## UCSD Spring school on Quantum Computation

A couple months from now Dorit AharonovDavid Gosset and myself will be giving a short 3.5-day “Spring School” that is meant to be an introduction to recent topics in quantum computing, directed at young researchers in theoretical computer science at large. The school is organized by Shachar Lovett at the University of California in San Diego, from March 19th to 22nd (these dates coincide with Spring break at many universities). Shachar has been organizing such schools successfully for multiple years now (last year’s school was taught by Boaz Barak and David Steurer on Sums of Squares), and we hope that this year’s will be just as fun (and instructive). The (free) registration deadline is on February 1st, and we have limited funds available to support travel for a few needy students apply here by February 1st.

The past two years, and possibly even more so the coming couple years, may well be remembered as the moment when quantum computing entered the mainstream. Most of us have heard of IBM’s quantum computer in the cloud, of Google’s effort in , and of Microsoft’s naturally fault-tolerant \href. Some of us might also have encountered a few of the dozens of startups promising everything from quantum hardware to quantum learning, that seem to be appearing out of nowhere, raising capital in just a few months.

It is an interesting question, better left for wiser times, whether these events will be remembered as the initial sparks of a revolution in computing, or as the height of a “quantum bubble”. Bubble or no bubble, quantum information science is here to stay: while current developments make topics such as the computational power of small-scale quantum computers, the possibilities for testing quantum mechanics, all the more exciting, quantum cryptography, the theory of quantum error-correction, the ever-increasing applications of “quantum techniques” to problems from theoretical computer science, do not hinge on the success of current experiments.

In guise of teaser, our plan for the school is roughly as follows. Each day will have about 6 hours of lecture, a couple hours of informal “TA sessions” (to learn a language, one needs to practice it!), and some time for social interaction. This is a fairly heavy schedule, but if these are the 3.5 days you are going to spend learning about quantum information in your career, we want them to be useful. What this means is that we’ll simultaneously aim to cover the basics, so as to establish a common language, while quickly zooming in to a selection of the most interesting questions, such as the power of alternate models of quantum computation, the theory of quantum error-correction and fault-tolerance, or problems in quantum testing and quantum delegation.

In a little more detail, and although you should not treat this as contractual information, here is a sketch of our program for the school:

Day 1: Introduction to quantum information: one qubit, ${n}$qubits, the quantum circuit model, simple algorithms and computational speed-ups in the query model. Introduction to quantum complexity: the class QMA and the local Hamiltonian problem.

Day 2: Protocols for delegating quantum computations. The adiabatic model of computation and its equivalence to the circuit model. Quantum error-correction, stabilizer codes, and fault tolerance.

Day 3: Restricted models of computation (shallow circuits, commuting circuits). Testing quantum systems. The quantum PCP conjecture and connection to many-body entanglement. Multi-prover interactive proofs with multiple provers sharing entanglement. Quantum linearity testing.

Day 4: More restricted models of computation. Quantum optimization algorithms. Stoquastic Hamiltonians. Quantum Monte-Carlo and simulation.

If you’re not an expert in quantum information, a lot of these topics might not make much sense a priori. This is why you should come! Our goal in these 3.5 days is to summarize what we believe ought to be the highlights of a couple semesters’ worth of graduate courses in quantum information. Aside from the basics in the first day, each lecture will cover a topic of current interest, giving you the ability to understand the importance of recent progress, and start thinking about some of the more TCS-friendly problems. Towards this, we’ll highlight as many open problems as we can think of (and fit in the alloted time), and allow ample time for questions, discussions, and hands-on exercise sessions. Join us: register here!

## About Thomas

I am a professor in the department of Computing and Mathematical Sciences (CMS) at the California Institute of Technology, where I am also a member of the Institute for Quantum Information and Matter (IQIM). My research is in quantum complexity theory and cryptography.
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