Using Quantum Computing to Learn Physics

Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve using existing computers for even modestly large systems. Here I will show that quantum computers can sometimes be used to address such problems and that quantum computer science can assign formal complexities to learning facts about nature. Hence, computer science should not only be regarded as an applied science; it is also of central importance to the foundations of science.

[1]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[2]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[3]  G. Brassard,et al.  Quantum Amplitude Amplification and Estimation , 2000, quant-ph/0005055.

[4]  D. Cory,et al.  Hamiltonian learning and certification using quantum resources. , 2013, Physical review letters.

[5]  Nathan Wiebe,et al.  Quantum Hamiltonian learning using imperfect quantum resources , 2013, 1311.5269.

[6]  John Preskill,et al.  Quantum Algorithms for Quantum Field Theories , 2011, Science.

[7]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[8]  Scott Aaronson,et al.  Bosonsampling is far from uniform , 2013, Quantum Inf. Comput..

[9]  Stephan Mertens Computational complexity for physicists , 2002, Comput. Sci. Eng..

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

[11]  J. Emerson,et al.  Corrigendum: Negative quasi-probability as a resource for quantum computation , 2012, 1201.1256.

[12]  A. Fowler,et al.  High-threshold universal quantum computation on the surface code , 2008, 0803.0272.

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

[14]  D. Aharonov A Simple Proof that Toffoli and Hadamard are Quantum Universal , 2003, quant-ph/0301040.

[15]  Seth Lloyd,et al.  Quantum algorithm for data fitting. , 2012, Physical review letters.

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

[17]  Michael J. Biercuk,et al.  Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins , 2012, Nature.

[18]  J. Whitfield,et al.  Simulating chemistry using quantum computers. , 2010, Annual review of physical chemistry.

[19]  Nathan Wiebe,et al.  Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics. , 2012, Physical review letters.

[20]  A. J. Short,et al.  Quantum equilibration in finite time , 2011, 1110.5759.

[21]  Jens Eisert,et al.  Boson-Sampling in the light of sample complexity , 2013, ArXiv.

[22]  Andrew G. White,et al.  Photonic Boson Sampling in a Tunable Circuit , 2012, Science.

[23]  Andrew M. Childs,et al.  Simulating Sparse Hamiltonians with Star Decompositions , 2010, TQC.

[24]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[25]  Daniel A. Spielman,et al.  Exponential algorithmic speedup by a quantum walk , 2002, STOC '03.

[26]  F. Haake Quantum signatures of chaos , 1991 .