Connecting ansatz expressibility to gradient magnitudes and barren plateaus

Zoë Holmes,1 Kunal Sharma,2, 3 M. Cerezo,3, 4 and Patrick J. Coles3 Information Sciences, Los Alamos National Laboratory, Los Alamos, NM, USA. Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA

[1]  J. Tangpanitanon,et al.  Expressibility and trainability of parametrized analog quantum systems for machine learning applications , 2020, Physical Review Research.

[2]  A. Harrow,et al.  Random Quantum Circuits are Approximate 2-designs , 2008, 0802.1919.

[3]  Patrick J. Coles,et al.  Large gradients via correlation in random parameterized quantum circuits , 2020, Quantum Science and Technology.

[4]  S. Yelin,et al.  Entanglement devised barren plateau mitigation , 2020, Physical Review Research.

[5]  Patrick J. Coles,et al.  Variational fast forwarding for quantum simulation beyond the coherence time , 2019, npj Quantum Information.

[6]  Travis S. Humble,et al.  Quantum supremacy using a programmable superconducting processor , 2019, Nature.

[7]  Peter D. Johnson,et al.  Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms , 2019, Advanced Quantum Technologies.

[8]  F. Brandão,et al.  Local random quantum circuits are approximate polynomial-designs: numerical results , 2012, 1208.0692.

[9]  Naoki Yamamoto,et al.  Expressibility of the alternating layered ansatz for quantum computation. , 2020 .

[10]  Masoud Mohseni,et al.  Layerwise learning for quantum neural networks , 2020, Quantum Machine Intelligence.

[11]  A. Harrow,et al.  Approximate Unitary t-Designs by Short Random Quantum Circuits Using Nearest-Neighbor and Long-Range Gates , 2018, Communications in Mathematical Physics.

[12]  Nicholas Hunter-Jones.  Unitary designs from statistical mechanics in random quantum circuits. , 2019, 1905.12053.

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

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

[15]  Ryan Babbush,et al.  The theory of variational hybrid quantum-classical algorithms , 2015, 1509.04279.

[16]  Liu Liu,et al.  Toward Trainability of Quantum Neural Networks. , 2020, 2011.06258.

[17]  Kunal Sharma,et al.  Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets , 2020, ArXiv.

[18]  Andrew T. Sornborger,et al.  Barren Plateaus Preclude Learning Scramblers. , 2020, Physical review letters.

[19]  Debbie W. Leung,et al.  Quantum data hiding , 2002, IEEE Trans. Inf. Theory.

[20]  Nathan Wiebe,et al.  Entanglement Induced Barren Plateaus , 2020, PRX Quantum.

[21]  Stefan Woerner,et al.  The power of quantum neural networks , 2020, Nature Computational Science.

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

[23]  Patrick J. Coles,et al.  Variational Quantum State Eigensolver , 2020, 2004.01372.

[24]  Rupak Biswas,et al.  From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz , 2017, Algorithms.

[25]  Alán Aspuru-Guzik,et al.  Quantum autoencoders for efficient compression of quantum data , 2016, 1612.02806.

[26]  Patrick J. Coles,et al.  Variational quantum state diagonalization , 2018, npj Quantum Information.

[27]  D. Gross,et al.  Evenly distributed unitaries: On the structure of unitary designs , 2006, quant-ph/0611002.

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

[29]  Omar Fawzi,et al.  Scrambling speed of random quantum circuits , 2012, 1210.6644.

[30]  Masoud Mohseni,et al.  Learning to learn with quantum neural networks via classical neural networks , 2019, ArXiv.

[31]  Patrick J. Coles,et al.  Variational consistent histories as a hybrid algorithm for quantum foundations , 2018, Nature Communications.

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

[33]  F. Petruccione,et al.  An introduction to quantum machine learning , 2014, Contemporary Physics.

[34]  Patrick J. Coles,et al.  Impact of Barren Plateaus on the Hessian and Higher Order Derivatives. , 2020 .

[35]  Kunal Sharma,et al.  Noise resilience of variational quantum compiling , 2019, New Journal of Physics.

[36]  Ying Li,et al.  Theory of variational quantum simulation , 2018, Quantum.

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

[38]  Y. Li,et al.  Variational Quantum Simulation of General Processes. , 2018, Physical review letters.

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

[40]  Jerome L. Myers,et al.  Research Design and Statistical Analysis: Third Edition , 1991 .

[41]  Akira Sone,et al.  Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks , 2020, ArXiv.

[42]  Alán Aspuru-Guzik,et al.  Quantum Chemistry in the Age of Quantum Computing. , 2018, Chemical reviews.

[43]  Kishor Bharti,et al.  Iterative quantum-assisted eigensolver , 2020, Physical Review A.

[44]  Kishor Bharti,et al.  Quantum Assisted Simulator , 2020 .

[45]  Tobias J. Osborne,et al.  No Free Lunch for Quantum Machine Learning , 2020, 2003.14103.

[46]  M. Cerezo,et al.  Noise-induced barren plateaus in variational quantum algorithms , 2020, Nature Communications.

[47]  M. Kunitski,et al.  Double-slit photoelectron interference in strong-field ionization of the neon dimer , 2018, Nature Communications.

[48]  A V Uvarov,et al.  On barren plateaus and cost function locality in variational quantum algorithms , 2021, Journal of Physics A: Mathematical and Theoretical.

[49]  Ryan LaRose,et al.  Quantum-assisted quantum compiling , 2018, Quantum.

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

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

[52]  Richard Andrew Low,et al.  Pseudo-randonmess and Learning in Quantum Computation , 2010, 1006.5227.

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

[54]  Patrick J. Coles,et al.  Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation , 2020, 2009.02559.

[55]  Daniel A. Roberts,et al.  Chaos and complexity by design , 2016, 1610.04903.

[56]  Jacob biamonte,et al.  Quantum machine learning , 2016, Nature.

[57]  Jaroslaw Adam Miszczak,et al.  Symbolic integration with respect to the Haar measure on the unitary group in Mathematica , 2011, ArXiv.

[58]  Edward Grant,et al.  An initialization strategy for addressing barren plateaus in parametrized quantum circuits , 2019, Quantum.

[59]  S. C. Choi.  Tests of equality of dependent correlation coefficients , 1977 .

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

[61]  Ken M. Nakanishi,et al.  Subspace variational quantum simulator , 2019, Physical Review Research.

[62]  Arthur Pesah,et al.  Absence of Barren Plateaus in Quantum Convolutional Neural Networks , 2020, Physical Review X.

[63]  Patrick J. Coles,et al.  Variational Quantum Fidelity Estimation , 2019, Quantum.

[64]  Jacob Biamonte,et al.  Abrupt transitions in variational quantum circuit training , 2020, Physical Review A.

[65]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[66]  Matteo A. C. Rossi,et al.  IBM Q Experience as a versatile experimental testbed for simulating open quantum systems , 2019, npj Quantum Information.