393 research outputs found
A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
The ability to perform classically intractable electronic structure
calculations is often cited as one of the principal applications of quantum
computing. A great deal of theoretical algorithmic development has been
performed in support of this goal. Most techniques require a scheme for mapping
electronic states and operations to states of and operations upon qubits. The
two most commonly used techniques for this are the Jordan-Wigner transformation
and the Bravyi-Kitaev transformation. However, comparisons of these schemes
have previously been limited to individual small molecules. In this paper we
discuss resource implications for the use of the Bravyi-Kitaev mapping scheme,
specifically with regard to the number of quantum gates required for
simulation. We consider both small systems which may be simulatable on
near-future quantum devices, and systems sufficiently large for classical
simulation to be intractable. We use 86 molecular systems to demonstrate that
the use of the Bravyi-Kitaev transformation is typically at least approximately
as efficient as the canonical Jordan-Wigner transformation, and results in
substantially reduced gate count estimates when performing limited circuit
optimisations.Comment: 46 pages, 11 figure
Quantum Commuting Circuits and Complexity of Ising Partition Functions
Instantaneous quantum polynomial-time (IQP) computation is a class of quantum
computation consisting only of commuting two-qubit gates and is not universal
in the sense of standard quantum computation. Nevertheless, it has been shown
that if there is a classical algorithm that can simulate IQP efficiently, the
polynomial hierarchy (PH) collapses at the third level, which is highly
implausible. However, the origin of the classical intractability is still less
understood. Here we establish a relationship between IQP and computational
complexity of the partition functions of Ising models. We apply the established
relationship in two opposite directions. One direction is to find subclasses of
IQP that are classically efficiently simulatable in the strong sense, by using
exact solvability of certain types of Ising models. Another direction is
applying quantum computational complexity of IQP to investigate (im)possibility
of efficient classical approximations of Ising models with imaginary coupling
constants. Specifically, we show that there is no fully polynomial randomized
approximation scheme (FPRAS) for Ising models with almost all imaginary
coupling constants even on a planar graph of a bounded degree, unless the PH
collapses at the third level. Furthermore, we also show a multiplicative
approximation of such a class of Ising partition functions is at least as hard
as a multiplicative approximation for the output distribution of an arbitrary
quantum circuit.Comment: 36 pages, 5 figure
Quantum Computing in the NISQ era and beyond
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the
near future. Quantum computers with 50-100 qubits may be able to perform tasks
which surpass the capabilities of today's classical digital computers, but
noise in quantum gates will limit the size of quantum circuits that can be
executed reliably. NISQ devices will be useful tools for exploring many-body
quantum physics, and may have other useful applications, but the 100-qubit
quantum computer will not change the world right away --- we should regard it
as a significant step toward the more powerful quantum technologies of the
future. Quantum technologists should continue to strive for more accurate
quantum gates and, eventually, fully fault-tolerant quantum computing.Comment: 20 pages. Based on a Keynote Address at Quantum Computing for
Business, 5 December 2017. (v3) Formatted for publication in Quantum, minor
revision
Simulating quantum field theory with a quantum computer
Forthcoming exascale digital computers will further advance our knowledge of
quantum chromodynamics, but formidable challenges will remain. In particular,
Euclidean Monte Carlo methods are not well suited for studying real-time
evolution in hadronic collisions, or the properties of hadronic matter at
nonzero temperature and chemical potential. Digital computers may never be able
to achieve accurate simulations of such phenomena in QCD and other
strongly-coupled field theories; quantum computers will do so eventually,
though I'm not sure when. Progress toward quantum simulation of quantum field
theory will require the collaborative efforts of quantumists and field
theorists, and though the physics payoff may still be far away, it's worthwhile
to get started now. Today's research can hasten the arrival of a new era in
which quantum simulation fuels rapid progress in fundamental physics.Comment: 22 pages, The 36th Annual International Symposium on Lattice Field
Theory - LATTICE201
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