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Entanglement and extended conformal field theory (or how to get a tensor network from a CFT path integral)

Gabriel Wong Harvard University
November 29, 2019

PIRSA:19110134
Quantum Information
PSI 2019/2020 - Quantum Field Theory II (David) - Lecture 12

Francois David CEA Saclay
November 29, 2019

PIRSA:19110023
Quantum Fields and Strings
The representation theory of the Clifford group, with applications to resource theories

David Gross Universität zu Köln
November 28, 2019

PIRSA:19110141
Quantum Information
Two-dimensional AKLT states as ground states of gapped Hamiltonians and resource for universal quantum computation

Tzu-Chieh Wei Stony Brook University
November 28, 2019

PIRSA:19110140
Quantum Information
No-go theorems for quantum resource purification

Zi-Wen Liu Tsinghua University
November 28, 2019

PIRSA:19110146
Quantum Information
Mapping class group actions on Hopf algebra lattice models

Thomas Voss University of Erlangen-Nuremberg
November 28, 2019

PIRSA:19110142
Quantum Gravity
How neutron star mergers can be used to study hadron-quark phase transitions

Elias Most Princeton University
November 28, 2019

PIRSA:19110147
Strong Gravity
PSI 2019/2020 - Condensed Matter (Wang) - Lecture 11

Chong Wang Perimeter Institute for Theoretical Physics
November 28, 2019

PIRSA:19110037
Condensed Matter
Stabilizer codes for prime power qudits

Daniel Gottesman University of Maryland, College Park
November 28, 2019

PIRSA:19110138
Quantum Information
Self-correction from symmetry

Sam Roberts PsiQuantum Corp.
November 28, 2019

PIRSA:19110137
Quantum Information
PSI 2019/2020 - Quantum Field Theory II (David) - Lecture 11

Francois David CEA Saclay
November 28, 2019

PIRSA:19110022
Quantum Fields and Strings
Towards local testability for quantum coding

Anthony Leverrier Inria Paris Centre
November 27, 2019

PIRSA:19110133
Quantum Information

Entanglement and extended conformal field theory (or how to get a tensor network from a CFT path integral)

Gabriel Wong Harvard University
November 29, 2019

PIRSA:19110134
Quantum Information
In a continuum field theory the Hilbert space does not factorize into local tensor products. How then can we define entanglement and the basic protocols of quantum information theory? In this talk we will show how the factorization problem can be solved in a class of 2D conformal field theories by directly appealing to the fusion rules. The solution suggests a tensor network description of a CFT path integral using the OPE data.
PSI 2019/2020 - Quantum Field Theory II (David) - Lecture 12

Francois David CEA Saclay
November 29, 2019

PIRSA:19110023
Quantum Fields and Strings
The representation theory of the Clifford group, with applications to resource theories

David Gross Universität zu Köln
November 28, 2019

PIRSA:19110141
Quantum Information
I will report on an ongoing project to work out and exploit an analogue of Schur-Weyl duality for the Clifford group. Schur-Weyl establishes a one-one correspondence between irreps of the unitary group and those of the symmetric group. A similar program can be carried out for Cliffords. The permutations are then replaced by certain discrete orthogonal maps. As is the case for Schur-Weyl, this duality has many applications for problems in quantum information. It can be used, e.g., to derive quantum property tests for stabilizerness and Cliffordness, a new direct interpretation of the sum-negativity of Wigner functions, bounds on stabilizer rank, the construction of designs using few non-Clifford resources, etc. [arXiv:1609.08172, arXiv:1712.08628, arXiv:1906.07230, arXiv:out.soon].
Two-dimensional AKLT states as ground states of gapped Hamiltonians and resource for universal quantum computation

