Cirq & OpenFermion Hands On Tutorial
Fermilab September 13, 2018 Tutorial Goal : Solve the Schrodinger Equation for the Fermi-Hubbard Model
Ground State Energy Tutorial Agenda
1. Hands on tutorial
2. Hands on tutorial
3. Hands on OpenFermion-Cirq tutorial Software pipeline
● Compute basis functions ● Obtain Hamiltonians ● Exploit symmetries ● Map to qubits
● Derive problem specific gates ● Layout algorithm primitives ● Encapsulate VQE ansatz ● Compile to hardware Cirq https://github.com/quantumlib/cirq
QSML 2018 P 6 core philosophies
● Hardware details need to be part of programming abstractions as they greatly impact the viability of NISQ algorithms.
● Hardware should drive features and diverse hardware will have diverse features.
● Data structures and abstractions should match context in which they are used (optimization, simulation, execution).
● Optimize for workflows that validate heuristics algorithms and for rapid iteration in exploring minimally sized circuits.
QSML 2018 P 7 OpenFermion The Electronic Structure Package for Quantum Computers www.openfermion.org/
OpenFermion is an Apache 2 open source project for quantum simulation: - Generate Hamiltonians for arbitrary molecules and materials in arbitrary basis sets - Automatically compiles quantum algorithms to circuits for execution on hardware - Google software engineering standards enforced; ~50K lines of code at 99.9% test coverage
OpenFermion is a community! Over two dozen contributors from over a dozen institutions
200 active (visible) forks and use in nearly all new papers suggests that nearly entire field is using it
Framework and platform agnostic - Works with Microsoft LIQUID, IBM QISKit, Google Cirq, Xandu Strawberry, Rigetti Forest, etc. - Runs on Linux, Mac, and Windows with optional Docker installation Software pipeline
● Compute basis functions ● Obtain Hamiltonians ● Exploit symmetries ● Map to qubits
● Derive problem specific gates ● Layout algorithm primitives ● Encapsulate VQE ansatz ● Compile to hardware Fermi-Hubbard model refresher
The Hubbard model is the simplest model to describe cuprate superconductor qualitatively.
hopping on-site interaction
Long-range Coulomb interaction is replaced by local on-site interaction. local chemical magnetic field potential field where σ = ↑, ↓ denotes the two spin states and denotes the occupation number operator of site j with spin σ. Quantum Simulation with QNN
NN = classical circuit, parameterized by weights, trained to learn data representations
QNN = quantum circuit, parameterized by gate durations, trained to learn quantum states
QNNs can learn representations of highly correlated distributions with only a few layers VQE Explanation
1. Parameterize a short quantum circuit with a polynomial number of variables
2. Use circuit to prepare complex quantum state (highly correlated distribution)
3. Measure desired properties of quantum state (usually energy) 4. Use classical optimizer to suggest new parameters Appendix State preparation for high-Tc Fermi-Hubbard model on-site interaction
superconductors local field The mean-field Bogoliubov state of the
Fermi-Hubbard model magnetic field
hopping 2D fermionic Fourier transformation.
Control representation of quantum hardware
Neill et. al. Science 2018