This page is meant to answer the question: How do I get into quantum computing (QC) research?
While I am still very early in my career I'd like to share the answers to this question
that would have helped me when I first started my undergraduate studies at UVA. These answers
assume you are attending a university. I will first list the essential and supplementary
topics from what I see as the most important fields that comprise QC: physics, mathematics
and computer science. Most colleges should have a dedicated class for most of the topics listed.
The field is still somewhat in it's infancy although progress is steadily increasing with every year.
Of course a PhD will maximize your chance of working in the industry but
whether you chose to pursue a PhD or not this list is in my view the minimum knowledge you need to really understand
the field at a deep level.
Physics
The essential topics here will give you a strong foundation to understand the 'quantum' in QC. Bra-ket notation, electrostatics and electrodynamics, hamiltonians, and many-particle systems are some of the topics relevant to QC that will be covered by these. The supplementary topics are where you can specialize in a particular experimental realization of QC such as superconducting QC, trapped ion QC, photonic QC etc.
Essential topics:
Quantum Mechanics
Electricity and Magnetism
Classical Mechanics
Statistical Mechanics
Computational Physics
Supplementary topics:
Solid State Physics (for superconducting based QC)
Atomic & Molecular Physics (for trapped ion based QC)
Photonics & Optics (for photonic based QC)
Computer Science
The essential topics here will give you a strong foundation to understand the 'computing' in QC. Asymptotic notation, algorithm design, data structures, and complexity classes are some of the topics relevant to QC that will be covered by these. The supplementary topics are where you can either specialize in a particular application of QC or the computational theory behind it.
Essential topics:
Object-oriented Programming with Data Structures
Design & Analysis of Algorithms
Theory of Computation
Discrete Mathematics
Supplementary topics:
Machine Learning
Classical & Quantum Complexity Theory
Computer Architecture
Cryptography
Mathematics
The essential topics here will give you a strong foundation to understand the math behind QC. Integration, matrix diagonalization, probability distributions, and group theory are some of the topics relevant to QC that will be covered by these. The supplementary topics are where you can learn math specialized towards things like quantum error correcting codes, quantum cryptography, or a particular physical realization of a quantum computer such as superconducting QC, trapped ion QC, photonic QC etc. I will mainly list those relevant to photonics as that is what I work with.
Essential topics:
Linear Algebra
Multi-variable Calculus
Probability Theory
Complex Analysis
Abstract Algebra
Discrete Mathematics
Ordinary and Partial Differential Equations
Supplementary topics:
Coding Theory
Cryptography
Group and Representation Theory
Abstract Geometry
Topology
Real Analysis