Tzu-Chieh Wei Stony Brook University
November 28, 2019

PIRSA:19110140
Quantum Information
Affleck, Kennedy, Lieb, and Tasaki (AKLT) constructed one-dimensional and two-dimensional spin models invariant under spin rotation. These are recognized as paradigmatic examples of symmetry-protected topological phases, including the spin-1 AKLT chain with a provable nonzero spectral gap that strongly supports Haldane’s conjecture on the spectral gap of integer chains. These states were shown to provide universal resource for quantum computation, in the framework of the measurement-based approach, including the spin-3/2 AKLT state on the honeycomb lattice and the spin-2 one on the square lattice, both of which display exponential decay in the correlation functions. However, the nonzero spectral in these 2D models had not been proved analytically for over 30 years, until very recently. I will review briefly our understanding of the quantum computational universality in the AKLT family. Then I will focus on demonstrating the nonzero spectral gap for several 2D AKLT models, including decorated honeycomb and decorated square lattices, and the undecorated degree-3 Archimedean lattices. In brief, we now have universal resource states that are ground states of provable gapped local Hamiltonians. Such a feature may be useful in creating the resource states by cooling the system and might further help the exploration into the quantum computational phases in generalized AKLT-Haldane phases.
No-go theorems for quantum resource purification

Zi-Wen Liu Tsinghua University
November 28, 2019

PIRSA:19110146
Quantum Information
The manipulation of quantum "resources" such as entanglement and coherence lies at the heart of quantum advantages and technologies. In practice, a particularly important kind of manipulation is to "purify" the quantum resources, since they are inevitably contaminated by noises and thus often lost their power or become unreliable for direct usage. Here we derive fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource. Remarkably, it is impossible to achieve perfect resource purification, even probabilistically. Our theorems indicate strong limits on the efficiency of distillation, a widely-used type of resource purification routine that underpins many key applications of quantum information science. In particular, we present explicit lower bounds on the resource cost of magic state distillation, a leading scheme for realizing scalable fault-tolerant quantum computation
Mapping class group actions on Hopf algebra lattice models

Thomas Voss University of Erlangen-Nuremberg
November 28, 2019

PIRSA:19110142
Quantum Gravity
Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
Our main result is the construction of a mapping class group action on these models, formulated under weaker assumptions than the associated topological quantum field theories, namely for pivotal Hopf algebras in symmetric monoidal categories. This description also yields new structures for semisimple finite-dimensional Hopf algebras. The action of the mapping class group is defined in terms of simple graph transformations and allows one to compute quantum Dehn twists explicitly.
How neutron star mergers can be used to study hadron-quark phase transitions

Elias Most Princeton University
November 28, 2019

PIRSA:19110147
Strong Gravity
With the detection of GW170817 we have observed the first multi messenger signal from two merging neutron stars. This signal carried a multitude of information about the underlying equation of state (EOS) of nuclear matter, which so far is not known for densities above nuclear saturation. In particular it is not known if exotic states or even a phase transition to quark matter can occur at densities so extreme that they can't be probed by any current experiment.

I will show how the information carried in the gravitational wave signal of GW170817 can be used to constrain the EOS at densities above saturation and what we can learn about the possible existence of phase transitions. I will
also comment on how we can improve on those limits with upcoming observations of the NICER mission.In the second part of the talk I will focus on what we can learn about exotic states of matter from neutron star mergers.I will comment briefly on the impact of high spins in mergers and the importance of accurate numerical modelling in the context of these studies.Finally I will show how neutron star mergers can be used to study quark phase transitions and the phase diagram of QCD.
PSI 2019/2020 - Condensed Matter (Wang) - Lecture 11

Chong Wang Perimeter Institute for Theoretical Physics
November 28, 2019

PIRSA:19110037
Condensed Matter
Stabilizer codes for prime power qudits

Daniel Gottesman University of Maryland, College Park
November 28, 2019

PIRSA:19110138
Quantum Information
There is a standard generalization of stabilizer codes to work with qudits which have prime dimension, and a slightly less standard generalization for qudits whose dimension is a prime power. However, for prime power dimensions, the usual generalization effectively treats the qudit as multiple prime-dimensional qudits instead of one larger object. There is a finite field GF(q) with size equal to any prime power, and it makes sense to label the qudit basis states with elements of the finite field, but the usual stabilizer codes do not make use of the structure of the finite field. I introduce the true GF(q) stabilizer codes, a subset of the usual prime power stabilizer codes which do make full use of the finite field structure. The true GF(q) stabilizer codes have nicer properties than the usual stabilizer codes over prime power qudits and work with a lifted Pauli group, which has some interesting mathematical aspects to it.
Self-correction from symmetry

