Quantum Information

Quantum mechanics redefines information and its fundamental properties. Researchers at Perimeter Institute work to understand the properties of quantum information and study which information processing tasks are feasible, and which are infeasible or impossible. This includes research in quantum cryptography, which studies the trade-off between information extraction and disturbance, and its applications. It also includes research in quantum error correction, which involves the study of methods for protecting information against decoherence. Another important side of the field is studying the application of quantum information techniques and insights to other areas of physics, including quantum foundations and condensed matter.

Displaying 865 - 876 of 1338

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
University of Waterloo
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
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
Light and matter: towards macroscopic quantum systems

Jacob Taylor
Office of Science and Technology Policy
November 20, 2013

PIRSA:13110060
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
Simulating Hamiltonian evolution with quantum computers

Richard Cleve
Institute for Quantum Computing (IQC)
October 16, 2013

PIRSA:13100097
Quantum Information

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
University of Waterloo
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.
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.
Light and matter: towards macroscopic quantum systems

Jacob Taylor
Office of Science and Technology Policy
November 20, 2013

PIRSA:13110060
Quantum Information
Advances in quantum engineering and material science are enabling new approaches for building systems that behave quantum mechanically on long time scales and large length scales. I will discuss how microwave and optical technologies in particular are leading to new domains of many-body physics, both classical and quantum, using photons and phonons as the constituent particles. Furthermore, I will highlight practical consequences of these advances, including improved force and acceleration sensing, efficient signal transduction, and topologically robust photonic circuits. Finally, I will consider how such large quantum systems may help us measure and constrain theories of quantum gravity and gravity-induced decoherence.
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}.
Simulating Hamiltonian evolution with quantum computers

Richard Cleve
Institute for Quantum Computing (IQC)
October 16, 2013

PIRSA:13100097
Quantum Information
In 1982, Richard Feynman proposed the concept of a quantum computer as a means of simulating physical systems that evolve according to the Schrödinger equation. I will explain various quantum algorithms that have been proposed for this simulation problem, including my recent work (jointly with Dominic Berry and Rolando Somma) that significantly improves the running time as a function of the precision of the output data.

Title	Speaker(s)	Date	Talk Type	Info link
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
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
Light and matter: towards macroscopic quantum systems	Jacob Taylor	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
Simulating Hamiltonian evolution with quantum computers	Richard Cleve	2013-10-16	Scientific Series	View details

Quantum Information

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