Perimeter Institute Quantum Discussions

428 talks

S006

Collection Type

Description

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.

Displaying 253 - 264 of 428

Homological Product Codes

Sergey Bravyi
IBM (United States)
November 27, 2013

PIRSA:13110091
Quantum Information
Quantum Adversary (Upper) Bound

Shelby Kimmel
Massachusetts Institute of Technology (MIT)
November 20, 2013

PIRSA:13110090
Quantum Information
Bulk-boundary correspondence in PEPS

Ignacio Cirac
Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
November 13, 2013

PIRSA:13110058
Quantum Information
A universal Hamiltonian simulator: the full characterization

Gemma De Las Cuevas
Universität Innsbruck
November 11, 2013

PIRSA:13110065
Quantum Information
Asymptotically Optimal Topological Quantum Compiling

Vadym Kliuchnikov
University of Waterloo
October 30, 2013

PIRSA:13100129
Quantum Information
Universal fault-tolerant quantum computation with only transversal gates and error correction

Adam Paetznick
September 25, 2013

PIRSA:13090069
Quantum Foundations
Generalized Relative Entropies, Entanglement Monotones and One-Shot Information Theory

Nilanjana Datta
University of Cambridge
June 17, 2013

PIRSA:13060003
Quantum Information
Information Theoretic Benefit of Entanglement in Classical Communication Settings

Salman Beigi
Institute for Research in Fundamental Sciences (IPM)
May 27, 2013

PIRSA:13050077
Quantum Information
Processing quantum information with relativistic motion of atoms

Eduardo Martin-Martinez
Institute for Quantum Computing (IQC)
May 13, 2013

PIRSA:13050017
Quantum Information
Laws of thermodynamics beyond the von Neumann regime

Oscar Dahlsten
City University of Hong Kong
April 29, 2013

PIRSA:13040112
Quantum Foundations
The continuum limit of tensor networks: a path integral representation

David Jennings
Imperial College London
April 22, 2013

PIRSA:13040113
Quantum Foundations
Continuous-variable entanglement distillation and non-commutative central limit theorems

Earl Campbell
University of Sheffield
April 15, 2013

PIRSA:13040122
Quantum Information

Homological Product Codes

Sergey Bravyi
IBM (United States)
November 27, 2013

PIRSA:13110091
Quantum Information
Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their potential applications in fault-tolerant quantum computing. However, all families of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good families of LDPC codes are known that combine constant encoding rate and linear distance. Here we propose the first family of good quantum codes with low-weight stabilizers. The new codes have a constant encoding rate, linear distance, and stabilizers acting on at most square root of n qubits, where n is the code length. For comparison, all previously known families of good quantum codes have stabilizers of linear weight. Our proof combines two techniques: randomized constructions of good quantum codes and the homological product operation from algebraic topology. We conjecture that similar methods can produce good stabilizer codes with stabilizer weight n^a for any a>0. Finally, we apply the homological product to construct new small codes with low-weight stabilizers. This is a joint work with Matthew Hastings.
Quantum Adversary (Upper) Bound

Shelby Kimmel
Massachusetts Institute of Technology (MIT)
November 20, 2013

PIRSA:13110090
Quantum Information
I discuss a technique - the quantum adversary upper bound - that uses the structure of quantum algorithms to gain insight into the quantum query complexity of Boolean functions. Using this bound, I show that there must exist an algorithm for a certain Boolean formula that uses a constant number of queries. Since the method is non-constructive, it does not give information about the form of the algorithm. After describing the technique and applying it to a class of functions, I will outline quantum algorithms that match the non-constructive bound.
Bulk-boundary correspondence in PEPS

Ignacio Cirac
Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
November 13, 2013

PIRSA:13110058
Quantum Information
TBA
A universal Hamiltonian simulator: the full characterization

