Quantum Computing

In recent years Quantum Computing has attracted a great deal of
attention in the scientific and technical communities. Interest in the field has expanded to include the popular press and various funding agencies. We discuss the origins of the idea of using quantum systems for computing. We then give an overview in recent developments in quantum hardware and software, as well as some potential applications for high energy physics.

• Where are we on the Hype Curve?
• According to Wikipedia: At the Beginning 18-07-12 Sexton/Amundson | Quantum Computing 7 Technology Trigger: A potential technology breakthrough kicks things off.Early proof-of-concept stories and media interest trigger significant publicity.Often no usable products exist and commercial viability is unproven.
Anything in any way beautiful derives its beauty from itself and asks nothing beyond itself.Praise is no part of it, for nothing is made worse or better by praise.
Trying to find a computer simulation of physics seems to me to be an excellent program to follow out . . . the real use of it would be with quantum mechanics . . .Nature isn't classical . . .and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy. -1981 • Peter Shor: A general-purpose quantum computer could be used to efficiently factor large numbers -Shor's Algorithm (1994) -Resource estimates from LA-UR-97-4986 "Cryptography, Quantum Computation and Trapped Ions," Richard J. Hughes (1997) Where • Classical Computing -"Easy" problems can be solved in "polynomial time" (P) -"Hard" problems require "nondeterministic polynomial time" (NP) • Proving P ≠ NP is a great unsolved problem in computer science • Quantum Computing -Some problems are easy in quantum computing, but hard in classical computing -> quantum complexity classification -Some problems appear to be hard either way    • At 2016 CHEP we heard how a 3 Qbit system was used to solve a Quantum Chemistry problem.Growth in size is as predicted.

Current Commercial Quantum Computing Efforts
18-07-12 Sexton/Amundson | Quantum Computing  -Machine Learning • Quantum Chemistry has the first big successes in quantum simulation.• GitHub has a project for general simulations of interacting fermions.
• However, interesting HEP systems, e.g., QCD, also require boson-fermion interactions.4 Interaction term evolution.The implementation of the electron-phonon interaction is similar to the one for single-particle electron operators which requires phase shift T (✓) or z-rotations R z (✓) gates acting on the electron qubits [6,7].The di↵erence is the value of the gate angle ✓, which is replaced by ✓x, where x is the eigenvalue of X corresponding to the phonon state |xi.

Successful
In Fig. 3 we show the implementation of exp( where |ii is the i fermion orbital and |x n i is the state of the HO n.
The circuit for exp( i✓ The nonlocality of the Jordan-Wigner mapping increases the circuit depth for fermion algorithms [4,6,7].However, the implementation of the electron hopping and electron-phonon terms can be combined.One can implement exp , and there will be no additional Jordan-Wigner strings due to electronphonon terms.The contribution to the circuit depth for long-range electron-phonon interactions is O(N ).
Input state preparation.The input state for the QPE algorithms must have a large overlap with the ground state.The input state can be obtained by the adiabatic method [32], starting with H 0 = H e + H p and slowly turning on the electron-phonon interaction.The ground state of H 0 is |f 0 i⌦| 0 i, where |f 0 i is the fermion Hamil- with phonons, has been addressed extensively in the literature.In the Holstein model [21] the phonons are described as set of independent oscillators located at every site.The electron density couples locally to the displacement of the HO, Phonon evolution.Within the Trotter approximation, the algorithm for the evolution of phonons requires  https://www.smbc-comics.com/comic/the-talk-3 . This is an old estimate; improvements have been made in the meantime.Analog of clock cycles in classical computing n classical 2-state systems: n bits of information b1 state systems: 2 n "bits" of information a1 … ak where k = 2 n | i = a 1 |0 . . .00i + a 2 |0 . . .01i + a 3 |0 . . .10i + . . .+ a k |1 . . .11i https://indico.cern.ch/event/587955/contributions/2935787/attachments/1683174/2707552/CHEP2018.QPR.HEP.pdfhard

•Fermilab•
Computationally intensive • Also under active investigation in the quantum world -Quantum Simulation • Good reason to believe that quantum systems should be well-suited to quantum computation Quantum Computing for Fermilab Science 18-07-12 Sexton/Amundson | Quantum Computing • Quantum Optimization and Machine Learning -Proposed work by Gabe Perdue, et al. • Quantum Information Science for Applied Quantum Field Theory -Marcela Carena, et al., including JFA (Amundson) -Scientific Computing Division/Theory Department collaboration • FNAL: James Amundson, Walter Giele, Roni Harnik, Kiel Howe, Ciaran Hughes, Joshua Isaacson, Andreas Kronfeld, Alexandru Macridin, Stefan Prestel, James Simone, Panagiotis Spentzouris, Dan Carney (U.Maryland/FNAL) • Also includes University of Washington (David Kaplan and Martin Savage) and California Institute of Technology (John Preskill) -First effort from Fermilab: Digital quantum computation of fermion-boson interacting systems Partnering with Lockheed Martin to bring quantum computing to bear on a machine learning project in astrophysics.• Several exploratory projects leveraging a D-wave annealer: star / galaxy classification, anomaly detection, and autoencoders (possibly for compression or simulation).• Large focus on exploring data representations (flexible resolution requirements, and multiple sorts of data available for each object), matching data representation to hardware, and building workflows.• Astrophysics chosen over some other domains (e.g.neutrino physics) because we have scientifically interesting data that is low enough in dimensionality to be compatible with modern quantum hardware.• Gabe Perdue and Brian Nord Quantum Optimization and Machine Learning 18-07-12 Sexton/Amundson | Quantum Computing github.com/quantumlib/OpenFermion • Previous encoding schemes for bosons on quantum computers had errors of O(noccupation/nqubits) • Alexandru Macridin, Panagiotis Spentzouris, James Amundson, Roni Harnik -Digital quantum computation of fermion-boson interacting systems • arXiv:1805.09928• Accurate and efficient simulation of fermion-boson systems; simple enough for use on near-term hardware -Electron-Phonon Systems on a Universal Quantum Computer • arXiv:1802.07347• First application was to polarons -electron dressed by phonons.Cross-disciplinary interest.
shown) is similar to the circuit shown in Fig. (9) of Ref. [7] or Table A1 of Ref. [6] for exp[ i✓(c † i c j + c † j c i )].The di↵erence is that R z (✓) is replaced by R z (✓x n ) (see Fig. 8 in Ref. [10]).
FIG. 4. nx = 6 qubits per HO.The energy (a) and quasiparticle weight (b) for the 2-site Holstein polaron versus coupling strength.(c) The phonon number distribution for di↵erent couplings.The open (full) symbols are computed using exact diagonalization (QPE algorithm on a quantum simulator).

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Quantum Computing will require the sort of infrastructure Fermilab already provides for classical computing -HEPCloud will extend to Quantum Computing -On-going testbed effort in collaboration with Google • Partially funded by Fermilab LDRD• Three promising areas for quantum applications in the HEP realm -Optimization• Area under active investigation in the quantum world • NP-hard problems • Quantum Approximate Optimization Algorithm (QAOA) -Farhi, Goldstone and Gutmann xarg proposed for finding approximate solutions to combinatorial optimization problems.

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Quantum computing holds the promise of remarkable new computational capabilities -The future is not here yet • … but we are getting there • Fermilab has quantum computing efforts on many fronts -Quantum Applications -HEP technology for QC -QC technology for HEP experiments Conclusions18-07-12Sexton/Amundson | Quantum Computing 26