Quantum chemistry on quantum computers James …Part 1: Quantum, chemistry, computers Quantum...
Transcript of Quantum chemistry on quantum computers James …Part 1: Quantum, chemistry, computers Quantum...
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James Daniel Whitfield Department of Physics and Astronomy Dartmouth College
Quantum chemistry on quantum computers
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Department of Physics and Astronomy
A community of over 100 graaduates and undergraduate students, postdocs, and faculty conducting world-leading research in a wide range of fields
PhD Programin Physics and Astronomy
Major research efforts include: astrophysics; gravitation and cosmology; quantum information and condensed matter;
physics of plasmas, fluids, and beams; and space physics.
Apply Here: app.applyyourself.com/?id=dart-grad
Learn more at: physics.dartmouth.edu/graduate
Contact: [email protected]
Deadline: January 15, 2019
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Course overviewLecture 1: QCQC (slides) Lecture 2: Technical introduction (board) Lecture 3: Quantum for simulation (slides/board)
Objectives1.Understand how quantum mechanics intersects chemistry 2.Connect quantum computation to quantum chemistry 3.Background knowledge to get start in the literature
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Part 1: Quantum, chemistry, computers
Quantum
Asttffffffffffffs
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Goals of computers: One who computes, reckons.
First use of word was in 1600’s
Goals of chemistry: Identification of the substances of which matter is composed; their properties and the ways in which they interact, combine, and change; and the use of these processes to form new substances.
Goals of quantum: To graduate from mechanics to engineers
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Quantum chemistry computers
F = − ∇Etot(RA) = m ··RA
Nuclear dynamicsVibration RotationBonding
Classical equations of motion
Goals of computational chemistry:
1. A priori; screening 2. Post facto; explanation 3. In silico; safety and feasibility
Programming is cheaper than experiments
DFT
CC, DMRG, CI, etc.
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Quantum chemistry computers
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Quantum chemistry computers
F = − ∇Etot(RA) = m ··RA
Nuclear dynamicsVibration RotationBonding
Classical equations of motion
Born-Oppenheimer approximation
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Quantum chemistry computers
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Quantum chemistry computers
Power of quantum computers
1. Superposition 2. Size of Hilbert space 3. Entanglement 4. All of the above
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Quantum chemistry computers
Power of quantum computers
1. Superposition 2. Size of Hilbert space 3. Entanglement 4. All of the above
See Ozols
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Quantum chemistry computers
Abbreviations
NP P
MA BPP
QMA BQP
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Quantum chemistry computers
Abbreviations
NP P
MA BPP
QMA BQP
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Quantum chemistry computers
Abbreviations
NP P
MA BPP
QMA BQP
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Quantum chemistry computers
?
Simulation
Including Preparation (molecular Instances)
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Quantum chemistry computers
QMA-hard for k>2
QMA-hard for k>1
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× 1025
Quantum chemistry computers
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Quantum chemistry computers
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Quantum chemistry computers
Formal statement of quantum chemistry problem
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Quantum chemistry computers
John Pople
1998 Nobel Prize Lecture
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Quantum chemistry computers
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Quantum chemistry computers
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Quantum chemistry computers
Tomorrow
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Quantum chemistry computersOutline
1. Formal Electronic Structure problem 1. Subspace of interest: one-body 2. Subspace of interest: N-body
2. Variants on Electronic Structure problem 1. Variants 2. Connected problems
3. Qubit Hamiltonians 1. Qubit/fermion algebras 2. Jordan-Wigner example
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Orbitals
ψL=0,ml=0(r) = poly(r)e−Zr
STOζ(r) = 𝒩e−ζr
GTOZ(r) = 𝒩e−Zr2
ψSTO−3G(r) =3
∑j=1
djGTOαj(r)
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