Prerequisites

Essential:

• Part II - Advanced Quantum Physics
• Part II - Theoretical Physics 1 & 2

Desirable:

Students will benefit from having done Quantum Condensed Matter (Part II) and Advanced Quantum Condensed Matter (Part III). It is highly recommended that students also take the Part III course on Quantum Information in parallel. For Part III students who did not do undergraduate degrees in Cambridge: The most important prerequisites includes fluency in bra-ket notation; density-matrix formalism; SU(2) algebra; quantum unitary evolution; and quantum condensed-matter theory.

Learning Outcomes and Assessment

Quantum-information processing is the field of using quantum systems for the purpose of processing information and conducting calculations. Currently, the most prominent and promising venues for quantum-information processing is metrology, computing and communication. This course focuses on the first two of these topics. (The third one is covered in the QI course.) Quantum metrology is the study of using quantum phenomena (such as coherence or entanglement) to improve measurements and estimations of unknown things. Quantum computers run algorithms that utilise quantum phenomena to speed up calculations that are very slow on standard computers. Instead of giving a broad overview of the field of quantum information, this course focuses on targeted case studies from theoretical quantum metrology and algorithms. The student will be introduced to actively researched topics ranging from hyper-sensitive measurements of magnetic fields to neural-network-like quantum simulations of molecules.

Synopsis

• Metrology
  1. Classical estimation theory
  2. Fisher information
  3. Quantum Fisher information
  4. Quantum probes
  5. Optimal quantum measurements
• Quantum phase estimation
  1. Kitaev’s phase-estimation algorithm
  2. Coherence-boosted metrology
  3. Entanglement-boosted metrology
• Quantum-enhanced interferometry
  1. Dirac description of bosonic interferometers
  2. Squeezed quantum states
  3. LIGO-style interferometry
• Quasi-probability distributions
  1. Alternative representations of quantum theory
  2. Wigner function
  3. Kirkwood-Dirac distribution
• Post-selected quantum metrogy
  1. Quantum filters
  2. Quantum negativity as a resource
  3. Mitigation of detector imperfection
• Introduction to quantum algorithms
  1. The Deutsch-Jozsa algorithm with exponential Hilbert space
  2. Oracular advantage
  3. Outline of complexity theory and potential quantum advantages
• Basic Quantum Algorithms
  1. Quantum amplitude amplification
  2. Quantum counting
• Quantum Machine Learning
  1. HHL algorithm for linear systems of equations
• Variational Quantum Algorithms
  1. Quantum chemistry
  2. Jordan-Wigner encoding
  3. The Variational Quantum Eigensolver (VQE) Algorithm
• Adiabatic-like algorithms
  1. QUBO problems
  2. Ising model
  3. Quantum Approximate Optimisation Algorithm
• Classical simulations of quantum circuits
  1. Stabiliser formalism
  2. Gottesman-Knill Theorem
• Quantum-Error-Correction Algorithms (If there is time)
  1. Surface Codes
  2. Derivation of fault-tolerance threshold