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This Semester

 

:: Fri 4/17, 1:30 in 6C-442

Lior Eldar (MIT)
On Quantum Inapproximability: or Can Entanglement Survive Outside the Fridge?

Quantum entanglement is considered to be a very delicate phenomenon that is hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated by a quest for a quantum analog of the PCP theorem, researches have tried to establish whether or not we can preserve quantum entanglement at constant temperature that is independent of system size. This would imply that any quantum state with energy at most, say 0.05 of the total available energy of the Hamiltonian, would be highly-entangled. However to this date, no such systems were found. Moreover, it became evident that even embedding local Hamiltonians on robust, albeit "non-physical" topologies, namely expanders, does not guarantee entanglement robustness. In this talk, I'll provide indication that such robustness may be possible after all, by showing a local Hamiltonian with the following property of inapproximability: any quantum state that violates a fraction at most 0.05 of all local terms cannot be even approximately simulated by classical circuits whose depth is sub-logarithmic in the number of qubits. In a sense, this implies that even providing a "witness" to the fact that the local Hamiltonian can be "almost" satisfied, requires long-range entanglement.


:: Fri 5/1, 2:00 in 6C-442

William Wooters (Williams College)
Cycling through mutually unbiased bases

Two orthogonal bases for a Hilbert space are called mutually unbiased if each vector in one basis is an equal-magnitude superposition of all the vectors in the other basis. The maximum number of mutually unbiased bases in a space of dimension d is d+1; so a set of d+1 such bases is called complete. Complete sets of mutually unbiased bases play significant roles in quantum cryptography and quantum tomography. For certain values of d, it is possible to find a single unitary transformation that, by repeated application, generates a complete set of mutually unbiased bases starting with the standard basis. This talk reviews our current understanding of such cycling unitaries and related transformations, and shows how their effects can be pictured in a discrete phase space.


:: Fri 5/8, 1:30 in 6C-442

Beni Yoshida (Caltech)
Holographic quantum error-correcting codes: Toy models for the AdS/CFT correspondence

We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators. The entire tensor network is a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindler-wedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT. This is a joint work with Daniel Harlow, Fernando Pastawski and John Preskill


:: Fri 5/15, 1:30 in 6C-442

Sergey Bravyi (IBM)
TBA

TBA


:: Mon 5/18, 1:30 in 6C-442

Lidia del Rio (University of Bristol)
TBA

TBA


:: Tue 6/23, 1:30 in 6C-442

Rotem Arnon Friedman (ETH Zurich)
TBA

TBA


:: Fri 6/26, 1:30 in 6C-442

Marco Tomamichel (The University of Sydney)
TBA

TBA


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