Quantum algorithms for computational nuclear physics

While quantum algorithms have been studied as an efficient tool for the stationary state energy determination in the case of molecular quantum systems, no similar study for analogical problems in computational nuclear physics (computation of energy levels of nuclei from empirical nucleon-nucleon or quark-quark potentials) have been realized yet. Although the difference between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on classical computer) of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy level computation will be carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei) for its possible practical realization on a real quantum computer.

[1]  Christof Zalka Simulating quantum systems on a quantum computer , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  Bikas K. Chakrabarti,et al.  Quantum Annealing and Other Optimization Methods , 2005 .

[3]  Alán Aspuru-Guzik,et al.  Exploiting Locality in Quantum Computation for Quantum Chemistry. , 2014, The journal of physical chemistry letters.

[4]  M. Hastings,et al.  Gate count estimates for performing quantum chemistry on small quantum computers , 2013, 1312.1695.

[5]  E. Wigner,et al.  Über das Paulische Äquivalenzverbot , 1928 .

[6]  The positive radial momentum operator , 2003, math-ph/0309055.

[7]  Samuel J. Lomonaco,et al.  Quantum information science and its contributions to mathematics : American Mathematical Society Short Course, January 3-4, 2009, Washington, DC , 2010 .

[8]  R. Wiringa,et al.  Accurate nucleon-nucleon potential with charge-independence breaking. , 1995, Physical review. C, Nuclear physics.

[9]  J. Whitfield,et al.  Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register. , 2014, ACS nano.

[10]  P. Love,et al.  The Bravyi-Kitaev transformation for quantum computation of electronic structure. , 2012, The Journal of chemical physics.

[11]  J. Whitfield,et al.  Simulation of electronic structure Hamiltonians using quantum computers , 2010, 1001.3855.

[12]  Hiromi Nakai,et al.  Quantum chemistry beyond Born-Oppenheimer approximation on a quantum computer: A simulated phase estimation study , 2015, 1507.03271.

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

[14]  D. Gross,et al.  Efficient quantum state tomography. , 2010, Nature communications.

[15]  Scott Aaronson,et al.  Limits on Efficient Computation in the Physical World , 2004, ArXiv.

[16]  D. Abrams,et al.  Simulation of Many-Body Fermi Systems on a Universal Quantum Computer , 1997, quant-ph/9703054.

[17]  Alán Aspuru-Guzik,et al.  Quantum algorithm for obtaining the energy spectrum of molecular systems. , 2008, Physical chemistry chemical physics : PCCP.

[18]  M. Head‐Gordon,et al.  Simulated Quantum Computation of Molecular Energies , 2005, Science.

[19]  Christof Zalka,et al.  Efficient Simulation of Quantum Systems by Quantum Computers , 1998 .

[20]  S. Lloyd,et al.  Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors , 1998, quant-ph/9807070.

[21]  Gilles Brassard,et al.  Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..

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

[23]  Lucas Visscher,et al.  Relativistic quantum chemistry on quantum computers , 2011, 1111.3490.

[24]  J. Pittner,et al.  Adiabatic state preparation study of methylene. , 2014, The Journal of chemical physics.

[25]  Alán Aspuru-Guzik,et al.  On the Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation , 2014, 1410.8159.

[26]  J. Pittner,et al.  Quantum computing applied to calculations of molecular energies: CH2 benchmark. , 2010, The Journal of chemical physics.

[27]  N. Gisin,et al.  Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memory , 2014, Nature Photonics.

[28]  Per-Olov Löwdin,et al.  STUDIES IN PERTURBATION THEORY. X. LOWER BOUNDS TO ENERGY EIGENVALUES IN PERTURBATION-THEORY GROUND STATE , 1964 .

[29]  E. Wigner,et al.  About the Pauli exclusion principle , 1928 .

[30]  A. Kitaev,et al.  Fermionic Quantum Computation , 2000, quant-ph/0003137.

[31]  Vogel,et al.  Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. , 1989, Physical review. A, General physics.

[32]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[33]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[34]  L M Delves,et al.  On the Temple lower bound for eigenvalues , 1972 .

[35]  Guang-Can Guo,et al.  Correction: Corrigendum: Demon-like algorithmic quantum cooling and its realization with quantum optics , 2012, Nature Photonics.

[36]  H. Hergert,et al.  Systematics of binding energies and radii based on realistic two-nucleon plus phenomenological three-nucleon interactions , 2010, 1005.1599.

[37]  Griffiths,et al.  Semiclassical Fourier transform for quantum computation. , 1995, Physical review letters.

[38]  H. Wolkowicz,et al.  Bounds for eigenvalues using traces , 1980 .

[39]  I. D. Johnston,et al.  A potential model representation of two-nucleon data below 315 MeV , 1962 .

[40]  N. Hatano,et al.  Finding Exponential Product Formulas of Higher Orders , 2005, math-ph/0506007.

[41]  B. Lanyon,et al.  Towards quantum chemistry on a quantum computer. , 2009, Nature chemistry.

[42]  Andrew M. Childs,et al.  Black-box hamiltonian simulation and unitary implementation , 2009, Quantum Inf. Comput..