Sam Roberts PsiQuantum Corp.
November 28, 2019

PIRSA:19110137
Quantum Information
A self-correcting quantum memory can store and protect quantum information for a time that increases without bound in the system size, without the need for active error correction. Unfortunately, the landscape of Hamiltonians based on stabilizer (subspace) codes is heavily constrained by numerous no-go results and it is not known if they can exist in three dimensions or less. In this talk, we will discuss the role of symmetry in self-correcting memories. Firstly, we will demonstrate that codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases can be self-correcting -- provided that they are protected by an appropriate subsystem symmetry. Secondly, we discuss the feasibility of self-correction in Hamiltonians based on subsystem codes, guided by the concept of emergent symmetries. We present ongoing work on a new exactly solvable candidate model in this direction based on the 3D gauge color code. The model is a non-commuting, frustrated lattice model which we prove to have an energy barrier to all bulk errors. Finding boundary conditions that encode logical qubits and retain the bulk energy barrier remains an open question.
PSI 2019/2020 - Quantum Field Theory II (David) - Lecture 11

Francois David CEA Saclay
November 28, 2019

PIRSA:19110022
Quantum Fields and Strings
Towards local testability for quantum coding

Anthony Leverrier Inria Paris Centre
November 27, 2019

PIRSA:19110133
Quantum Information
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the p-faces of the n-cube (for n>p) and stabilizer constraints with faces of dimension (p±1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into N=2n−p−1(np) physical qubits and displays local testability with a soundness of Ω(log−2(N)) beating the current state-of-the-art of log−3(N) due to Hastings. We exploit this local testability to devise an efficient decoding algorithm that corrects arbitrary errors of size less than the minimum distance, up to polylog factors. We then extend this code family by considering the quotient of the n-cube by arbitrary linear classical codes of length n. We establish the parameters of these generalized hemicubic codes. Interestingly, if the soundness of the hemicubic code could be shown to be 1/log(N), similarly to the ordinary n-cube, then the generalized hemicubic codes could yield quantum locally testable codes of length not exceeding an exponential or even polynomial function of the code dimension. (joint work with Vivien Londe and Gilles Zémor)

Title	Date	Collection	Type	Info
Entanglement and extended conformal field theory (or how to get a tensor network from a CFT path integral)	2019‑11‑29	Symmetry, Phases of Matter, and Resources in Quantum Computing	Conference	View details
PSI 2019/2020 - Quantum Field Theory II (David) - Lecture 12	2019‑11‑29	PSI 2019/2020 - Quantum Field Theory II (David)	Course	View details
The representation theory of the Clifford group, with applications to resource theories	2019‑11‑28	Symmetry, Phases of Matter, and Resources in Quantum Computing	Conference	View details
Two-dimensional AKLT states as ground states of gapped Hamiltonians and resource for universal quantum computation	2019‑11‑28	Symmetry, Phases of Matter, and Resources in Quantum Computing	Conference	View details
No-go theorems for quantum resource purification	2019‑11‑28	Symmetry, Phases of Matter, and Resources in Quantum Computing	Conference	View details
Mapping class group actions on Hopf algebra lattice models	2019‑11‑28	Quantum Gravity	Scientific Series	View details
How neutron star mergers can be used to study hadron-quark phase transitions	2019‑11‑28	Strong Gravity	Scientific Series	View details
PSI 2019/2020 - Condensed Matter (Wang) - Lecture 11	2019‑11‑28	PSI 2019/2020 - Condensed Matter (Wang)	Course	View details
Stabilizer codes for prime power qudits	2019‑11‑28	Symmetry, Phases of Matter, and Resources in Quantum Computing	Conference	View details
Self-correction from symmetry	2019‑11‑28	Symmetry, Phases of Matter, and Resources in Quantum Computing	Conference	View details
PSI 2019/2020 - Quantum Field Theory II (David) - Lecture 11	2019‑11‑28	PSI 2019/2020 - Quantum Field Theory II (David)	Course	View details
Towards local testability for quantum coding	2019‑11‑27	Symmetry, Phases of Matter, and Resources in Quantum Computing	Conference	View details

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