Search results in Quantum Physics from PIRSA
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Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.
Ravi Kunjwal Funds for Scientific Research - FNRS
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The computational power of matchgates and the XY interaction on arbitrary graphs
Daniel Brod Universidade Federal Fluminense
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The Bose-Hubbard model is QMA-complete
David Gosset Institute for Quantum Computing (IQC)
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Rebuilding Mathematics on a Quantum Logical Foundation
Richard deJonghe University of Illinois at Chicago
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Quantum Mechanics as Classical Physics
Charles Sebens University of Michigan–Ann Arbor
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Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States
Elie Wolfe Perimeter Institute for Theoretical Physics
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Quantum Adversary (Upper) Bound
Shelby Kimmel Massachusetts Institute of Technology (MIT)
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Light and matter: towards macroscopic quantum systems
Jacob Taylor Office of Science and Technology Policy
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Bulk-boundary correspondence in PEPS
Ignacio Cirac Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
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Entanglement farming: Harnessing the properties of fixed points in quantum evolution
Eduardo Martin-Martinez University of Waterloo
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. -
Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.
Ravi Kunjwal Funds for Scientific Research - FNRS
The purpose of this talk is twofold: First, following Spekkens, to motivate noncontextuality as a natural principle one might expect to hold in nature and introduce operational noncontextuality inequalities motivated by a contextuality scenario first considered by Ernst Specker. These inequalities do not rely on the assumption of outcome-determinism which is implicit in the usual Kochen-Specker (KS) inequalities. We argue that they are the appropriate generalization of KS inequalities, serving as a test for the possibility of noncontextual explanations of experimental data. This is very much in the spirit of Bell inequalities, which provide theory-independent tests for local hidden variable explanations of experimental data without relying on the assumption of outcome-determinism. The second purpose is to point out a curious feature of quantum theory, motivated by the connections between (in)compatibility and (non)contextuality: namely, that it admits all conceivable (in)compatibility relations between observables. -
The computational power of matchgates and the XY interaction on arbitrary graphs
Daniel Brod Universidade Federal Fluminense
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)
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. -
Rebuilding Mathematics on a Quantum Logical Foundation
Richard deJonghe University of Illinois at Chicago
It is not unnatural to expect that difficulties lying at the foundations of quantum mechanics can only be resolved by literally going back and rethinking the quantum theory from first principles (namely, the principles of logic). In this talk, I will present a first-order quantum logic which generalizes the propositional quatum logic originated by Birkhoff and von Neumann as well as the standard classical predicate logic used in the development of virtually all of modern mathematics. I will then use this quantum logic to begin to build the foundations of a new ``quantum mathematics'' --- in particular a quantum set theory and a quantum arithmetic --- which has the potential to provide a completely new mathematical framework in which to develop the theory of quantum
mechanics. -
Direct Detection of Classically Undetectable Dark Matter through Quantum Decoherence
Jess Riedel NTT Research
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. -
Quantum Mechanics as Classical Physics
Charles Sebens University of Michigan–Ann Arbor
On the face of it, quantum physics is nothing like classical physics. Despite its oddity, work in the foundations of quantum theory has provided some palatable ways of understanding this strange quantum realm. Most of our best theories take that story to include the existence of a very non-classical entity: the wave function. Here I offer an alternative which combines elements of Bohmian mechanics and the many-worlds interpretation to form a theory in which there is no wave function. According to this theory, all there is at the fundamental level are particles interacting via Newtonian forces. In this sense, the theory is classical. However, it is still undeniably strange as it posits the existence of many worlds. Unlike the many worlds of the many-worlds interpretation, these worlds are fundamental, not emergent, and are interacting, not causally isolated. The theory will be presented as a fusion of the many-worlds interpretation and Bohmian mechanics, but can also be seen as a foundationally clear version of quantum hydrodynamics. A key strength of this theory is that it provides a simple and compelling story about the connection between the amplitude-squared of the wave function and probability. The theory also gives a natural explanation of the way the wave function transforms under time reversal and Galilean boosts. -
Homological Product Codes
Sergey Bravyi IBM (United States)
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. -
Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States
Elie Wolfe Perimeter Institute for Theoretical Physics
We present a method for determining the maximum possible violation of any linear Bell inequality per quantum mechanics. Essentially this amounts to a constrained optimization problem for an observable’s eigenvalues, but the problem can be reformulated so as to be analytically tractable. This opens the door for an arbitrarily precise characterization of quantum correlations, including allowing for non-random marginal expectation values. Such a characterization is critical when contrasting QM to superficially similar general probabilistic theories. We use such marginal-involving quantum bounds to estimate the volume of all possible quantum statistics in the complete 8-dimensional probability space of the Bell-CHSH scenario, measured relative to both local hidden variable models as well as general no-signaling theories. See arXiv:1106.2169. Time permitting, we’ll also discuss how one might go about trying to prove that a given mixed state is, in fact, not entangled. (The converse problem of certifying non-zero entanglement has received extensive treatment already.) Instead of directly asking if any separable representation exists for the state, we suggest simply checking to see if it “fits” some particular known-separable form. We demonstrate how a surprisingly valuable sufficient separability criterion follows merely from considering a highly-generic separable form. The criterion we generate for diagonally-symmetric mixed states is apparently completely tight, necessary and sufficient. We use integration to quantify the “volume” of states captured by our criterion, and show that it is as large as the volume of states associated with the PPT criterion; this simultaneously proves our criterion to be necessary as well as the PPT criterion to be sufficient, on this family of states. The utility of a sufficient separability criterion is evidenced by categorically rejecting Dicke-model superradiance for entanglement generation schema. See arXiv:1307.5779. -
Quantum Adversary (Upper) Bound
Shelby Kimmel Massachusetts Institute of Technology (MIT)
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
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)
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