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# 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.

## Untangling entanglement and chaos

Mercredi jan 09, 2019
Speaker(s):

How does classical chaos affect the generation of quantum entanglement? What signatures of chaos exist at the quantum level and how can they be quantified? These questions have puzzled physicists for a couple of decades now. We answer these questions in spin systems by analytically establishing a connection between entanglement generation and a measure of delocalization of a quantum state in such systems. While delocalization is a generic feature of quantum chaotic systems, it is more nuanced in regular systems.

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## Undecidability of the spectral gap in one dimension

Mercredi oct 24, 2018
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The spectral gap problem consist in deciding, given a local interaction, whether the corresponding translationally invariant Hamiltonian on a lattice has a spectral gap independent of the system size or not. In the simplest case of nearest-neighbour frustration-free qubit interactions, there is a complete classification. On the other extreme, for two (or higher) dimensional models with nearest-neighbour interactions this problem can be reduced to the Halting Problem, and it is therefore undecidable.

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## The role of entropy in topological quantum error correction

Mercredi oct 17, 2018
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Ubiquitous in the behavior of physical systems is the competition between an energy term E and an entropy term S of their free energy F = E - beta S. These concepts are also relevant for error correction, where the energy E is the number of qubits afflicted by an error, the `entropy' S(E) is the logarithm of the number of energy-E failing errors, and beta relates to the probability of each qubit's error. Error-correction schemes with larger minimum free energy have better performance.

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## Fault-tolerant magic state preparation with flag qubits

Jeudi oct 11, 2018

Despite considerable effort, magic state distillation remains one of the leading candidates to achieve universal fault-tolerant quantum computation. However, when analyzing magic state distillation schemes, it is often assumed that gates belonging to the Clifford group can be implemented perfectly. In many current quantum technologies, two-qubit Cliffords gates are amongst the noisiest components of quantum computers. In this talk I will present a new scheme for preparing magic states with very low overhead that uses flag qubits.

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## Fault-tolerant gates via homological product codes

Mercredi oct 03, 2018

I will present a method for the implementation of a universal set of fault-tolerant logical gates using homological product codes. In particular, I will show how one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.

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## Adiabatic optimization without a priori knowledge of the spectral gap

Mercredi sep 19, 2018
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Performing a quantum adiabatic optimization (AO) algorithm with the time-dependent Hamiltonian H(t) requires one to have some idea of the spectral gap γ(t) of H(t) at all times t.

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## Single-shot interpretations of von Neumann entropy

Mercredi aoû 29, 2018
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In quanum physics, the von Neumann entropy usually arises in i.i.d settings, while single-shot settings are commonly characterized by smoothed min- or max-entropies. In this talk, I will discuss new results that give single-shot interpretations to the von Neumann entropy under appropriate conditions. I first present new results that give a single-shot interpretation to the Area Law of entanglement entropy in many-body physics in terms of compression of quantum information on the boundary of a region of space.

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## Coherence distillation machines are impossible in quantum thermodynamics

Mercredi aoû 15, 2018
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The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence a "coherence distillation machine", i.e. a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate.

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## Certified Randomness from Quantum Supremacy

Mercredi juil 25, 2018
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I’ll describe a novel application for near-term quantum computers with 50-70 qubits: namely, generating cryptographic random bits, whose randomness can be certified even if the quantum computer is untrusted (e.g., has been backdoored by an adversary).  Unlike schemes based on Bell inequality violation, ours requires only a single device able to solve classically hard sampling problems.  Our protocol harvests the outputs of the sampling process and feeds them into a randomness extractor, while occasionally verifying the outputs using exponential classical time.  I’ll also compare to the beau

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## Analytical techniques for finding optimal quantum measurements

Mercredi juil 11, 2018
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For many optimal measurement problems of interest, the problem may be re-cast as a semi-definite program, for which efficient numerical techniques are available. Nevertheless, numerical solutions give limited insight into more general instances of the problem, and further, analytical solutions may be desirable when an optimised measurement appears as a sub-problem in a larger problem of interest.

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## LECTURES ON-DEMAND

### Jocelyn Bell Burnell: University of Oxford

Speaker: Jocelyn Bell Burnell