martin j savage quantum computing - indico-fnal (indico) · 2018-09-14 · quantum computing - we...
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Martin J Savage
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Quantum Field Theory with Quantum Computing
Next Steps in Quantum Science for HEP FermiLab, September 12-14, 2018
Natalie Klco(INT/UW)
Pavel LougovskiRaphael Pooser
(ORNL)
See many talks at this meeting
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The paper that Caught Our Attention
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(2016)
Based upon a string of 40Ca+ trapped-ion quantum system Simulates 4 qubit system with long-range couplings = 2-spatial-site Schwinger Model> 200 gates per Trotter step
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Inelastic ProcessesFragmentation Vacuum and In-Medium
Free-space and in-medium
Diagnostic of state of dense and hot matter - heavy-ion collisions (e.g., jet quenching)- finite density and time evolution
Highly-tuned phenomenology and pQCD calculations
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Time evolution of system with baryon number, isospin, electric charge, strangeness, …..Currents, viscosity, non-equilibrium dynamics - real-time evolution
h✓̂i ⇠Z
DUµ ✓̂[Uµ] det[[Uµ]] e�SY M
Complex for non-zero chemical potential
“ Features - Finite Density “
Sign Problem
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“ Features “
Signal to Noise Problem[Sign Problem]
Statistical sampling of the path integral is the limiting element
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Quantum Computing- We are now Entering the NISQ Era
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Extrapolation to
~ 1/a
E
k
Lattice Quantum Chromodynamics- Discretized Spacetime
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Lattice Spacing :1/Λχa << m⇡L >> 2⇡
Lattice Volume :
(Nearly Continuum) (Nearly Infinite Volume)
Digitization of Theory onto Qubits
a = 0 and L =1 and δΦ = 0
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QFT with QCs- Foundational Works
Detailed formalism for 3+1 quenched Hamiltonian Gauge Theory
Phys.Rev. A73 (2006) 022328
Quantum Information and Computation 14, 1014-1080 (2014)
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Quantum Field Theory- recent examples
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Gauge Field Theoriese.g. QCD
323 lattice requires naively > 4 million qubits !Natalie Klco
State Preparation - a critical element
| random > = a |0> + b |(pi pi)> + c | (pi pi pi pi ) > + …. + d | (GG) > + ….
Conventional lattice QCD likely to play a key role in QFT on QC
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u1u2u3u4
up-quark qubits
+ d,s,c
(Very) Naive Mapping of QCD onto QC
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Gauge Theories - more complicated
Naive mapping:
Most states mapped to qubits do not satisfy constraints
Exponentially large redundancies - gauge symmetries
Methods to compress Hilbert space to physical
State preparation and role of classical calcs.
Chiral gauge theories?
Near term: move along paths with presently ``doable’’ but informative quantum calculations towards real-time and finite density QCD
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Early DaysQPU Accelerators
Classical Acceleratorse.g., GPUs
Classical Processors
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Early DaysQPU Accelerators and Hybrid Computations
Classical-Quantum Hybrid calculations appear to be the near futuree.g. Bayesian estimations on classical computers to specify quantum computation
• Speed-up bootleneck components of Lattice QCD computations• contractions ? propagators ?
• Identify appropriate components• How to push/pull to/from QPU• Similar approach, but different in substance, to GPUs
Classical Processors
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Starting Simple 1+1 Dim QEDConstruction
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Derek Leinweber Natalie Klco
• Charge screening, confinement• fermion condensate
Quantum-Classical Dynamical Calculations of the Schwinger Model using Quantum Computers N. Klco, E.F. Dumitrescu, A.J. McCaskey, T.D. Morris, R.C. Pooser, M. Sanz, E. Solano, P. Lougovski, M.J. Savage. arXiv:1803.03326 [quant-ph] . To appear in PRA.
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Starting Simple 1+1 Dim QEDState Compression
16Quantum-Classical Dynamical Calculations of the Schwinger Model using Quantum Computers N. Klco, E.F. Dumitrescu, A.J. McCaskey, T.D. Morris, R.C. Pooser, M. Sanz, E. Solano, P. Lougovski, M.J. Savage. arXiv:1803.03326 [quant-ph] . To appear in PRA.
