Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session D33: Focus Session: Quantum Foundations: What Powers Quantum Advantages for Information Processing? |
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Sponsoring Units: GQI Chair: Joseph Emerson, University of Waterloo Room: 706 |
Monday, March 3, 2014 2:30PM - 2:42PM |
D33.00001: Contextuality supplies the magic for Quantum Computation Mark Howard, Joel Wallman, Victor Veitch, Joseph Emerson Quantum computers are poised to deliver a dramatic increase in computational power, which can be used to perform difficult tasks such as simulating molecules for medical research much more efficiently than any current computer. However, it is notoriously difficult to characterize what is needed for a quantum computer to be useful. In this paper we prove that two characteristic quantum phenomena, namely, negative probabilities and contextuality, are equivalent in the most well-known and promising architecture for fault-tolerant quantum computation using $d$-level quantum systems ($d$ odd prime). Together with recent work, this implies that contextuality is necessary for quantum computers based upon this architecture to outperform any current computer. Our results are also relevant to the question of identifying the largest ``classical'' subtheory of quantum mechanics. [Preview Abstract] |
Monday, March 3, 2014 2:42PM - 2:54PM |
D33.00002: Mixing nonclassical pure states in a linear-optical network almost always generates modal entanglement Zhang Jiang, Mattihas Lang, Carlton Caves In quantum optics a pure state is considered classical, relative to the statistics of photodetection, if and only if it is a coherent state. A different and newer notion of nonclassicality is based on modal entanglement. One example that relates these two notions is the Hong-Ou-Mandel effect, where modal entanglement is generated by a beamsplitter from the nonclassical photon-number state $\vert 1 \rangle \otimes\vert 1\rangle$. This suggests the beamsplitter or, more generally, linear-optical networks as a mediator of the two notions of nonclassicality. We show the following: Given a nonclassical pure product state input to an $N$-port linear-optical network, the output is almost always mode entangled; the only exception is a product of squeezed states, all with the same squeezing strength, input to a network that does not mix the squeezed and anti-squeezed quadratures. Our work thus gives a necessary and sufficient condition for a linear network to generate modal entanglement from pure product inputs, a result that is of immediate relevance to the boson sampling problem. [Preview Abstract] |
Monday, March 3, 2014 2:54PM - 3:06PM |
D33.00003: Quantum computational universality of Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice Tzu-Chieh Wei Universal quantum computation can be achieved by simply performing single-spin measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states has recently been explored; for example, the spin-1 AKLT chain can be used to simulate single-qubit gate operations on a single qubit, and the spin-3/2 two-dimensional AKLT state on the honeycomb lattice can be used as a universal resource. However, it is unclear whether such universality is a coincidence for the specific state or a shared feature in all two-dimensional AKLT states. Here we consider the family of spin-3/2 AKLT states on various trivalent Archimedean lattices and show that in addition to the honeycomb lattice, the spin-3/2 AKLT states on the square octagon $(4,8^2)$ and the `cross' $(4,6,12)$ lattices are also universal resources, whereas the AKLT state on the `star' $(3,12^2)$ lattice is likely not due to geometric frustration. Ref. T.-C. Wei, arXiv:1306.1420. [Preview Abstract] |
Monday, March 3, 2014 3:06PM - 3:42PM |
D33.00004: Local orthogonality as a foundational principle Invited Speaker: Antonio Acin |
Monday, March 3, 2014 3:42PM - 3:54PM |
D33.00005: A measure of Quantum Unspeakable Information Davide Girolami A piece of information is said unspeakable if it cannot be encoded into a sequence of bits. For example, the transformation law between the coordinates of two distant laboratories cannot be specified without a shared reference frame. This condition has been proven to be equivalent to constrain local operations in the two labs by means of a superselection rule [Rev. Mod. Phys. 79, 555 (2007)]. I introduce a measure of unspeakable information based on the skew information [PNAS 49, 910 (1963)], which evaluates the ability of a quantum state to act as a reference frame under a specific superselection rule. Then, I show that evaluating unspeakable information is equivalent to measuring the amount of quantum coherence of a state with respect to a given basis. I propose a proof of concept experiment in optical set-up to evaluate the amount of unspeakable information, i.e. of relative coherence, of a quantum state without fully reconstructing its density matrix. [Preview Abstract] |
Monday, March 3, 2014 3:54PM - 4:06PM |
D33.00006: Contextuality in Measurement-based Quantum Computation Robert Raussendorf We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a non-linear Boolean function with high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a super-polynomial speedup over the best known classical algorithm, namely the quantum algorithm that solves the `Discrete Log' problem. [Preview Abstract] |
