Perimeter Institute Quantum Discussions

This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.

Seminar Series Events/Videos

Currently there are no upcoming talks in this series.


Wednesday Feb 12, 2020

The quantum Fisher information (QFI) measures the amount of information that a quantum state carries about an unknown parameter. Given a quantum channel, its entanglement-assisted QFI is the maximum QFI of the output state assuming an input state over the system and an arbitrarily large ancilla. Consider N identical copies of a quantum channel, the channel QFI grows either linearly or quadratically with N asymptotically. Here we obtain a simple criterion that determines whether the scaling is linear or quadratic.


Wednesday Jan 29, 2020

Motivated by puzzles in quantum gravity AdS/CFT, Lenny Susskind posed the following question: supposing one had the technological ability to distinguish a macroscopic superposition of two given states |v> and |w> from incoherent mixture of those states, would one also have the technological ability to map |v> to |w> and vice versa?  More precisely, how does the quantum circuit complexity of the one task relate to the quantum circuit complexity of the other?  Here we resolve Susskind's question -- showing that the two complexities are essentially identical, even for approximate v


Wednesday Dec 11, 2019


Wednesday Dec 04, 2019

This talk is a progress report on ongoing research. I will explain what resource theories have to do with real algebraic geometry, and then present a preliminary result in real algebraic geometry which can be interpreted as a theorem on asymptotic and catalytic resource orderings.

It reproves the known criterion for asymptotic and catalytic majorization in terms of Rényi entropies, and generalizes it to any resource theory which satisfies a mild boundedness hypothesis. I will sketch the case of matrix majorization as an example.



Wednesday Nov 20, 2019

We show that a generic many-body Hamiltonian can be uniquely reconstructed from a single pair of initial-final states under the unitary time evolution. Interesting it is, this method is not practical due to its high complexity. We then propose a practical method for Hamiltonian reconstruction from multiple pairs of initial-final states. The stability of this method is mathematically proved and numerically verified.

This work is joint with Liujun Zou and Timothy Hsieh.

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Thursday Nov 14, 2019


Wednesday Nov 13, 2019

In quantum spin systems, the existence of a spectral gap above the ground state has strong implications for the low-energy physics. We survey recent results establishing spectral gaps in various frustration-free spin systems by verifying finite-size criteria. The talk is based on collaborations with Abdul-Rahman, Lucia, Mozgunov, Nachtergaele, Sandvik, Yang, Young, and Wang.


Wednesday Nov 06, 2019

Connections between 2D gapped quantum phases and the anyon fusion theory have been proven in various ways under different settings. In this work, we introduce a new framework connecting them by only assuming a conjectured form of entanglement area law for 2D gapped systems. We show that one can systematically define topological charges and fusion rules from the area law alone, in a well-defined way. We then derive the fusion rules of charges satisfy all the axioms required in the algebraic theory of anyons.

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Wednesday Oct 30, 2019

 Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. HQECC give a mapping of states and observables. However, they do not map local bulk Hamiltonians to local Hamiltonians on the boundary. In this work, we combine HQECC with Hamiltonian simulation theory to construct a bulk-boundary mapping between local Hamiltonians, whilst retaining all the features of the HQECC duality.


Monday Oct 28, 2019

We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. The class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms.
This is joint work with Fernando Brandao (Caltech) and Daniel Stilck Franca (QMATH, Copenhagen).