On April 23-24, 2018, Zhengwei Liu and Arthur Jaffe from the Picture Language Project at Harvard organized a workshop on Quantum Information at the Center of Mathematical Sciences and Application, under the auspices of Shing-Tung Yau. Although this workshop focused mostly on local Cambridge, Massachusetts participation, a small number of key speakers came both nationally and internationally. The scheduled list of talks is below.
However, because of logistical reasons which prevented some speakers from attending, additional speakers were added. These added talks include:
- Kaifeng Bu spoke on Resource theory of magic states.
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 |
Title: The enduring surprises of SU(2)
Abstract: The dynamics of a qubit have long been understood to be at the heart of quantum algorithms and quantum protocols, from search to one-qubit teleportation. And cascaded single-qubit operations, known as composite quantum gates, have provided powerful ways to correct systematic errors. Here, we generalize these understandings based on new results addressing the nonlinearity of single qubit dynamics: a methodology for solving the inverse mathematical problem, to find a sufficient gate sequence, given a desired response function. |
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 |
Emil Khabiboulline Harvard |
Title: Nonlocal Interferometry with Quantum Networks
Abstract: We propose a method for optical interferometry in telescope arrays connected via networks consisting of entangled quantum mechanical nodes. In our approach, the quantum states of photons from weak distant sources, including their arrival time, are stored in quantum memories in a binary qubit encoding. These stored states are subsequently interrogated via coherent, nonlocal readout by means of entanglement-assisted parity checks across the array, which effectively circumvents transmission losses between the nodes, allowing for imaging of faint sources with improved angular resolution. The state transfer to memory enables processing such as a quantum Fourier transform applied over the network. Compared with prior proposals, our scheme offers an exponential decrease in required entanglement resources, making its experimental implementation feasible with near-term technology. |
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 |
Adam Bene Watts
MIT |
Title : Algorithms and Bounds for XOR Games.
Abstract : The entangled value of an XOR game is the maximal win probability obtained by players who cannot communicate, but share a quantum state of possibly unbounded dimension. Studying gives us a precise tool for characterizing the power of entanglement. For any two player XOR game is easy to compute, as Tsirelson gave an efficient semidefinite program which exactly computes a game’s value. Conversely, for XOR games with three or more players computing is at least NP-hard, and the best known algorithm runs with no guarantee on its convergence time. |
11:20 – 1:20pm | Lunch | |
1:20 – 2:20pm |
Mikhail D. Lukin
Harvard |
Title: Quantum machines based on Rydberg atom arrays |
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 time
Abstract: 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. |