Perimeter Institute Quantum Discussions

428 talks

S006

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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 241 - 252 of 428

A non-commuting stabilizer formalism

Xiaotong Ni
Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 09, 2014

PIRSA:14040136
Quantum Foundations

Quantum Gravity
Quantum Computing with Noninteracting Particles

Alex Arkhipov
Massachusetts Institute of Technology (MIT)
April 02, 2014

PIRSA:14040077
Quantum Information
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure

Roger Mong
University of Pittsburgh
March 19, 2014

PIRSA:14030118
Quantum Information
Maximal Privacy Without Coherence

Debbie Leung
Institute for Quantum Computing (IQC)
March 12, 2014

PIRSA:14030105
Quantum Information
Probabilistic protocols in quantum information

Joshua Combes
University of Colorado Boulder
February 13, 2014

PIRSA:14020138
Quantum Information
Applications of Information Theory in Direct Sum and Direct Product Problems
February 12, 2014

PIRSA:14020142
Quantum Information
Bosonic particle-correlated states

Zhang Jiang
University of New Mexico
February 06, 2014

PIRSA:14020135
Quantum Information
Hardness of correcting errors on a stabilizer code

Pavithran Iyer
January 22, 2014

PIRSA:14010099
Quantum Information
Entanglement farming: Harnessing the properties of fixed points in quantum evolution

Eduardo Martin-Martinez
Institute for Quantum Computing (IQC)
January 15, 2014

PIRSA:14010104
Quantum Information
The computational power of matchgates and the XY interaction on arbitrary graphs

Daniel Brod
Universidade Federal Fluminense
January 08, 2014

PIRSA:14010085
Quantum Information
The Bose-Hubbard model is QMA-complete

David Gosset
Institute for Quantum Computing (IQC)
December 18, 2013

PIRSA:13120067
Quantum Information
Direct Detection of Classically Undetectable Dark Matter through Quantum Decoherence

Jess Riedel
NTT Research
December 04, 2013

PIRSA:13120053
Quantum Information

A non-commuting stabilizer formalism

Xiaotong Ni
Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 09, 2014

PIRSA:14040136
Quantum Foundations

Quantum Gravity
We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of single-qubit operators drawn from the group {\alpha I, X,S}, where \alpha=e^{i\pi/4} and S=diag(1,i). We provide techniques to efficiently compute various properties, related to e.g. bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians etc. We also highlight significant differences compared to the Pauli stabilizer formalism. In particular we give examples of states in our formalism which cannot arise in the Pauli stabilizer formalism, such as topological models that supports non-abelian anyons. This is a joint work with O. Buerschaper and M. van den Nest.
Quantum Computing with Noninteracting Particles

Alex Arkhipov
Massachusetts Institute of Technology (MIT)
April 02, 2014

PIRSA:14040077
Quantum Information
We introduce an abstract model of computation corresponding to an experiment in which identical, non-interacting bosons are sent through a non-adaptive linear circuit before being measured. We show that despite the very limited nature of the model, an exact classical simulation would imply a collapse of the polynomial hierarchy. Moreover, under plausible conjectures, a "noisy" approximate simulation would do the same. This gives evidence that quantum computers can sample a distribution that classical computers cannot even approximate, even when restricted to use no entanglement except that arising from particles being identical. We briefly discuss experimental prospects for realizing this model. This talk is based on The Computational Complexity of Linear Optics [STOC '11], which is joint work with Scott Aaronson.
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure

Roger Mong
University of Pittsburgh
March 19, 2014

PIRSA:14030118
Quantum Information
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. The Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support Ising non-Abelian anyons, also referred to as Majorana zero modes. Here we construct a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles, and like the Z3 Read-Rezayi state, harbors Fibonacci anyons that--unlike Ising anyons--allow for universal topological quantum computation solely through braiding.
Maximal Privacy Without Coherence

Debbie Leung
Institute for Quantum Computing (IQC)
March 12, 2014

PIRSA:14030105
Quantum Information
Privacy and coherence have long been considered closely related properties of a quantum state. Indeed, a coherently transmitted quantum state is inherently private. Surprisingly, coherent quantum communication is not always required for privacy: there are quantum channels that are too noisy to transmit quantum information but it can send private classical information. Here, we ask how different the private classical and the quantum capacities can be. We present a class of channels N_d with input dimension d^2, quantum capacity Q(N_d) <= 1, and private classical capacity P(N_d) = log d. These channels asymptotically saturate an interesting inequality P(N) <= (log d_A + Q(N))/2 for any channel N with input dimension d_A, and capture the essence of privacy stripped of the confounding influence of coherence.
Probabilistic protocols in quantum information