Gemma De Las Cuevas
Universität Innsbruck
November 11, 2013

PIRSA:13110065
Quantum Information
We show that if the ground state energy problem of a classical spin model is NP-hard, then there exists a choice parameters of the model such that its low energy spectrum coincides with the spectrum of \emph{any} other model, and, furthermore, the corresponding eigenstates match on a subset of its spins. This implies that all spin physics, for example all possible universality classes, arise in a single model. The latter property was recently introduced and called ``Hamiltonian completeness'', and it was shown that several different models had this property. We thus show that Hamiltonian completeness is essentially equivalent to the more familiar complexity-theoretic notion of NP-completeness. Additionally, we also show that Hamiltonian completeness implies that the partition functions are the same. These results allow us to prove that the 2D Ising model with fields is Hamiltonian complete, which is substantially simpler than the previous examples of complete Hamiltonians. Joint work with Toby Cubitt.
Asymptotically Optimal Topological Quantum Compiling

Vadym Kliuchnikov
University of Waterloo
October 30, 2013

PIRSA:13100129
Quantum Information
In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations for non-abelian quasiparticles described by the Fibonacci anyon model. We develop a probabilistically polynomial algorithm that outputs a braid pattern to approximate a given single-qubit unitary to a desired precision. We also classify the single-qubit unitaries that can be implemented exactly by a Fibonacci anyon braid pattern and present an efficient algorithm to produce their braid patterns. Our techniques produce braid patterns that meet the uniform asymptotic lower bound on the compiled circuit depth and thus are depth-optimal asymptotically. Our compiled circuits are significantly shorter than those output by prior state-of-the-art methods, resulting in improvements in depth by factors ranging from 20 to 1000 for precisions ranging between 10^{−10} and 10^{−30}.
Universal fault-tolerant quantum computation with only transversal gates and error correction

Adam Paetznick
September 25, 2013

PIRSA:13090069
Quantum Foundations
Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. It is known, however, that transversal gates alone cannot be computationally universal. I will show that the limitation on universality can be circumvented using only fault-tolerant error correction, which is already required anyway. This result applies to ``triorthogonal'' stabilizer codes, which were recently introduced by Bravyi and Haah for state distillation. I will show that triothogonal codes admit transversal implementation of the controlled-controlled-Z gate, and then demonstrate a transversal Hadamard construction which uses error correction to preserve the codespace. I will also discuss how to adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.
Generalized Relative Entropies, Entanglement Monotones and One-Shot Information Theory

Nilanjana Datta
University of Cambridge
June 17, 2013

PIRSA:13060003
Quantum Information
We introduce two relative entropy quantities called the min- and max-relative
entropies and discuss their properties and operational meanings.

These relative entropies act as parent quantities for tasks such as data compression, information
transmission and entanglement manipulation in one-shot information theory. Moreover, they lead us to define entanglement monotones which have interesting operational interpretations.
Information Theoretic Benefit of Entanglement in Classical Communication Settings

Salman Beigi
Institute for Research in Fundamental Sciences (IPM)
May 27, 2013

PIRSA:13050077
Quantum Information
Expressions of several information theoretic quantities involve an optimization over auxiliary quantum registers. Entanglement-assisted version of some classical communication problems provides examples of such expressions. Evaluating these expressions requires bounds on the dimension of these auxiliary registers. In the classical case such a bound can usually be obtained based on the
Caratheodory theorem, but we know almost no method to bound the dimension of auxiliary quantum registers. In this talk to compare the classical and quantum sides of the problem the notion of “quantum convexification” will be defined. It will be shown that quantum convexification is strictly richer that the usual classical convexification. Moreover some techniques will be discussed which might be useful for bounding the dimension of quantum auxiliary registers.
Processing quantum information with relativistic motion of atoms

Eduardo Martin-Martinez
Institute for Quantum Computing (IQC)
May 13, 2013

PIRSA:13050017
Quantum Information
We show that particle detectors, such as 2-level atoms, in non-inertial motion (or in gravitational fields) could be used to build quantum gates for the processing of quantum information. Concretely, we show that through suitably chosen non-inertial trajectories of the detectors the interaction Hamiltonian's time dependence can be modulated to yield arbitrary rotations in the Bloch sphere due to relativistic quantum effects. Ref. Phys. Rev. Lett. 110, 160501 (2013)
Laws of thermodynamics beyond the von Neumann regime

