Quantum Information

Junwen Zou and Stephen Hogan Resonant dipole-dipole interactions between Rydberg helium atoms and cold ground-state ammonia molecules allow Förster resonance energy transfer between the electronic degrees of freedom in the atom, and the nuclear degrees of freedom associated with the inversion of the molecule [1,2]. In this talk I will describe recent experiments in which we have exploited the Stark effect in the triplet Rydberg states in helium, with values of the principal quantum number n between 38 and 40, to tune these interactions through resonance using electric fields below 10 V/cm. Resonance widths as narrow as 70 MHz have been observed in this work. These are indicative of mean centre-of-mass collision speeds on the order of 10 m/s, and collisions that occur at temperatures significantly below 1 K. Studies of Förster resonances in this collision system are of interest in the search for dipole-bound states [3] of Rydberg atoms or molecules and polar ground-state molecules, in the exploitation of long-range dipole-dipole interactions to regulate access to ion-molecule chemistry that can occur if the polar molecule penetrates inside the Rydberg electron charge distribution [4], and for coherent control and non-destructive detection [5,6]. [1] V. Zhelyazkova and S. D. Hogan, Phys. Rev. A 95, 042710 (2017) [2] K. Gawlas and S. D. Hogan, J. Phys. Chem. Lett. 11, 83 (2020) [3] S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Côté, E. E. Eyler and P. L. Gould, Phys. Rev. Lett. 91, 183002 (2003). [4] V. Zhelyazkova, F. B. V. Martins, J. A. Agner, H. Schmutz and F. Merkt, Phys. Rev. Lett. 125, 263401 (2020) [5] E. Kuznetsova, S. T. Rittenhouse, H. R. Sadeghpour and S. F. Yelin, Phys. Chem. Chem. Phys. 13, 17115 (2011) [6] M. Zeppenfeld, Euro. Phys. Lett. 118, 13002 (2017)

"A quantum system evolving on a manifold of discrete states can be viewed as a particle moving in a real-space lattice potential. Such a synthetic dimension provides a powerful tool for quantum simulation because of the ability to engineer many aspects of the Hamiltonian describing the system. In this talk, I will describe a synthetic dimension created from Rydberg levels in an 84-Sr atom, in which coupling between the states is induced with millimeter-waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger Hamiltonian, a paradigmatic model of topological matter. I will also briefly describe our recent results creating ultralong-range Rydberg molecule (ULRRM) dimers in an interacting Bose gas and probing nonlocal three-body spatial correlations with ULRRM trimers. Kanungo, S.K., Whalen, J.D., Lu, Y. et al. Realizing topological edge states with Rydberg-atom synthetic dimensions. Nat Commun 13, 972 (2022). https://doi.org/10.1038/s41467-022-28550-y "

Simulation of quantum magnetism with AMO systems is now a fully fledged enterprise. In this talk, I will discuss how Rydberg molecular interactions can be exploited to simulate indirect spin-spin coupling, with Rydberg atoms acting as localized impurities. Engineering chiral spin Hamiltonians with Rydberg atoms is also described.

"We present our recent studies on Rydberg atom-Ion interactions and the spatial imaging of a novel type of molecular ion using a high-resolution ion microscope. The ion microscope provides an exceptional spatial and temporal resolution on a single atom level, where a highly tuneable magnification ranging from 200 to over 1500, a resolution better than 200nm and a depth of field of more than 70µm were demonstrated [1]. A pulsed operation mode of the microscope combined with the excellent electric field compensation enables the study of highly excited Rydberg atoms and ion-Rydberg atom hybrid systems. Using the ion microscope, we observed a novel molecular ion, where the bonding mechanism is based on the interaction between the ionic charge and an induced flipping dipole of a Rydberg atom [2]. Furthermore, we could measure the vibrational spectrum and spatially resolve the bond length and the angular alignment of the molecule. The excellent time resolution of the microscope enables probing of the interaction dynamics between the Rydberg atom and the ion. [1] C. Veit, N. Zuber, O. A. Herrera-Sancho, V. S. V. Anasuri, T. Schmid, F. Meinert, R. Löw, and T. Pfau, Pulsed Ion Microscope to Probe Quantum Gases, Phys. Rev. X 11, 011036 (2021). [2] N. Zuber, V. S. V. Anasuri, M. Berngruber, Y.-Q. Zou, F. Meinert, R. Löw, T. Pfau, Spatial imaging of a novel type of molecular ions, Nature 5, 453 (2022)"

While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop algorithms for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing.

