The Center of Mathematical Sciences and Applications will be hosting a workshop on Quantum Information on April 2324, 2018. In the days leading up to the conference, the American Mathematical Society will also be hosting a sectional meeting on quantum information on April 2122. You can find more information here.
The following speakers are confirmed:
 Fernando G.S.L Brandão (CalTech)
 Jacob Biamonte (Skoltech)
 Isaac Chuang (MIT)
 Iris Cong (Harvard)
 Aram Harrow (MIT)
 Ke Li (HIT)
 Mikhail D. Lukin (Harvard)
 Shunlong Luo (AMSS)
 Renato Renner (ETH Zürich)
 Peter Shor (MIT)
Schedule:
Monday, April 23
Time  Speaker  Title/Abstract 
8:30 – 9:00am  Breakfast  
9:00 – 10:00am  Fernando G.S.L Brandão
Caltech 
Title: New Directions in Quantum Algorithms: Thermalization meets Convex Optimization Abstract: I will discuss recent results on quantum algorithms for semidefinite programming, an important class of convex optimization problems with widespread applications (from resource allocation to approximating hard combinatorial problems). I will present a connection of the task of solving semidefinite programs (SDPs) to the task of quantum Gibbs sampling (which consists of computing properties of thermal states at finite temperature on a quantum computer). I will then discuss results on the time of thermalization of manybody quantum systems and show that they directly give quantum speedups for SDPs. I will also argue that the quantum algorithm for SDPs can be seen as a generalization of quantum annealing and is a good candidate for realisation on small quantum computers. 
10:00 – 10:20am  Break  
10:20 – 11:20am  Iris Cong
Harvard 
Title: Universal Quantum Computation with Gapped Boundaries
Abstract: In this talk, I will discuss topological quantum computation with gapped boundaries of twodimensional topological phases. I will first introduce the algebraic framework for topological quantum computation and gapped boundaries. Next, I will present systematic methods to encode quantum information topologically using gapped boundaries, and to perform topologically protected operations on this encoding. In particular, I will introduce a new computational primitive of topological charge measurement and present a symmetryprotected implementation of this primitive. Throughout the talk, a concrete physical example – the case of bilayer fractional quantum Hall 1/3 systems [mathematically, D(Z3)], will be discussed. For this example, we have a qutrit encoding and an abstract universal gate set. If a practical implementation is found for the required topological charge measurement, these boundaries will give rise to a direct physical realization of a universal quantum computer based on a purely Abelian topological phase. 
11:20 – 1:20pm  Lunch  
1:20 – 2:20pm  Isaac Chuang
MIT 

2:20 – 2:40pm  Break  
2:40 – 3:40pm  Renato Renner
ETH Zürich 
Title: Quantum information and foundations
Abstract: The black hole information paradox is a prominent example of a thought experiment which indicates that the law that quantum states evolve unitarily may not be valid universally. In this talk, I will present another informationtheoretic thought experiment, which also leads to contradictions if one takes the universal validity of unitary state evolution for granted. However, in contrast to the black hole information paradox, the experiment does not require any assumptions about gravity. 
3:40 – 4:00pm  Break  
4:00 – 5:00pm  Ke Li
HIT 
Tuesday, April 24
Time  Speaker  Title/Abstract 
8:30 – 9:00am  Breakfast  
9:00 – 10:00am  Aram Harrow
MIT 
Title: Small quantum computers and large classical data sets
Abstract: Can we use Grover’s algorithm to quadratically speed up finding the best model fitting a data set? What about adiabatic optimization, quantum variational methods, or other more sophisticated algorithms? The answer is not obvious if we are not given the ability to query the data set in superposition. One approach is to choose a representative subset of the data and run quantum optimization algorithms on this subset. This talk will explore methods for doing so that use a classical computer either offline or in an interactive protocol together with the quantum computer. These methods allow Groverlike speedups for problems that include clustering in metric spaces and saddlepoint optimization. 
