Session 2
Speaker: Andrew White (University of Queensland)
Title: Quantum Chemistry on a Quantum Computer: First Steps and Prospects
We use a photonic quantum computer to simulate the hydrogen molecule. This is the first experimental demonstration of efficient quantum chemistry, which promises to be a powerful new tool in biology, chemistry, and materials science.
In principle, it is possible to model any physical system exactly using quantum mechanics; in practice, it quickly becomes infeasible. Recognising this, Richard Feynman suggested that quantum systems be used to model quantum problems. For example, the fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a molecule as well as most other properties, can be calculated by solving the Schrodinger equation. However, the computational resources required to obtain exact solutions on a conventional computer generally increase exponentially with the number of atoms involved. In the late 1990's an efficient algorithm was proposed to enable a quantum processor to calculate molecular energies using resources that increase only polynomially in the molecular size. Despite the many different physical architectures that have been explored experimentally since that time---including ions, atoms, superconducting circuits, and photons---this appealing algorithm has not been demonstrated to date.
Here we take advantage of recent advances in photonic quantum computing to present an optical implementation of the smallest quantum chemistry problem: obtaining the energies of H_2, the hydrogen molecule, in a minimal basis. We perform a key algorithmic step---the iterative phase estimation algorithm---in full, achieving a high level of precision and robustness to error. We implement other algorithmic steps with assistance from a classical computer, and explain how this non-scalable approach could be avoided. Finally we provide new theoretical results which lay the foundations for the next generation of simulation experiments using quantum computers. We have made early experimental progress towards the long term goal of exploiting quantum information to speed up quantum chemistry calculations.
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Speaker: Steve Flammia (Perimeter Institute)
Title: Ultrafast quantum state tomography
Everybody hates tomography. And with good reason! Experimentalists hate it because it is inefficient and difficult. Theorists hate it because it isn't very "quantum." But because of our current lack of meso-scale quantum computers capable of convincingly performing non-classical calculations, tomography seems like a necessary evil. In this talk, I will attempt to banish quantum state tomography to the Hell of Lost Paradigms where it belongs. I hope to achieve this by introducing several heuristics for learning quantum states more efficiently, in some cases exponentially so. One such heuristic runs in polynomial time and outputs a polynomial-sized classical approximation of the state (in matrix product state form.) Another takes advantage of the fact that most interesting states are close to pure states to get a quadratic speedup using ideas from compressed sensing. Both algorithms come with rigorous error bounds.
This is joint work with S. Bartlett, D. Gross, R. Somma (first result), and S. Becker, J. Eisert, D. Gross, and Y.-K. Liu (second result).
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Speaker: Shohini Ghose (Wilfrid Laurier University)
Title: Entanglement and nonlocality in multiqubit pure states
Coauthors: N. Sinclair, S. Debnath, P. Rungta and R. Stock
Multiqubit entanglement is a crucial ingredient for large-scale quantum information processing and can also play a role in quantum criticality phenomena in condensed matter systems. Entanglement between qubits can lead to violations of Bell-type inequalities, indicating the nonlocal nature of the correlations between qubits. We have derived relationships between genuine multiqubit entanglement and nonlocality for families of 3-qubit pure states. Our results show that these relationships are counterintuitive and can be quite different from the well-known relationship between 2-qubit entanglement and violation of the Bell-CHSH inequality. We identify tripartite entangled states that do not violate the Svetlichny inequality, which tests for genuine tripartite nonlocal correlations. On the other hand, we show that all members of a set of states called the maximal slice states violate the Svetlichny inequality and analogous to the 2-qubit case, the amount of violation increases with the amount of entanglement. The generalized GHZ states and the maximal slice states have unique tripartite entanglement and nonlocality properties in the set of all pure states. Our results can be simply generalized to analyze multiqubit entanglement and nonlocality in systems of 4 or more qubits.
Paper reference: arXiv:0812.3695
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Speaker: Kyung Soo Choi (California Institute of Technology)
Title: Multipartite entanglement for one photon shared among four optical modes
Coauthors: S. B. Papp, H. Deng, P. Lougovski, S. J. van Enk, H. J. Kimble
Access to genuine multipartite entanglement of quantum states enables advances in quantum information science and also contributes to the understanding of strongly correlated quantum systems. A critical requirement for realizing these extraordinary promises, however, is an efficient and unambiguous method to detect and characterize the purported entanglement. We report the detection and characterization of heralded entanglement in a multipartite quantum state composed of four optical modes that share one photon, a so-called W state [1]. By reducing the relative phase coherence between bipartite components of the W state, we observe the transitions from four- to three- to two-mode entanglement. These observations are possible for our system because our entanglement verification protocol makes use of quantum uncertainty relations to simultaneously detect the entangled states that span the Hilbert space of interest [2].
Paper reference: [1] Science 324, 764 (2009); [2] New J. Phys. 11, 063029 (2009).