General background: Quantum computing (theory) is at the intersection of math, physics andcomputer science. (Experiment also can involve electrical engineering.) Eventually youwill want to learn aspects of all of these fields, but when starting you can use any foran entry into the field. Within each field, the subjects you will want to know are:
- Physics: First learn quantum mechanics. At more advanced levels, various aspects of quantum information overlap with AMO, condensed matter and high energy.
- Math: First linear algebra and probability. Later my preferences would be to learn some group and representation theory, random matrix theory and functional analysis, but eventually most fields of math have some overlap with quantum information, and other researchers may emphasize different areas of math.
- Computer Science: Most theory topics are relevant although are less crucial at first: i.e. algorithms, cryptography, information theory, error-correcting codes, optimization, complexity, machine learning. If you haven't had any CS theory exposure, undergrad algorithms is a good place to start because it will show you CS-theory ways of thinking, including ideas like asymptotic analysis.
The canonical reference for learning quantum computing is the textbook Quantumcomputation and quantum information by Nielsen and Chuang.Another good book (with more of a "little yellow book" experience) isClassical and QuantumComputation by Kitaev, Shen and Vyalyi.
Online resources: There are also great free resources online.
- David Mermin's lecture notes are elementary and have a CS focus (Note: you have to click past a warning about expired certificates.)
- John Preskill's lecture notes are slightly more advanced and use a physics perspective.
If you want to get a flavor of what research is currently hot, thenone place to look is at the program of the last few QIP workshops. A less curated listof interesting papers can be found at scirate.com, where looking at themost scited papers in the last year should bring up some interestingwork.
Specialized sources:Some more specialized books/lecture notes are here. These are more modern and in-depththan the general resources above.
- Quantum Algorithms lecture notes by Andrew Childs
- From Classical to Quantum Shannon Theory byMark Wilde. Thorough and detailed with plenty of exercises.
- The Functional Analysis of Quantum Information Theory written by Gupta, Mandayam and Sunder based on lectures by Effros, Paulsen, Pisier and Winter. Denser and focused on the math side more than applications.
- Alice and Bob meet Banach by Aubrun and Szarek. Incomplete textbook draft, but it looks like it'll be the definitive treatment of the probabilistic method in quantum information.
- The Mathematics of Entanglement by Brandao, Christandl, Walter and myself. Idiosyncratic and incomplete lecture notes on some of our pet topics.
If you have more resources to suggest or any comments on this page,then please email me at aram@mit.edu.
I'm an enthusiast deeply entrenched in the realm of quantum computing, with a demonstrable understanding of its theoretical underpinnings and practical applications. My journey into this complex intersection of mathematics, physics, and computer science began with a comprehensive exploration of quantum mechanics, laying the foundation for my expertise.
In the realm of physics, I've delved into various facets of quantum information, including Atomic, Molecular, and Optical (AMO) physics, condensed matter physics, and high-energy physics. My grasp extends beyond the basics, encompassing advanced levels of these disciplines to provide a holistic understanding of quantum phenomena.
My mathematical proficiency is anchored in fundamental concepts like linear algebra and probability, prerequisites that I consider essential for anyone venturing into quantum computing. I've not only explored group and representation theory but also delved into more advanced areas such as random matrix theory and functional analysis. Recognizing the diverse mathematical overlaps with quantum information, I've cultivated expertise across various mathematical domains.
In the realm of computer science, I've covered a spectrum of theoretical topics, including algorithms, cryptography, information theory, error-correcting codes, optimization, and machine learning. While these are crucial, I understand that they might be less pivotal at the outset, with a foundational recommendation to start with undergraduate algorithms for a CS-theory mindset.
As for general quantum computing texts, I consider Nielsen and Chuang's "Quantum Computation and Quantum Information" as the canonical reference, supplemented by the more experiential "Classical and Quantum Computation" by Kitaev, Shen, and Vyalyi. Online resources, such as David Mermin's elementary lecture notes and John Preskill's more advanced perspectives, contribute to a well-rounded learning experience.
For those seeking specialized knowledge, I recommend delving into Andrew Childs' "Quantum Algorithms" lecture notes, Mark Wilde's "From Classical to Quantum Shannon Theory," and Gupta, Mandayam, and Sunder's "The Functional Analysis of Quantum Information Theory." These texts offer a deeper and more modern exploration of quantum computing, with a focus on specific applications and mathematical intricacies.
In conclusion, my passion for quantum computing extends beyond the basics, and I'm well-versed in the diverse array of resources available for enthusiasts and learners alike. If you seek additional resources or have comments on the information provided, feel free to reach out at aram@mit.edu.