10:00 – 10:20am  Break  
10:20 – 11:20am  Shunlong Luo
AMSS 
Title: Complementarity and Coherence in StateChannel Interaction
Abstract: While Bohr’s complementarity principle constitutes a bedrock for quantum mechanics with profound implications, coherence, as a defining feature of the quantum realm originated from the superposition principle, pervades almost every quantum consideration. By exploiting the algebraic and geometric structure of statechannel interaction, we show that a quantitative symmetryasymmetry complementarity and an informationtheoretic measure of coherence emerge naturally \ from the formalism of quantum mechanics. This is achieved by decomposing the statechannel interaction into a symmetric part and an asymmetric part, which satisfy a conservation relation. The symmetric part is represented by the symmetric Jordan product, and the asymmetric part is synthesized by the skewsymmetric Lie product. The latter further leads to a significant extension of the celebrated WignerYanase skew information, and has an operational interpretation as quantum coherence of a state with respect to a channel. This not only presents a basic and alternative framework for addressing complementarity, but also puts the study of coherence in a broad context involving channels. Fundamental properties of the symmetryasymmetry complementarity are revealed, applications and implications are illustrated via several prototypical channels as well as the MachZehnder interferometry, in which the fringe visibility is linked to symmetry and the whichpath is linked to asymmetry. A natural path from coherence to entanglement is illustrated by concatenating the identifications of entanglement as minimal quantum correlations and quantum correlations as minimal coherence, which renders entanglement as minimal coherence. 
11:20 – 1:20pm  Lunch  
1:20 – 2:20pm  Mikhail D. Lukin
Harvard 

2:20 – 2:40pm  Break  
2:40 – 3:40pm  Jacob Biamonte
Skoltech 
Title: Quantum Machine Learning Matrix Product States Abstract: Matrix product states minimize bipartite correlations to compress the classical data representing quantum states. Matrix product state algorithms and similar tools—called tensor network methods—form the backbone of modern numerical methods used to simulate manybody physics. Matrix product states have a further range of applications in machine learning. Finding matrix product states is in general a computationally challenging task, a computational task which we show quantum computers can accelerate. We present a quantum algorithm which returns a classical description of a $k$rank matrix product state approximating an eigenvector given blackbox access to a unitary matrix. Each iteration of the optimization requires $O(n\cdot k^2)$ quantum gates, yielding sufficient conditions for our quantum variational algorithm to terminate in polynomialtime. Implications include: (i) Applications of quantum random access memory are severely limited from the general restriction imposed by quantum theory in which a quantum memory itself is modified by access. Our method recursively optimizes a rank$k$ description of a quantum state: this in turn can be accessed {\it in situ} and hence our results augment the efficiency of quantum random access memory. (ii) Recently lowdepth quantum circuits for various tasks have taken center stage. We augment these studies by providing a missing theoretical backbone, both quantifying algorithms in terms of entanglement and providing lower bounds for the gatedepth needed for a computation to generate specific quantities of entanglement. (iii) Matrix product structure allows many operations to be done efficiently classically (provided one has the matrix product state to begin with). Hence, our method opens the door for hybrid quantum/classical algorithms which utilize quantum effects to determine a matrix product state and then utilizes various classical/quantum subroutines to calculate properties of matrix product states. This brings with it a host of applications in the simulation of physics and chemistry as well as in machine learning. (iv) The algorithm is general in that it works given only blackbox access to a unitary matrix. In the discussion however, we drop this restriction and cast the steps needed to perform a meaningful nearterm demonstration of this algorithm on a quantum computer, providing a lowrank approximation to eigenvectors of the quantum computers free (or closely related effective) Hamiltonian, taking a large step towards a practically useful task with lowgate counts. 
3:40 – 4:00pm  Break  
4:00 – 5:00pm  Peter Shor
MIT 
Title: Quantum information, black holes, and scrambling timeAbstract: The scrambling time of a black hole is the amount of time it takes for the black hole to evolve from a nearly unentangled state — a state where there is not much entanglement between two hemisphered to a Haarrandom state, where there is nearly maximal entanglement between the two hemispheres. Recently, the conjecture has been made that the scrambling time of a black hole is order M log M, where M is the mass of the black hole in natural units. We present an argument that implies that for this conjecture to be true, there must be nonstandard physics occuring well outside the stretched horizon of a black hole. 