When and Where
Class will meet at 11.00-12.20am on Tuesdays and Thursday of each week in PAB B143 during the Spring Quarter (March 27 - June 2, 2023)
The Final Exam is scheduled for : TBD, June nn, 2023.
Prerequisites : Graduate-level Quantum Mechanics
Text(s) : There is no required text for this class - the lectures will be self contained. There are a number of great books on QIS, but currently not one related to quantum simulation as the field is still that young. Classic related books that will be of value are :
Quantum Continuous Variables, by A. Serafini (2017)
Quantum Computation and Quantum Information, by M.A. Nielson and I.L. Chuang (2000)
Quantum Information, by G. Jaeger, Springer (2007)
Quantum Computing and Quantum Communications, First NASA International Conference QCQC'98, Palm Springs, edited by Colin P. Williams
Communication : I intend to have most communication regarding the class happen through a slack channel
Reading : I will assign reading to the class when appropriate. They will indicated on the Homework page.
Problem Sets : There will be problem sets assigned on a regular basis. The scores obtained in these homeworks will determine your grade of a Cr or NCr. The assignment and due date will appear on the Homework page and be discussed in class. Please feel free to discuss the problems with others in the class, but the solution(s) you present must be your own. If you are unsure of a given situation, please come and see me.
Grades : A grade of Cr or NCr will be determined from your scores on the Problem Sets.
Religious Accommodations : Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities.
The UW’s policy, including more information about how to request an accommodation, is available at Religious Accommodations Policy (https://registrar.washington.edu/staffandfaculty/religious-accommodations-policy/).
Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form (https://registrar.washington.edu/students/religious-accommodations-request/).
Syllabus and Schedule
(Disclaimer: As this is a (nearly) new course, there will likely be adjustments to the content and schedule as the quarter proceeds)
Week-1 : 27 March - 31 March
Introduction and Orientation
The background, vision and complexity of classical and quantum simulation of quantum systems, including long-term scientific goals, universal quantum computing and bounded error computation. Challenges facing classical computation - sign problems and signal-to-noise in Euclidean-space lattice QCD. Introduction/reminder to entanglement, quantum circuits, teleportation.
Week-2 : 3 April - 7 April
Quantum Circuits for Digital Quantum Computation
1-qubit operations: rotations, measurements, Solovay-Kitaev, exact operations. 2-qubit circuits: SU(4) and SO(4), entangling gates, Cartan sub-algebra, Molmer-Sorensen gates, controlled operators and state preparation. Qutrits: SU(3) rotations and Givens rotations. Hamiltonian evolution, classical shadows. Begin discussion of relevant aspects of Entanglement, Schmidt decomposition.
Week-3 : 10 April - 14 April
Entanglement Measures and Scalar Fields
Ensembles and density matrices of pure and mixed states, separability, Werner states. Entanglement entropy, Renyi entropy. Distillable entanglement, concurrence, partial transpose and negativity, n-tangle. Quantum correlations. GHZ- and W-states. Angular momentum eigenstates. Continuum scalar field theory, path integral and Green functions, Hamiltonian, lattice discretization. One- and two- lattice site systems, momentum mode expansion, wavefunctions.
Week-4 : 17 April - 21 April
Quantum Simulation of Lattice Scalar Field Theory
Hamiltonian for arbitrary numbers of lattice sites. Complexity of such simulations, and BQP completeness. Field digitization, local quantum Fourier transforms (QFT), Nyquist-Shannon sampling, exact Vs finite-difference momentum space operations. Symmetric QFT. Quantum circuits for quantum simulations of scalar field theory (time evolution).
Week-5 : 21 April - 28 April
State Preparation of Scalar Field Theory, Adiabaticity and Dark States
d-dimensional lattice scalar field theory, sequency, adiabatic state preparation, "Somma inflation" for preparing Gaussian wavefunctions, Berry's phase. Adiabatic evolution and "Dark states", multi-leaf-multi-spin systems. Preparing wavepackets ala Jordan-Lee-Preskill, detectors in simulations and measuring particle fluxes.
Week-6 : 1 May - 5 May
Time Evolution of Quantum Systems : Techniques and Algorithms
Bounded-error evolution for complete Hilbert space and low-energy subspaces - trade-offs among device noise and theoretical/algorithmic truncations. Trotter evolution - leading order, multi-operator, higher-order improvements. QDrift its pros and cons. Lnear Combinations of Unitaries (LCU). Quantum Imaginery Time Propagation (QITP).
Week-7 : 8 May - 12 May
Simulations in 1+1 Dimensions: Systems with Fermions
Lattice fermions in 1+1 dimensions, left and right movers and chirality. Free-fermion Hamiltonian. Jordan-Wigner mapping of the Kogut-Susskind Hamiltonian, anti-ferromagnetic ground states, fermion-antifermion pair-creation and annihilation. Quantum circuits, Local-four-Fermi interactions.
Week-8 : 15 May - 19 May
1+1 D Gauge Theories
Simulations of Yukawa-theory (fermions and scalars) and the Schwinger model (1+1 D quantum electrodynamics). Topology, kinks, nuclei. Quantum simulation of 1+1 D lattice QED. Gauge-fixing - nonlocal operators Vs local gauge fields. Associated resource requirements. Theta terms in lattice QED. Nflavors=2 lattice QED
Week-9 : 22 May - 26 May
Gauge Theories Continued: Mitigation Algorithms, and Yang-Mills in Higher Dimensions
Background charges and chemical potentials. The Kogut-Susskind Hamiltonian for lattice gauge theories and basis states for 1+1 D lattice QCD. The Byrnes-Yamamoto mapping of Yang-Mills lattice gauge theory to quantum devices.
Week-10 : 29 May - 2 June
Yang-Mills in Higher Dimensions and Beyond
Quantum simulations of Yang-Mills lattice gauge-field theories. Error mitigation strategies in quantum simulations using NISQ-era devices. Dynamic Decoupling, Post-Selection, CNOT extrapolations, Measurement error correction, Decoherence Renormalization, Gauge-Variant completions. The Byrnes-Yamamoto mapping of the Kogut-Susskind Hamiltonian for lattice gauge theory to qubit and qudit registers.
Exam Week : 3 June - 9 June
Logistics
I intend to make use of available quantum simulators for some of the homework assignments. I suggest installing qiskit or cirq or both onto your local compute environment, along with python and the anaconda environment and use jupyter notebooks.
I find it helpful to use Mathematica to construct and test quantum circuits before writing actual quantum simulator/computer scripts. I suggest that you have access to Mathematica or Matlab (or whatever you like best) as an environment to develop your physics ideas and for quantum circuit design.