Monday, March 3, 2014 4:06PM - 4:18PM |
D33.00007: Scalable Implementation of Boson Sampling with Trapped Ions Chao Shen, Zhen Zhang, Luming Duan Boson sampling solves a classically intractable problem by sampling from a probability distribution given by matrix permanents. We propose a scalable implementation of Boson sampling using local transverse phonon modes of trapped ions to encode the Bosons. The proposed scheme allows deterministic preparation and high-efficiency readout of the Bosons in the Fock states and universal mode mixing. With the state-of-the-art trapped ion technology, it is feasible to realize Boson sampling with tens of Bosons by this scheme, which would outperform the most powerful classical computers and constitute an effective disproof of the famous extended Church-Turing thesis. [Preview Abstract] |
Monday, March 3, 2014 4:18PM - 4:30PM |
D33.00008: Whirling waves in Interference experiments Urbasi Sinha, Rahul Sawant, Joseph Samuel, Aninda Sinha, Supurna Sinha In a double slit interference experiment, the wave function at the screen with both slits open is not exactly the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well- known text books in quantum mechanics implicitly and/or explicitly use this assumption, the wave function hypothesis, which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in interference experiments which provide a measurable deviation from the wave function hypothesis [1]. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence. I will also describe some ongoing experimental efforts towards testing our theoretical findings. \\[4pt] [1] Whirling waves in interference experiments, R.Sawant, J.Samuel, A.Sinha, S.Sinha and U.Sinha, arXiv: 1308.2022. [Preview Abstract] |
Monday, March 3, 2014 4:30PM - 4:42PM |
D33.00009: Quantum Computing from Addition-rule-based Cellular Automata Cheng Wu We argue that addition rules must be imposed first for a general-purpose quantum computing. This brings the addition operation into the architecture of one-dimensional cellular automaton with dual bits per cell. The four symbolic substitution rules are transformed into a 16 specific right-nearest-neighbor cell-to-cell rules. Thus addition operation is only one set out of roughly 4.3 billion available sets to be found in the cellular automaton. When the half-adder fundamental processors are wired together differently and become addition-rule incompatible, gliders or oscillations between two configurations will result as a new kind of science. Those examples as well as the cellular automaton's connection to the main-stream qubit approach will be presented and discussed. [Preview Abstract] |
Monday, March 3, 2014 4:42PM - 4:54PM |
D33.00010: Long-Range Entanglement Is Necessary for a Topological Storage of Quantum Information Isaac Kim A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum state, we obtain an upper bound on the number of distinct states that are locally indistinguishable from it. The upper bound is determined only by the entanglement entropy of some local subsystems. As an example, we show that $\log N \leq 2\gamma$ for a large class of topologically ordered systems on a torus, where $N$ is the number of topologically protected states and $\gamma$ is the constant subcorrection term of the entanglement entropy. We discuss applications to quantum many-body systems that do not have any low-energy topological quantum field theory description, as well as tradeoff bounds for general quantum error correcting codes. [Preview Abstract] |
Monday, March 3, 2014 4:54PM - 5:06PM |
D33.00011: Quantum mechanics over sets David Ellerman In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, ${\rm Z}_{2}$, since ${\rm Z}_{2}$ vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over ${\rm Z}_{2}$ (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2$^{\mathrm{n}}$ function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over ${\rm Z}_{2}$ \textit{just like classical computing}. This shows definitively that the source of quantum speedup is \textit{not} in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition. [Preview Abstract] |
Monday, March 3, 2014 5:06PM - 5:18PM |
D33.00012: Sudden Decoherence Transitions for Quantum Discord Hyungjun Lim, Robert Joynt We formulate the computation of quantum discord in terms of the generalized Bloch vector, which gives useful insights on the time evolution of quantum coherence for the open system, particularly the comparison of entanglement and discord. We present an efficient numerical method to calculating the quantum discord for a certain important class of multipartite states, and show that the analytical calculation of the global geometric discord is NP-hard in the number of qubits. In agreement with previous work for 2-qubit cases, (Mazzola \textit{et al.} Phys. Rev. Lett. 104, 200401 (2010)), we find situations where under decohering influences there is a sudden transition from classical to quantum decoherence characterized by the discord remaining relatively robust until a certain point from which it begins decaying quickly. However, we find that as the number of qubits increases, the chance of this kind of transition occurring becomes small. This work was supported in part by ARO (W911NF-12-1-0607). [Preview Abstract] |
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