Canonical Structure and Conservation Laws of General Relativity on Null Surfaces and at Null Infinity

The first part of this thesis addresses the canonical structure of general relativity on generic null surfaces. The pre-symplectic potential of metric general relativity, evaluated on a null surface, is decomposed into variables describing the intrinsic and extrinsic geometry of the null surface, without fixing the gauge. Canonical pairs on the null surface and its boundary are identified and interpreted. Boundary contributions to the action corresponding to Dirichlet boundary conditions are identified. The constraints on a null surface are written in the same variables, and naturally take the form of conservation laws mirroring those at null infinity, equating the divergence of a relativistic current intrinsic to the null surface to a flux which has a canonical form. The conservation laws are interpreted canonically and related to Noether’s theorem. The second part of this thesis addresses the problem that in asymptotically simple spacetimes, such as asymptotically flat spacetimes, the pre-symplectic potential of field theories on constant-radius surfaces generically diverges in the radius. A scheme is introduced for electromagnetism and gravity which, on-shell, for any spacetime dimension, allows one to absorb the divergences into counterterms, which correspond to the ambiguities of the pre-symplectic potential. The counterterms are local including in the radius, and render also the action and the pre-symplectic potential on constant-time surfaces finite. The scheme employs Penrose’s conformal compactification of spacetime. The scheme is introduced and explored for electromagnetism in D ≥ 5 dimensions. The equations of motion are analyzed in an asymptotic expansion for asymptotically flat spacetimes, and the free data and dependencies among the data entering the symplectic potential are identified. The gauge generators are identified, and are rendered independent of subleading orders of the gauge parameter by introducing further local, finite counterterms. The generators and their fluxes coincide with expressions derived from soft theorems of quantum electrodynamics in even dimensions. Finally, the renormalization scheme is developed for general relativity in asymptotically simple spacetimes, where it applies in D ≥ 3 dimensions and for any cosmological constant, and does not require any boundary or gauge conditions beyond asymptotic simplicity and some degree of regularity. The resulting expression for the pre-symplectic potential is specialized to a relaxation of the Bondi gauge conditions for four-dimensional asymptotically flat spacetimes, and an existing result is recovered. The scheme is compared to holographic renormalization in four and five spacetime dimensions, and the renormalized stress-energy tensors on asymptotically AdS space are recovered up to scheme-dependent terms. The canonical generators of diffeomorphisms under the renormalized symplectic form are computed

Compact Pulse Schedules for High-Fidelity Single-Flux Quantum Qubit Control

In the traditional approach to controlling superconducting qubits using microwave pulses, the field of pulse shaping has emerged in order to assist in the removal of leakage and increase gate fidelity. However, the challenge of scaling microwave control electronics has created an opportunity to explore alternative methods such as single-flux quantum (SFQ) pulses. For qubits controlled by SFQ pulses, high fidelity gates can be achieved by optimizing the binary control sequence. We extend the notion of the derivative removal by adiabatic gate (DRAG) framework a transmon qubit controlled by SFQ drivers and propose pulse sequences that can be stored in 22 bits or fewer, with gate fidelities exceeding 99.99%. This modest memory requirement could help reduce the footprint of the SFQ coprocessors and power dissipation while preserving their inherent advantages of scalability and cost-effectiveness

Autonomous quantum error correction of Gottesman-Kitaev-Preskill states

The Gottesman-Kitaev-Preskill (GKP) code encodes a logical qubit into a bosonic system with resilience against single-photon loss, the predominant error in most bosonic systems. Here we present experimental results demonstrating quantum error correction of GKP states based on reservoir engineering of a superconducting device. Error correction is made autonomous through an unconditional reset of an auxiliary transmon qubit. The lifetime of the logical qubit is shown to be increased from quantum error correction, therefore reaching the point at which more errors are corrected than generated.Comment: 6 pages, 3 figures + 26 pages, 12 figure

Holographic Formulation of 3D Metric Gravity with Finite Boundaries

In this work we construct holographic boundary theories for linearized 3D gravity, for a general family of finite or quasi-local boundaries. These boundary theories are directly derived from the dynamics of 3D gravity by computing the effective action for a geometric boundary observable, which measures the geodesic length from a given boundary point to some center in the bulk manifold. We identify the general form for these boundary theories and find that these are Liouville-like with a coupling to the boundary Ricci scalar. This is illustrated with various examples, which each offer interesting insights into the structure of holographic boundary theories