Quantum Information

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

The past decade has seen an explosion of research into resource theories—simple, quantum-information-theoretic models for constrained agents. Resource theories have provided foundational insights about thermodynamics, entanglement, and more. Yet whether resource theories can inform science outside our neighborhood of quantum information theory has been an outstanding question. I will present what is, to my knowledge, the first application of a resource theory to answer a pre-existing question in another field. Molecular switches, or photoisomers, surface across nature and technologies, from our eyes to solar-fuel cells. What probability does a switch have of switching? A general answer defies standard chemistry tools, as photoisomers are small, quantum and far from equilibrium. I will bound the switching probability by modeling a photoisomer within a thermodynamic resource theory. This work has helped pave the path for resource theories to impact science broadly.

References
• NYH and Limmer, Phys. Rev. A 101, 042116 (2020). https://journals.aps.org/pra/
abstract/10.1103/PhysRevA.101.042116
• NYH, in Eddington, Wheeler, and the Limits of Knowledge, Eds. Durham and
Rickles, Springer (2017) arXiv:1509.03873.

Zoom Link: https://pitp.zoom.us/j/99315796008?pwd=dDJBMjR2ckRmdlhtdWJZeHJuNUI1QT09

We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal gates and qubit permutations only. To demonstrate our approach, we specifically consider a [[30, 8, 3]] hyperbolic quantum code called Bring's code. Further, we show that by restricting the logical subspace of Bring's code to four qubits, we can obtain the full Clifford group on that subspace.

Zoom Link: https://pitp.zoom.us/j/94852018243?pwd=RmFHM1QyNS9CK0RMRm5yUEt0MzdSZz09