXiv.

[40]  D. Bacon,et al.  Quantum approximate optimization of non-planar graph problems on a planar superconducting processor , 2020, Nature Physics.

[41]  Costin Iancu,et al.  Classical Optimizers for Noisy Intermediate-Scale Quantum Devices , 2020, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE).

[42]  Silas Dilkes,et al.  t|ket⟩: a retargetable compiler for NISQ devices , 2020, Quantum Science and Technology.

[43]  Hyungjun Kim,et al.  BinaryDuo: Reducing Gradient Mismatch in Binary Activation Network by Coupling Binary Activations , 2020, ICLR.

[44]  Hayato Ushijima-Mwesigwa,et al.  Multilevel Combinatorial Optimization across Quantum Architectures , 2019, ACM Transactions on Quantum Computing.

[45]  K. Fujii,et al.  Constructing a virtual two-qubit gate by sampling single-qubit operations , 2019, New Journal of Physics.

[46]  Marc Coram,et al.  Quantum optimization with a novel Gibbs objective function and ansatz architecture search , 2019, Physical Review Research.

[47]  Yuchun Wu,et al.  Effects of Quantum Noise on Quantum Approximate Optimization Algorithm , 2019, Chinese Physics Letters.

[48]  Mahabubul Alam,et al.  Analysis of Quantum Approximate Optimization Algorithm under Realistic Noise in Superconducting Qubits , 2019, ArXiv.

[49]  Giacomo Nannicini,et al.  Improving Variational Quantum Optimization using CVaR , 2019, Quantum.

[50]  Ilya Safro,et al.  A Hybrid Approach for Solving Optimization Problems on Small Quantum Computers , 2019, Computer.

[51]  Maris Ozols,et al.  Simulating Large Quantum Circuits on a Small Quantum Computer. , 2019, Physical review letters.

[52]  Nicolas P. D. Sawaya,et al.  Quantum Chemistry in the Age of Quantum Computing. , 2018, Chemical reviews.

[53]  Larry Rudolph,et al.  A Closer Look at Deep Policy Gradients , 2018, ICLR.

[54]  Alán Aspuru-Guzik,et al.  Potential of quantum computing for drug discovery , 2018, IBM J. Res. Dev..

[55]  Ilya Safro,et al.  Network Community Detection on Small Quantum Computers , 2018, Advanced Quantum Technologies.

[56]  Rolando L. La Placa,et al.  How many qubits are needed for quantum computational supremacy? , 2018, Quantum.

[57]  Ryan Babbush,et al.  Barren plateaus in quantum neural network training landscapes , 2018, Nature Communications.

[58]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[59]  Kristan Temme,et al.  Error Mitigation for Short-Depth Quantum Circuits. , 2016, Physical review letters.

[60]  A. Harrow,et al.  Quantum Supremacy through the Quantum Approximate Optimization Algorithm , 2016, 1602.07674.

[61]  J. Smolin,et al.  Trading Classical and Quantum Computational Resources , 2015, 1506.01396.

[62]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[63]  Yazhen Wang,et al.  Quantum Computation and Quantum Information , 2012, 1210.0736.

[64]  Arthur B. Yeh,et al.  A Modern Introduction to Probability and Statistics , 2007, Technometrics.

[65]  Alfio Quarteroni,et al.  Numerical Mathematics (Texts in Applied Mathematics) , 2006 .

[66]  Thomas Zeugmann,et al.  Clustering Pairwise Distances with Missing Data: Maximum Cuts Versus Normalized Cuts , 2006, Discovery Science.

[67]  E. Knill,et al.  Optimal quantum measurements of expectation values of observables , 2006, quant-ph/0607019.

[68]  ReineltGerhard,et al.  An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design , 1988 .

[69]  Martin Grötschel,et al.  An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design , 1988, Oper. Res..

[70]  Xiaogang Ma.  Data Repository , 2022, Encyclopedia of Big Data.

[71]  Frederik Michel Dekking,et al.  A Modern Introduction to Probability and Statistics , 2005 .

[72]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[73]  高等学校計算数学学報編輯委員会編.  高等学校計算数学学報 = Numerical mathematics , 1979 .

[74]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[75]  P. Erd6s,et al.  On the Evolution of Random Graphs , 2022 .

[76]  F. Leymann,et al.  Configurable Readout Error Mitigation in Quantum Workflows , 2022 .