Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session A8: Quantum Information meets Many-Particle Physics |
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Sponsoring Units: GQI Chair: David DiVincenzo, IBM Watson Room: 414/415 |
Monday, March 16, 2009 8:00AM - 8:36AM |
A8.00001: Preparing ground states of quantum many-body systems on a quantum computer Invited Speaker: The simulation of quantum many-body systems is a notoriously hard problem in condensed matter physics, but it could easily be handled by a quantum computer [4,1]. There is however one catch: while a quantum computer can naturally implement the dynamics of a quantum system --- i.e. solve Schr\"odinger's equation --- there was until now no general method to initialize the computer in a low-energy state of the simulated system. We present a quantum algorithm [5] that can prepare the ground state and thermal states of a quantum many-body system in a time proportional to the square-root of its Hilbert space dimension. This is the same scaling as required by the best known algorithm to prepare the ground state of a classical many-body system on a quantum computer [3,2]. This provides strong evidence that for a quantum computer, preparing the ground state of a quantum system is in the worst case no more difficult than preparing the ground state of a classical system. \begin{thebibliography}{1} \bibitem{AT03b} {\sc D.~Aharonov and A.~Ta-Shma}, {\em Adiabatic quantum state generation and statistical zero knowledge}, Proc. 35th Annual ACM Symp. on Theo. Comp., (2003), p.~20. \bibitem{B82a} {\sc F.~Barahona}, {\em On the computational complexity of ising spin glass models}, J. Phys. A. Math. Gen., 15 (1982), p.~3241. \bibitem{BBBV97a} {\sc C.~H. Bennett, E.~Bernstein, G.~Brassard, and U.~Vazirani}, {\em Strengths and weaknessess of quantum computing}, SIAM J. Comput., 26 (1997), pp.~1510--1523, quant-ph/9701001. \bibitem{Llo96b} {\sc S.~Lloyd}, {\em Universal quantum simulators}, Science, 273 (1996), pp.~1073--1078. \bibitem{PW08a} {\sc D.~Poulin and P.~Wocjan}, {\em Preparing ground states of quantum many-body systems on a quantum computer}, 2008, arXiv:0809.2705. \end{thebibliography} [Preview Abstract] |
Monday, March 16, 2009 8:36AM - 9:12AM |
A8.00002: Topological Quantum Order from Symmetry and the Role of Temperature Invited Speaker: What does a fractional quantum Hall liquid and Kitaev's proposals for topological quantum computation have in common? It turns out that they are physical systems that exhibit degenerate ground states with properties seemingly different than ordinary (Landau-type) phases of matter, such as ferromagnets. For example, those (topologically quantum ordered) states cannot be characterized by (local) order parameters such as magnetization. How does one characterize this new order? I will present a unifying framework which will allow us to engineer physical systems displaying topological quantum order. What are the physical properties of these new orders? How robust are they to temperature effects? What are they useful for? Topologically quantum ordered states of matter seem to be ideal physical systems to store and manipulate quantum information since they are believed to be robust against decoherence with an environment, and thus appropriate for building a quantum computer and quantum memories. I will discuss the role of temperature in the protection of quantum information. Have we finally found a new technological application for quantum Hall liquids? [Preview Abstract] |
Monday, March 16, 2009 9:12AM - 9:48AM |
A8.00003: Tensor-entanglement renormalization Invited Speaker: Traditional mean-field theory is a simple generic variational approach for analyzing various symmetry breaking phases. However, this simple approach only applies to symmetry breaking states with short-range entanglement. Tensor-entanglement renormalization group (TERG) is a generic approach for studying 2D quantum phases with long-range entanglement (such as topological phases) based on a new class of trial wavefucntions - the tensor product states (TPS), also known as projected entangled pair states (PEPS). Those TPS (PEPS) are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry breaking states) and states with long-range entanglement (such as topological/quantum order). TERG is a real space renormalization group algorithm that can efficiently simulate expectation values for TPS wave functions in 2D and higher dimensions. As an attempt in this direction, we demonstrate our algorithm by studying several simple 2D quantum spin models, including both symmetry breaking phase transitions and topological phase