Zoom Link: https://pitp.zoom.us/j/92831825506?pwd=T2VUQ2M2QlZERmRmUHZ0T1VOelkzZz09

Quantum information science was initially motivated by questions about information processing. For example, what are the consequences of quantum mechanics for computation? Or for cryptography? More recently, quantum information has also become a perspective through which we can study questions in theoretical physics more broadly, including in condensed matter and quantum gravity. While quantum information considers the constraints of quantum mechanics, there are additional constraints on information implied by relativity. In particular, it is impossible to send information faster than the speed of light. In this talk, I consider constraints on information processing imposed by quantum mechanics and relativity together, and the consequences of these constraints for quantum gravity. Doing so reveals novel aspects of how gravitational degrees of freedom can be recorded into a quantum mechanical system, and how an extra dimension can be recorded into ``holographic'' field theories.

Zoom Link: https://pitp.zoom.us/j/99249375009?pwd=QWZyZzQrNXJwSGYyYTZheGwwaVRndz09

We are used to thinking of there being different types of fault-tolerant gates allowing reliable computation on states in a noisy quantum computer: Some are transversal, some involve measurement and magic states, some involve topological manipulations, etc.  In this talk, we will demonstrate that transversal gates can be seen as a topological effect, and we will propose an over-arching framework for thinking about fault tolerance in terms of fiber bundles over the Grassmanian, the manifold of subspaces of Hilbert space.  The violin will harmonize with the chalkboard to put the talk to music.

Zoom Link: https://pitp.zoom.us/j/97600230984?pwd=NDJ4VjdvUS9palA4YzFnZHBwcnJkUT09

Quantum error correction and symmetries are two key notions in quantum information and physics. The competition between them has fundamental implications in fault-tolerant quantum computing, many-body physics and quantum gravity. We systematically study the competition between quantum error correction and continuous symmetries associated with a quantum code in a quantitative manner. We derive various forms of trade-off relations between the quantum error correction inaccuracy and three types of symmetry violation measures. We introduce two frameworks for understanding and establishing the trade-offs based on the notions of charge fluctuation and gate implementation error. From the perspective of fault-tolerant quantum computing, we demonstrate fundamental limitations on transversal logical gates. We also analyze the behaviors of two near-optimal codes: a parametrized extension of the thermodynamic code, and quantum Reed–Muller codes.

Zoom Link: TBD

We study the entanglement dynamics of quantum many-body systems at long times. For upper bounds, we prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy is bounded away from the maximum entropy at all times with high probability. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy is bounded away from the maximum entropy at all times. We also extend these results to any unitary evolution with charge conservation and to the Sachdev-Ye-Kitaev model. For lower bounds, we say that a Hamiltonian is an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. These results imply ``unbounded growth of entanglement’’ in many-body localized systems.
References: arXiv:2102.07584 & 2104.02053

Zoom Link: https://pitp.zoom.us/j/96027097746?pwd=R2V2ZktJZUV1VkliN3pzM0IzbGR0UT09

I will outline our recent approach to a theory of quantum networks, which we base on the graphical tensor calculus of Penrose. We aim to use this approach as a means to unite quantum computation, condensed matter physics and tensor network states with a long history of existing methods and techniques. I will sketch the status of our approach and focus on methods we have developed to reason and control the states created by specific networks of contracted tensors, as well as tensor contractions capturing the key properties of algebraic invariants of operators and states.