Joshua Combes
University of Colorado Boulder
February 13, 2014

PIRSA:14020138
Quantum Information
Probabilistic protocols in quantum information are an attempt to improve performance by occasionally reporting a better result than could be expected from a deterministic protocol. Here we show that probabilistic protocols can never improve performance beyond the quantum limits on the corresponding deterministic protocol. To illustrate this result we examine three common probabilistic protocols: probabilistic amplification, weak value amplification, and probabilistic metrology. In each of these protocols we show explicitly that the optimal deterministic protocol is better than the corresponding probabilistic protocol when the probabilistic nature of the protocol is correctly accounted for.
Applications of Information Theory in Direct Sum and Direct Product Problems
February 12, 2014

PIRSA:14020142
Quantum Information
A fundamental question in complexity theory is how much resource is needed to solve k independent instances of a problem compared to the resource required to solve one instance. Suppose solving one instance of a problem with probability of correctness p, we require c units of some resource in a given model of computation. A direct sum theorem states that in order to compute k independent instances of a problem, it requires k times units of the resource needed to compute one instance. A strong direct product theorem states that, with o(k • c) units of the resource, one can only compute all the k instances correctly with probability exponentially small in k. In this talk, I am going to present some of recent progress on direct sum and direct product theorems in the model of communication complexity and two-prover one-round games with information-theoretic approach. The talk is based on parts of my doctoral work.
Bosonic particle-correlated states

Zhang Jiang
University of New Mexico
February 06, 2014

PIRSA:14020135
Quantum Information
Quantum many-body problems are notorious hard. This is partly because the Hilbert space becomes exponentially big with the particle number N. While exact solutions are often considered intractable, numerous approaches have been proposed using approximations. A common trait of these approaches is to use an ansatz such that the number of parameters either does not depend on N or is proportional to N, e.g., the matrix-product state for spin lattices, the BCS wave function for superconductivity, the Laughlin wave function for fractional quantum Hall effects, and the Gross-Pitaecskii theory for BECs. Among them the product ansatz for BECs has precisely predicted many useful properties of Bose gases at ultra-low temperature. As particle-particle correlation becomes important, however, it begins to fail. To capture the quantum correlations, we propose a new
set of states, which constitute a natural generalization of the product-state ansatz. Our state of N=d& times;n identical particles is derived by symmetrizing the n-fold product of a d-particle quantum state. For fixed d, the parameter space of our state does not grow with N. Numerically, we show that our ansatz gives the right description for the ground state and time evolution of the two-site Bose-Hubbard model.
Hardness of correcting errors on a stabilizer code

Pavithran Iyer
January 22, 2014

PIRSA:14010099
Quantum Information
Problems in computer science are often classified based on the scaling of the runtimes for algorithms that can solve the problem. Easy problems are efficiently solvable but often in physics we encounter problems that take too long to be solved on a classical computer. Here we look at one such problem in the context of quantum error correction. We will further show that no efficient algorithm for this problem is likely to exist. We will address the computational hardness of a decoding problem, pertaining to quantum stabilizer codes considering independent X and Z errors on each qubit. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the decoding problem consists of determining the most likely recovery given the syndrome. The corresponding classical problem is known to be NP-Complete, and a similar decoding problem for quantum codes is known to be NP-Complete too. However, this decoding strategy is not optimal in the quantum setting as it does not take into account error degeneracy, which causes distinct errors to have the same effect on the code. Here, we show that optimal decoding of stabilizer codes is computationally much harder than optimal decoding of classical linear codes, it is #P-Complete.
Entanglement farming: Harnessing the properties of fixed points in quantum evolution