transitions. However, as any variational method, the TERG approach could not find all the degenerate ground states for gapped systems and generally could not give out (approximately) correct critical exponent for critical systems. To solve these problems, we study the renormalization group flow of a Lagrangian (partition function) by representing its path integral through a tensor network. Using a tensor-entanglement-filtering renormalization group (TEFRG) method that removes local entanglement and coarse grains the lattice, we show that the renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors characterize various phases. The tensor fixed points can describe both the symmetry breaking phases and topological phases. The ground state degeneracy for gapped systems can be easily read out from the fixed point tensor. The scaling dimensions, the central charge and dynamic correlation functions for the critical systems that describe the continuous phase transitions between symmetry breaking and/or topological phases can also be calculated from the TEFRG approach. [Preview Abstract] |
Monday, March 16, 2009 9:48AM - 10:24AM |
A8.00004: Can multi-particle systems be too entangled to be useful for quantum computation? Invited Speaker: In the context of ``quantum information meets many-particle physics'', we pose the question of the role of entanglement in the quantum computational power of many-particle quantum systems (1). It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs sufficient entanglement for this speedup to be manifest. In measurement-based quantum computing, the need for a highly entangled initial state is particularly obvious. In this work we show that, remarkably, quantum states can be too entangled - in the sense of having a too large geometric entanglement - to be useful for the purpose of computation. What is more, we can prove that this phenomenon occurs for the dramatic majority of all states: the fraction of pure states on n qubits not subject to the problem is smaller than e$^{-n{^2}}$. Our results show that computational universality is actually a rare property in quantum states. For the proof we make use of a link between the ``quantum probabilistic method'' and ideas on quantum many-body systems. This work stresses a new aspect of the question concerning the role entanglement plays for quantum computational speed-ups. We will also investigate a new classification of primitives from projected entangled pair states (PEPS) that can be used in order to systematically construct new models for measurement-based computation (2,3). In an outlook, I will - if time allows - mention other recent group activities related to quantum information and many-particle physics, including dynamical area laws and relaxation statements (4,5). \\[4pt] (1) ``Most quantum states are too entangled to be useful as computational resources'', Phys. Rev. Lett., in press (2009)\\[0pt] (2) ``Quantum computational webs'', arXiv:0810.2542\\[0pt] (3) ``Novel schemes for measurement-based quantum computation'', Phys. Rev. Lett. 98, 220503 (2007)\\[0pt] (4) ``Exact relaxation in a class of nonequilibrium quantum lattice systems'', Phys. Rev. Lett. 100, 030602 (2008)\\0[pt] (5) ``Area laws for the entanglement entropy'', Rev. Mod. Phys., in press (2009). [Preview Abstract] |
Monday, March 16, 2009 10:24AM - 11:00AM |
A8.00005: Quantum-limited metrology and many-body physics Invited Speaker: Questions about quantum limits on measurement precision were once viewed from the perspective of how to reduce or avoid the effects of the quantum noise that is a consequence of the uncertainty principle. With the advent of quantum information science came a paradigm shift to proving rigorous bounds on measurement precision. These bounds have been interpreted as saying, first, that the best achievable sensitivity scales as $1/N$, where $N$ is the number of particles one has available for a measurement and, second, that the only way to achieve this Heisenberg-limited sensitivity is to use quantum entanglement. I will review these results and discuss a new perspective based on using nonlinear quantum dynamics to improve sensitivity. Using quadratic couplings of $N$ particles to a parameter to be estimated, one can achieve sensitivities that scale as $1/N^2$ if one uses entanglement, but even in the absence of any entanglement at any time during the measurement protocol, one can achieve a super-Heisenberg scaling of $1/N^{3/2}$. Such sensitivity scalings might be achieved in Bose-Einstein condensates or in nanomechanical resonators. [Preview Abstract] |
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