Automated Quantum Circuit Design With Nested Monte Carlo Tree Search

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability.

[1]  Min-Hsiu Hsieh,et al.  Quantum Circuit Architecture Search on a Superconducting Processor , 2022, Entropy.

[2]  Lvzhou Li,et al.  Quantum Architecture Search with Meta‐Learning , 2021, Advanced Quantum Technologies.

[3]  Min-Hsiu Hsieh,et al.  Quantum circuit architecture search for variational quantum algorithms , 2020, npj Quantum Information.

[4]  Chang-Yu Hsieh,et al.  Differentiable quantum architecture search , 2020, Quantum Science and Technology.

[5]  D. Hassabis,et al.  Advancing mathematics by guiding human intuition with AI , 2021, Nature.

[6]  Oriol Vinyals,et al.  Highly accurate protein structure prediction with AlphaFold , 2021, Nature.

[7]  Yao-Lung L. Fang,et al.  Quantum Architecture Search via Deep Reinforcement Learning , 2021, ArXiv.

[8]  Chang-Yu Hsieh,et al.  Neural predictor based quantum architecture search , 2021, Mach. Learn. Sci. Technol..

[9]  Xingjun Ma,et al.  Neural Architecture Search via Combinatorial Multi-Armed Bandit , 2021, 2021 International Joint Conference on Neural Networks (IJCNN).

[10]  Maria Schuld,et al.  Machine Learning with Quantum Computers , 2021, Quantum Science and Technology.

[11]  Xutao Yu,et al.  Quantum Circuit Architecture Optimization for Variational Quantum Eigensolver via Monto Carlo Tree Search , 2021, IEEE Transactions on Quantum Engineering.

[12]  R. Socher,et al.  Theory-Inspired Path-Regularized Differential Network Architecture Search , 2020, NeurIPS.

[13]  Patrick J. Coles,et al.  Variational Quantum Linear Solver. , 2020 .

[14]  Timothy C. Berkelbach,et al.  Recent developments in the PySCF program package. , 2020, The Journal of chemical physics.

[15]  Wei Wang,et al.  Understanding Architectures Learnt by Cell-based Neural Architecture Search , 2019, ICLR.

[16]  Yue Sun,et al.  Option Pricing using Quantum Computers , 2019, Quantum.

[17]  Alán Aspuru-Guzik,et al.  Quantum computational chemistry , 2018, Reviews of Modern Physics.

[18]  Yuandong Tian,et al.  Neural Architecture Search Using Deep Neural Networks and Monte Carlo Tree Search , 2018, AAAI.

[19]  Simon C. Benjamin,et al.  Variational Circuit Compiler for Quantum Error Correction , 2019, Physical Review Applied.

[20]  Joschka Roffe,et al.  Quantum error correction: an introductory guide , 2019, Contemporary Physics.

[21]  K. B. Whaley,et al.  Generalized Unitary Coupled Cluster Wave functions for Quantum Computation. , 2018, Journal of chemical theory and computation.

[22]  Yiming Yang,et al.  DARTS: Differentiable Architecture Search , 2018, ICLR.

[23]  Nathan Killoran,et al.  PennyLane: Automatic differentiation of hybrid quantum-classical computations , 2018, ArXiv.

[24]  Jonathan Carter,et al.  Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm , 2018 .

[25]  Quoc V. Le,et al.  Efficient Neural Architecture Search via Parameter Sharing , 2018, ICML.

[26]  R. Pooser,et al.  Cloud Quantum Computing of an Atomic Nucleus. , 2018, Physical Review Letters.

[27]  Li Fei-Fei,et al.  Progressive Neural Architecture Search , 2017, ECCV.

[28]  Sandeep Sharma,et al.  PySCF: the Python‐based simulations of chemistry framework , 2018 .

[29]  Peter D. Johnson,et al.  QVECTOR: an algorithm for device-tailored quantum error correction , 2017, 1711.02249.

[30]  Demis Hassabis,et al.  Mastering the game of Go without human knowledge , 2017, Nature.

[31]  J. Gambetta,et al.  Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets , 2017, Nature.

[32]  Jonathan Carter,et al.  Implementing a Variational Quantum Eigensolver using Superconducting Qubits , 2017 .

[33]  Ying Li,et al.  Efficient Variational Quantum Simulator Incorporating Active Error Minimization , 2016, 1611.09301.

[34]  Demis Hassabis,et al.  Mastering the game of Go with deep neural networks and tree search , 2016, Nature.

[35]  Alán Aspuru-Guzik,et al.  The theory of variational hybrid quantum-classical algorithms , 2015, 1509.04279.

[36]  P. Coveney,et al.  Scalable Quantum Simulation of Molecular Energies , 2015, 1512.06860.

[37]  M. Hastings,et al.  Progress towards practical quantum variational algorithms , 2015, 1507.08969.

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

[39]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[40]  Santiago Ontañón,et al.  The Combinatorial Multi-Armed Bandit Problem and Its Application to Real-Time Strategy Games , 2013, AIIDE.

[41]  Tristan Cazenave,et al.  Nested Monte-Carlo Search , 2009, IJCAI.

[42]  A. Harrow,et al.  Quantum algorithm for linear systems of equations. , 2008, Physical review letters.

[43]  Pieter Spronck,et al.  Monte-Carlo Tree Search: A New Framework for Game AI , 2008, AIIDE.

[44]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[45]  Peter Auer,et al.  Using Confidence Bounds for Exploitation-Exploration Trade-offs , 2003, J. Mach. Learn. Res..

[46]  Yishay Mansour,et al.  Policy Gradient Methods for Reinforcement Learning with Function Approximation , 1999, NIPS.

[47]  J. J. Sakurai,et al.  Modern Quantum Mechanics , 1986 .