Orbital optimized unitary coupled cluster theory for quantum computer

We propose an orbital optimized method for unitary coupled cluster theory (OO-UCC) within the variational quantum eigensolver (VQE) framework for quantum computers. OO-UCC variationally determines the coupled cluster amplitudes and also molecular orbital coefficients. Owing to its fully variational nature, first-order properties are readily available. This feature allows the optimization of molecular structures in VQE without solving any additional equations. Furthermore, the method requires smaller active space and shallower quantum circuit than UCC to achieve the same accuracy. We present numerical examples of OO-UCC using quantum simulators, which include the geometry optimization of the water and ammonia molecules using analytical first derivatives of the VQE.

[1]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[2]  Werner Kutzelnigg,et al.  Quantum chemistry in Fock space. I. The universal wave and energy operators , 1982 .

[3]  W. Kutzelnigg,et al.  Quantum chemistry in Fock space. II. Effective Hamiltonians in Fock space , 1983 .

[4]  Henry F. Schaefer,et al.  On the evaluation of analytic energy derivatives for correlated wave functions , 1984 .

[5]  W. Kutzelnigg.  Quantum chemistry in Fock space. IV. The treatment of permutational symmetry. Spin‐free diagrams with symmetrized vertices , 1985 .

[6]  Anna I. Krylov,et al.  Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+ , 1998 .

[7]  Martin Head-Gordon,et al.  Benchmark variational coupled cluster doubles results , 2000 .

[8]  Claudia Filippi,et al.  Optimized Jastrow-Slater wave functions for ground and excited states: application to the lowest states of ethene. , 2004, The Journal of chemical physics.

[9]  J. Olsen,et al.  Orbital-optimized coupled-cluster theory does not reproduce the full configuration-interaction limit. , 2005, The Journal of chemical physics.

[10]  Andrew G. Taube,et al.  New perspectives on unitary coupled‐cluster theory , 2006 .

[11]  Garnet Kin-Lic Chan,et al.  Canonical transformation theory for multireference problems. , 2006, The Journal of chemical physics.

[12]  C J Umrigar,et al.  Optimization of quantum Monte Carlo wave functions by energy minimization. , 2007, The Journal of chemical physics.

[13]  Rohini C. Lochan,et al.  Orbital-optimized opposite-spin scaled second-order correlation: an economical method to improve the description of open-shell molecules. , 2007, The Journal of chemical physics.

[14]  Isaiah Shavitt,et al.  Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory , 2009 .

[15]  Frank Neese,et al.  Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics. , 2009, Journal of chemical theory and computation.

[16]  Debashree Ghosh,et al.  Accelerating convergence in iterative solution for large-scale complete active space self-consistent-field calculations , 2009 .

[17]  A. Hesselmann,et al.  The role of orbital transformations in coupled-pair functionals , 2010 .

[18]  Bridgette Cooper,et al.  Benchmark studies of variational, unitary and extended coupled cluster methods. , 2010, The Journal of chemical physics.

[19]  Hongjun Luo.  Complete optimisation of multi-configuration Jastrow wave functions by variational transcorrelated method. , 2011, The Journal of chemical physics.

[20]  Uğur Bozkaya,et al.  Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory. , 2011, The Journal of chemical physics.

[21]  Francesco A Evangelista,et al.  Alternative single-reference coupled cluster approaches for multireference problems: the simpler, the better. , 2011, The Journal of chemical physics.

[22]  Peter J Knowles,et al.  Quasi-variational coupled cluster theory. , 2012, The Journal of chemical physics.

[23]  Rodney J. Bartlett,et al.  Coupled‐cluster theory and its equation‐of‐motion extensions , 2012 .

[24]  Frank Neese,et al.  The ORCA program system , 2012 .

[25]  H. Schaefer,et al.  Symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method: improving upon CCSD(T) and CCSD(T)(Λ): preliminary application. , 2012, The Journal of chemical physics.

[26]  T. Yanai,et al.  Correlated one-body potential from second-order Møller-Plesset perturbation theory: alternative to orbital-optimized MP2 method. , 2013, The Journal of chemical physics.

[27]  Uğur Bozkaya,et al.  Orbital-optimized coupled-electron pair theory and its analytic gradients: accurate equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions. , 2013, The Journal of chemical physics.

[28]  Peter J Knowles,et al.  Rigorously extensive orbital-invariant renormalized perturbative triples corrections from quasi-variational coupled cluster theory. , 2013, The Journal of chemical physics.

[29]  Patrick Bultinck,et al.  Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal. , 2014, The Journal of chemical physics.

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

[31]  Qiming Sun,et al.  Stochastic Multiconfigurational Self-Consistent Field Theory. , 2015, Journal of chemical theory and computation.

[32]  Ali Alavi,et al.  Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins. , 2016, Journal of chemical theory and computation.

