An Outlook for Quantum Computing [Point of View]

We have ubiquitous presence of computers today, ranging from simple controllers in modern appliances to smartphones in our pockets that provide a wide range of everyday services, to powerful supercomputers and large data centers that carry out the most computationally intensive tasks. These computational machines have a few things in common: for example, the information they handle is stored in bits (0 or 1), and the procedure for processing the information is specified by a program. A great deal is known about the limits of what such computational machines can and cannot do efficiently. There are many important computational problems that are believed to be very difficult to solve using even the most powerful computers, where the resource requirement—whether it is the size of the machine or the time it takes to finish the task—increases exponentially as a function of the problem size.

[1]  D. Stick,et al.  Design, fabrication and experimental demonstration of junction surface ion traps , 2011 .

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

[3]  Samuel A. Kutin.  Shor's algorithm on a nearest-neighbor machine , 2006 .

[4]  DiVincenzo.  Two-bit gates are universal for quantum computation. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[5]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[6]  Curtis Volin,et al.  Demonstration of integrated microscale optics in surface-electrode ion traps , 2011, 1105.4905.

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

[8]  C. Monroe,et al.  Scaling the Ion Trap Quantum Processor , 2013, Science.

[9]  I. Chuang,et al.  Optimal Hamiltonian Simulation by Quantum Signal Processing. , 2016, Physical review letters.

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

[11]  R. Cleve,et al.  Efficient Quantum Algorithms for Simulating Sparse Hamiltonians , 2005, quant-ph/0508139.

[12]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[13]  N. Linke,et al.  High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit. , 2014, Physical Review Letters.

[14]  Hartmut Neven,et al.  Quantum simulation of chemistry with sublinear scaling in basis size , 2018, npj Quantum Information.

[15]  S. Debnath,et al.  Demonstration of a small programmable quantum computer with atomic qubits , 2016, Nature.

[16]  Dmitri Maslov,et al.  Experimental comparison of two quantum computing architectures , 2017, Proceedings of the National Academy of Sciences.

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

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

[19]  M. Suzuki,et al.  General theory of fractal path integrals with applications to many‐body theories and statistical physics , 1991 .

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

[21]  H. Neven,et al.  Characterizing quantum supremacy in near-term devices , 2016, Nature Physics.