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Starting Simple 1+1 Dim QEDVQE - GS preparation
Classical-Quantum Hybrid Calculation
17Quantum-Classical Dynamical Calculations of the Schwinger Model using Quantum Computers N. Klco, E.F. Dumitrescu, A.J. McCaskey, T.D. Morris, R.C. Pooser, M. Sanz, E. Solano, P. Lougovski, M.J. Savage. arXiv:1803.03326 [quant-ph] . To appear in PRA.
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Starting Simple 1+1 Dim QEDLiving NISQ - IBM
Apply Classically Computed U(t)
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ibmqx2 - cloud-access8K shots per point
Cartan sub-algebra
r1r3r5r7Extrapolation
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Starting Simple 1+1 Dim QEDLiving NISQ - IBM - Hybrid
Trotter Evolution U(t)
193.6 QPU-s and 260 IBM units[ ``Capacity computing’’ - required only 2 of the 5 qubits on the chip ]
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Digitizing Scalar Field Theory- see also Natalie Klco’s talk
Jordan, Lee and Preskill - several works
What is the optimal way to map scalar field theory onto NISQ-era quantum computers?
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Digitizing Scalar Field Theory- works
Jordan, Lee and Preskill - several works
Digitization of Scalar Fields for NISQ-Era Quantum Computing Natalie Klco, Martin Savage e-Print: arXiv:1808.10378 [quant-ph]
Electron-Phonon Systems on a Universal Quantum Computer Alexandru Macridin, Panagiotis Spentzouris, James Amundson, Roni Harnik (Fermilab) e-Print: arXiv:1802.07347 [quant-ph]
Quantum simulation of quantum field theory using continuous variables Kevin Marshall (Toronto U.), Raphael Pooser (Oak Ridge & Tennessee U.), George Siopsis (Tennessee U.), Christian Weedbrook (Unlisted, CA). Phys.Rev. A92 (2015) no.6, 063825 , e-Print: arXiv:1503.08121 [quant-ph]
Quantum Computation of Scattering Amplitudes in Scalar Quantum Electrodynamics Kübra Yeter-Aydeniz (Tennessee Tech. U.), George Siopsis (Tennessee U.). Sep 7, 2017. 9 pp. Published in Phys.Rev. D97 (2018) no.3, 036004 e-Print: arXiv:1709.02355 [quant-ph]
Simulating physical phenomena by quantum networksR. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. LaflammePhys. Rev. A 65, 042323 – Published 9 April 2002
[MSAH]
[JLP]
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Discretizing Scalar Field Theoryon Spatial Grid
• Discretize 3-d Space• Define Hamiltonian on grid• Trotterized time evolution• Technology transfer from Lattice QCD
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Discretizing Scalar Field Theoryon Spatial Grid
Momentum Mode Expansion
e.g. 1-dim with a = 1 and L=2k = 0 and +π
|ψ> = |n1> ⊗ |n2>
Quantum simulation of quantum field theory using continuous variables Kevin Marshall, Raphael Pooser, George Siopsis, Christian Weedbrook. Phys.Rev. A92 (2015) no.6, 063825 , e-Print: arXiv:1503.08121 [quant-ph]
Extensive and non-local interactions in k-space
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Discretizing Scalar Field Theoryon Spatial Grid
Position-Space Formulations
Parallelizes easily at the circuit level- dual layer application per Trotter step
x
Φ
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Digitizing Scalar Field Theoryat each Spatial Site
Position-Space Formulations
• Eigenstates of field operator (JLP)• Discretized Harmonic Oscillator (MSAH)• Eigenstates of Harmonic Oscillator
Determine basis to define field and conjugate momentum at each spatial site
JLP MSAH HO
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Digitizing Scalar Field Theoryat each Spatial Site
• Nyquist-Shannon Sampling Theorem (MSAH)• QuFoTr allows application of exact conjugate momentum operator (not finite difference approx)• Noise provides limit to precision in energy eigenvalues from exact Hamiltonian• Optimal run-parameter tuning depends on device noise
Field-operator basis
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Digitizing Scalar Field Theory
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Summary
• Address Grand Challenge problems in HEP• real-time evolution and finite density• high energy processes, fragmentation • Rigetti’s $1M ????
• Mapping QFTs, particularly gauge theories, onto quantum devices is a present-day challenge.
• Algorithm and circuit design are critical• fundamental change in thinking• likely to benefit others areas
• Exploration of available hardware important
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FIN