Overhead-constrained circuit knitting for variational quantum dynamics

Simulating the dynamics of large quantum systems is a formidable yet vital pursuit for obtaining a deeper understanding of quantum mechanical phenomena. While quantum computers hold great promise for speeding up such simulations, their practical application remains hindered by limited scale and pervasive noise. In this work, we propose an approach that addresses these challenges by employing circuit knitting to partition a large quantum system into smaller subsystems that can each be simulated on a separate device. The evolution of the system is governed by the projected variational quantum dynamics (PVQD) algorithm, supplemented with constraints on the parameters of the variational quantum circuit, ensuring that the sampling overhead imposed by the circuit knitting scheme remains controllable. We test our method on quantum spin systems with multiple weakly entangled blocks each consisting of strongly correlated spins, where we are able to accurately simulate the dynamics while keeping the sampling overhead manageable. Further, we show that the same method can be used to reduce the circuit depth by cutting long-ranged gates.

[1]  Anima Anandkumar,et al.  Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits , 2023, 2309.05693.

[2]  S. Vallecorsa,et al.  Hybrid Ground-State Quantum Algorithms based on Neural Schrödinger Forging , 2023, Physical Review Research.

[3]  Yogesh L. Simmhan,et al.  Parallelizing Quantum-Classical Workloads: Profiling the Impact of Splitting Techniques , 2023, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE).

[4]  J. Nys,et al.  Variational quantum time evolution without the quantum geometric tensor , 2023, Physical Review Research.

[5]  A. Green,et al.  Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer , 2022, Nature Communications.

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

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

[8]  W. D. de Jong,et al.  Quantum simulation of nonequilibrium dynamics and thermalization in the Schwinger model , 2021, Physical Review D.

[9]  Tobias Haug,et al.  Optimal training of variational quantum algorithms without barren plateaus , 2021, ArXiv.

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

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

[12]  Giuseppe Carleo,et al.  An efficient quantum algorithm for the time evolution of parameterized circuits , 2021, Quantum.

[13]  M. Lukin,et al.  Quantum phases of matter on a 256-atom programmable quantum simulator , 2020, Nature.

[14]  H. Neven,et al.  Accurately computing the electronic properties of a quantum ring , 2020, Nature.

[15]  Masoud Mohseni,et al.  Observation of separated dynamics of charge and spin in the Fermi-Hubbard model , 2020, 2010.07965.

[16]  P. Barkoutsos,et al.  Quantum HF/DFT-embedding algorithms for electronic structure calculations: Scaling up to complex molecular systems. , 2020, The Journal of chemical physics.

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

[18]  Kevin J. Sung,et al.  Hartree-Fock on a superconducting qubit quantum computer , 2020, Science.

[19]  Jin-Guo Liu,et al.  Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design , 2019, Quantum.

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

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

[22]  Lei Wang,et al.  Variational quantum eigensolver with fewer qubits , 2019, Physical Review Research.

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

[24]  E. Altman Many-body localization and quantum thermalization , 2018, Nature Physics.

[25]  A. Chiesa,et al.  Quantum hardware simulating four-dimensional inelastic neutron scattering , 2018, Nature Physics.

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

[27]  Ryan Babbush,et al.  Low rank representations for quantum simulation of electronic structure , 2018, npj Quantum Information.

[28]  Takeshi Yamazaki,et al.  Towards the Practical Application of Near-Term Quantum Computers in Quantum Chemistry Simulations: A Problem Decomposition Approach , 2018, ArXiv.

[29]  Dmitri Maslov,et al.  Low-cost quantum circuits for classically intractable instances of the Hamiltonian dynamics simulation problem , 2018, npj Quantum Information.

[30]  Alexandru Paler,et al.  Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity , 2018, Physical Review X.

[31]  Kristan Temme,et al.  Supervised learning with quantum-enhanced feature spaces , 2018, Nature.

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

[33]  Dmitri Maslov,et al.  Toward the first quantum simulation with quantum speedup , 2017, Proceedings of the National Academy of Sciences.

[34]  C. Monroe,et al.  Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator , 2017, Nature.

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

[36]  Klaas Gunst,et al.  Block product density matrix embedding theory for strongly correlated spin systems , 2017, 1702.04285.

[37]  Qiming Sun,et al.  Quantum Embedding Theories. , 2016, Accounts of chemical research.

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

[39]  Q. Jie,et al.  Cluster density matrix embedding theory for quantum spin systems , 2015, 1504.05344.

[40]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[41]  Alan Edelman,et al.  Julia: A Fresh Approach to Numerical Computing , 2014, SIAM Rev..

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

[43]  U. Schollwoeck The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[44]  J. Eisert,et al.  Colloquium: Area laws for the entanglement entropy , 2010 .

[45]  C. Marianetti,et al.  Electronic structure calculations with dynamical mean-field theory , 2005, cond-mat/0511085.

[46]  R. Feynman Simulating physics with computers , 1999 .

[47]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[48]  P. Dirac Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.

[49]  Michael A. Nielsen,et al.  Quantum Computation and Quantum Information (10th Anniversary edition) , 2016 .

[50]  A. D. McLachlan,et al.  A variational solution of the time-dependent Schrodinger equation , 1964 .