[33]  Qiming Sun,et al.  A general second order complete active space self-consistent-field solver for large-scale systems , 2016, 1610.08394.

[34]  A. Lüchow,et al.  Full Wave Function Optimization with Quantum Monte Carlo and Its Effect on the Dissociation Energy of FeS. , 2017, The journal of physical chemistry. A.

[35]  M. Troyer,et al.  Elucidating reaction mechanisms on quantum computers , 2016, Proceedings of the National Academy of Sciences.

[36]  Adam A Holmes,et al.  Cheap and Near Exact CASSCF with Large Active Spaces. , 2017, Journal of chemical theory and computation.

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

[38]  Yudong Cao,et al.  OpenFermion: the electronic structure package for quantum computers , 2017, Quantum Science and Technology.

[39]  Rolf H. Myhre,et al.  Demonstrating that the nonorthogonal orbital optimized coupled cluster model converges to full configuration interaction , 2017, 1711.10285.

[40]  Scott N. Genin,et al.  Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer. , 2018, Journal of chemical theory and computation.

[41]  Joonho Lee,et al.  Regularized Orbital-Optimized Second-Order Møller-Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers. , 2018, Journal of chemical theory and computation.

[42]  D. Tew,et al.  Relaxing Constrained Amplitudes: Improved F12 Treatments of Orbital Optimization and Core-Valence Correlation Energies. , 2018, Journal of chemical theory and computation.

[43]  Frank Neese,et al.  Software update: the ORCA program system, version 4.0 , 2018 .

[44]  Toru Shiozaki,et al.  On the difference between variational and unitary coupled cluster theories. , 2017, The Journal of chemical physics.

[45]  J. McClean,et al.  Application of fermionic marginal constraints to hybrid quantum algorithms , 2018, 1801.03524.

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

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

[48]  Himadri Pathak,et al.  Time-dependent optimized coupled-cluster method for multielectron dynamics , 2017, 1712.09044.

[49]  John C. Platt,et al.  Quantum supremacy using a programmable superconducting processor , 2019, Nature.

[50]  Harper R. Grimsley,et al.  Is the Trotterized UCCSD Ansatz Chemically Well-Defined? , 2019, Journal of chemical theory and computation.

[51]  K. B. Whaley,et al.  A non-orthogonal variational quantum eigensolver , 2019, New Journal of Physics.

[52]  Scott N. Genin,et al.  Constrained Variational Quantum Eigensolver: Quantum Computer Search Engine in the Fock Space. , 2018, Journal of chemical theory and computation.

[53]  Travis S. Humble,et al.  Quantum chemistry as a benchmark for near-term quantum computers , 2019, npj Quantum Information.

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

[55]  Daniel Kats,et al.  Orbital-Optimized Distinguishable Cluster Theory with Explicit Correlation. , 2019, Journal of chemical theory and computation.

[56]  Tzu-Ching Yen,et al.  Unitary partitioning approach to the measurement problem in the Variational Quantum Eigensolver method. , 2019, Journal of chemical theory and computation.

[57]  Harper R. Grimsley,et al.  An adaptive variational algorithm for exact molecular simulations on a quantum computer , 2018, Nature Communications.

[58]  Nicholas P. Bauman,et al.  Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms. , 2019, The Journal of chemical physics.

[59]  Nicholas P. Bauman,et al.  Quantum simulations of excited states with active-space downfolded Hamiltonians. , 2019, The Journal of chemical physics.

[60]  Exact parameterization of fermionic wave functions via unitary coupled cluster theory. , 2019, The Journal of chemical physics.

[61]  K. Mood,et al.  Full Wave Function Optimization with Quantum Monte Carlo - A study of the Dissociation Energies of ZnO, FeO, FeH, and CrS. , 2019, Journal of chemical theory and computation.

[62]  P. Deglmann,et al.  Accuracy and Resource Estimations for Quantum Chemistry on a Near-term Quantum Computer. , 2018, Journal of chemical theory and computation.

[63]  P. Barkoutsos,et al.  Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents? , 2019, The Journal of chemical physics.

[64]  T. Imamichi,et al.  Efficient evaluation of quantum observables using entangled measurements , 2019, npj Quantum Information.

[65]  Tzu-Ching Yen,et al.  Measuring all compatible operators in one series of single-qubit measurements using unitary transformations. , 2019, Journal of chemical theory and computation.

[66]  Yuki Kurashige,et al.  A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits , 2019, 1909.12410.

[67]  Vladyslav Verteletskyi,et al.  Measurement optimization in the variational quantum eigensolver using a minimum clique cover. , 2019, The Journal of chemical physics.

[68]  Artur F. Izmaylov,et al.  Iterative Qubit Coupled Cluster approach with efficient screening of generators. , 2019, Journal of chemical theory and computation.