# Workshop on Quantum Information

The Center of Mathematical Sciences and Applications will be hosting a workshop on Quantum Information on April 23-24, 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 21-22. You can find more information here.

Register for the event here.

The following speakers are confirmed:

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 many-body quantum systems and show that they directly give quantum speed-ups 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 two-dimensional 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 symmetry-protected 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 information-theoretic 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 Grover-like speedups for problems that include clustering in metric spaces and saddle-point optimization. 10:00 – 10:20am Break 10:20 – 11:20am Shunlong Luo AMSS Title: Complementarity and Coherence in State-Channel 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 state-channel interaction, we show that a quantitative symmetry-asymmetry complementarity and an information-theoretic measure of coherence emerge naturally \ from the formalism of quantum mechanics. This is achieved by decomposing the state-channel 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 skew-symmetric Lie product. The latter further leads to a significant extension of the celebrated Wigner-Yanase 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 symmetry-asymmetry complementarity are revealed, applications and implications are illustrated via several prototypical channels as well as the Mach-Zehnder interferometry, in which the fringe visibility is linked to symmetry and the which-path 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 many-body 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 black-box 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 polynomial-time.  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 low-depth 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 gate-depth 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 black-box access to a unitary matrix.  In the discussion however, we drop this restriction and cast the steps needed to perform a meaningful near-term demonstration of this algorithm on a quantum computer, providing a low-rank approximation to eigenvectors of the quantum computers free- (or closely related effective) Hamiltonian, taking a large step towards a practically useful task with low-gate 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 Haar-random 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 non-standard physics occuring well outside the stretched horizon of a black hole.