Oscar Dahlsten
City University of Hong Kong
April 29, 2013

PIRSA:13040112
Quantum Foundations
A recent development in information theory is the generalisation of quantum Shannon information theory to the operationally motivated smooth entropy information theory, which originates in quantum cryptography research. In a series of papers the first steps have been taken towards creating a statistical mechanics based on smooth entropy information theory. This approach turns out to allow us to answer questions one might not have thought were possible in statistical mechanics, such as how much work one can extract in a given realisation, as a function of the failure-probability. This is in contrast to the standard approach which makes statements about average work. Here we formulate the laws of thermodynamics that this new approach gives rise to. We show in particular that the Second Law needs to be tightened. The new laws are motivated by our main quantitative result which states how much work one can extract or must invest in order to affect a given state change with a given probability of success. For systems composed of very large numbers of identical and uncorrelated subsystems, which we call the von Neumann regime, we recover the standard von Neumann entropy statements.

Joint work with Egloff, Renner and Vedral

http://arxiv.org/abs/1207.0434
The continuum limit of tensor networks: a path integral representation

David Jennings
Imperial College London
April 22, 2013

PIRSA:13040113
Quantum Foundations
I will discuss a path-integral representation of continuum tensor networks that extends the continuous MPS class for 1-D quantum fields to arbitrary spatial dimensions while encoding desirable symmetries. The physical states can be interpreted as arising through a continuous measurement process by a lower dimensional virtual field with Lorentz symmetry. The resultant physical states naturally obey entropy area laws, with the expectation values of observables determined by the dissipative dynamics of the boundary field. The class offers the prospect of powerful new analytical and computational tools to describe the physics of strongly interacting field systems.
Continuous-variable entanglement distillation and non-commutative central limit theorems

Earl Campbell
University of Sheffield
April 15, 2013

PIRSA:13040122
Quantum Information
Entanglement distillation transforms weakly entangled noisy states into highly entangled states, a primitive to be used in quantum repeater schemes and other protocols designed for quantum communication and key distribution. In this work, we present a comprehensive framework for continuous-variable entanglement distillation schemes that convert noisy non-Gaussian states into Gaussian ones in many iterations of the protocol. Instances of these protocols include the recursive Gaussifier protocol and the pumping Gaussifier protocol. The flexibility of these protocols give rise to several beneficial trade-offs related to success probabilities or memory requirements that can be adjusted to reflect experimental specifics. Despite these protocols involving measurements, we relate the convergence in this protocols to new instances of non-commutative central limit theorems. Implications of the findings for quantum repeater schemes are discussed.

Title	Speaker(s)	Date	Talk Type	Info
Homological Product Codes	Sergey Bravyi	2013-11-27	Scientific Series	View details
Quantum Adversary (Upper) Bound	Shelby Kimmel	2013-11-20	Scientific Series	View details
Bulk-boundary correspondence in PEPS	Ignacio Cirac	2013-11-13	Scientific Series	View details
A universal Hamiltonian simulator: the full characterization	Gemma De Las Cuevas	2013-11-11	Scientific Series	View details
Asymptotically Optimal Topological Quantum Compiling	Vadym Kliuchnikov	2013-10-30	Scientific Series	View details
Universal fault-tolerant quantum computation with only transversal gates and error correction	Adam Paetznick	2013-09-25	Scientific Series	View details
Generalized Relative Entropies, Entanglement Monotones and One-Shot Information Theory	Nilanjana Datta	2013-06-17	Scientific Series	View details
Information Theoretic Benefit of Entanglement in Classical Communication Settings	Salman Beigi	2013-05-27	Scientific Series	View details
Processing quantum information with relativistic motion of atoms	Eduardo Martin-Martinez	2013-05-13	Scientific Series	View details
Laws of thermodynamics beyond the von Neumann regime	Oscar Dahlsten	2013-04-29	Scientific Series	View details
The continuum limit of tensor networks: a path integral representation	David Jennings	2013-04-22	Scientific Series	View details
Continuous-variable entanglement distillation and non-commutative central limit theorems	Earl Campbell	2013-04-15	Scientific Series	View details

Perimeter Institute Quantum Discussions

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