Eduardo Martin-Martinez
Institute for Quantum Computing (IQC)
January 15, 2014

PIRSA:14010104
Quantum Information
We show that in certain generic circumstances the state of light of an optical cavity traversed by beams of atoms is naturally driven towards a non-thermal metastable state. This state can be such that successive pairs of unentangled particles sent through the cavity will reliably emerge significantly entangled thus providing a renewable source of quantum entanglement. Significant for possible experimental realizations is the fact that this entangling fixed point state of the cavity can be reached largely independently of the initial state in which the cavity was prepared. Our results suggest that reliable entanglement farming on the basis of such a fixed point state should be possible also in various other experimental settings, namely with the to-be-entangled particles replaced by arbitrary qudits and with the cavity replaced by a suitable reservoir system.
The computational power of matchgates and the XY interaction on arbitrary graphs

Daniel Brod
Universidade Federal Fluminense
January 08, 2014

PIRSA:14010085
Quantum Information
Matchgates are a restricted set of two-qubit gates known to be classically simulable when acting on nearest-neighbor qubits on a path, but universal for quantum computation when the gates can also act on more distant qubits. In this talk, I will address the power of matchgates when they can act on pairs of qubits according to the edges of arbitrary graphs. Specifically, we show that matchgates are universal on any connected graph other than a path or a cycle, and that they are classically simulable on a cycle. We also prove that the same dichotomy holds for the XY interaction, a proper subset of matchgates that arises naturally in some implementations of quantum computing. This is based on a joint work with Ernesto Galvão and another with Andrew Childs.
The Bose-Hubbard model is QMA-complete

David Gosset
Institute for Quantum Computing (IQC)
December 18, 2013

PIRSA:13120067
Quantum Information
The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete. In our QMA-hardness proof, we encode the history of an n-qubit computation in the subspace with at most one particle per site (i.e., hard-core bosons). This feature, along with the well-known mapping between hard-core bosons and spin systems, lets us prove a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model. By avoiding the use of perturbation theory in our analysis, we circumvent the need to multiply terms in the Hamiltonian by large coefficients. This is joint work with Andrew Childs and Zak Webb.
Direct Detection of Classically Undetectable Dark Matter through Quantum Decoherence

Jess Riedel
NTT Research
December 04, 2013

PIRSA:13120053
Quantum Information
Although various pieces of indirect evidence about the nature of dark matter have been collected, its direct detection has eluded experimental searches despite extensive effort. If the mass of dark matter is below 1 MeV, it is essentially imperceptible to conventional detection methods because negligible energy is transferred to nuclei during collisions. Here I propose directly detecting dark matter through the quantum decoherence it causes rather than its classical effects such as recoil or ionization. I show that quantum spatial superpositions are sensitive to low-mass dark matter that is inaccessible to classical techniques. This provides new independent motivation for matter interferometry with large masses, especially on spaceborne platforms. The apparent dark matter wind we experience as the Sun travels through the Milky Way ensures interferometers and related devices are directional detectors, and so are able to provide unmistakable evidence that decoherence has galactic origins.

Title	Speaker(s)	Date	Talk Type	Info
A non-commuting stabilizer formalism	Xiaotong Ni	2014-04-09	Scientific Series	View details
Quantum Computing with Noninteracting Particles	Alex Arkhipov	2014-04-02	Scientific Series	View details
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure	Roger Mong	2014-03-19	Scientific Series	View details
Maximal Privacy Without Coherence	Debbie Leung	2014-03-12	Scientific Series	View details
Probabilistic protocols in quantum information	Joshua Combes	2014-02-13	Scientific Series	View details
Applications of Information Theory in Direct Sum and Direct Product Problems		2014-02-12	Scientific Series	View details
Bosonic particle-correlated states	Zhang Jiang	2014-02-06	Scientific Series	View details
Hardness of correcting errors on a stabilizer code	Pavithran Iyer	2014-01-22	Scientific Series	View details
Entanglement farming: Harnessing the properties of fixed points in quantum evolution	Eduardo Martin-Martinez	2014-01-15	Scientific Series	View details
The computational power of matchgates and the XY interaction on arbitrary graphs	Daniel Brod	2014-01-08	Scientific Series	View details
The Bose-Hubbard model is QMA-complete	David Gosset	2013-12-18	Scientific Series	View details
Direct Detection of Classically Undetectable Dark Matter through Quantum Decoherence	Jess Riedel	2013-12-04	Scientific Series	View details

Perimeter Institute Quantum Discussions

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