Universality and quantized response in bosonic nonfractionalized tunneling

We show that tunneling involving bosonic wires and/or boson integer quantum Hall (bIQH) edges is characterized by universal features which are absent in their fermionic counterparts. Considering a pair of minimal geometries, we find a low energy enhancement and a universal high versus zero energy relation for the tunnel conductance that holds for all wire/bIQH edge combinations. Features distinguishing bIQH edges include a current imbalance to chemical potential bias ratio that is quantized despite the lack of conductance quantization in the bIQH edges themselves. The predicted phenomena require only initial states to be thermal and thus are well suited for tests with ultracold bosons forming wires and bIQH states. For the latter, we highlight a potential realization based on single component bosons in the recently observed Harper-Hofstadter bandstructure

A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation

Majorana zero modes (MZMs) are promising candidates for topologically-protected quantum computing hardware, however their large-scale use will likely require quantum error correction. Majorana surface codes (MSCs) have been proposed to achieve this. However, many MSC properties remain unexplored. We present a unified framework for MSC "twist defects" \unicode{x2013} anyon-like objects encoding quantum information. We show that twist defects in MSCs can encode twice the amount of topologically protected information as in qubit-based codes or other MSC encoding schemes. This is due to twists encoding both logical qubits and "logical MZMs," with the latter enhancing the protection microscopic MZMs can offer. We explain how to perform universal computation with logical qubits and logical MZMs while using far fewer resources than in other MSC schemes. All Clifford gates can be implemented on logical qubits by braiding twist defects. We introduce measurement-based techniques for computing with logical MZMs and logical qubits, achieving the effect of Clifford gates with zero time overhead. We also show that logical MZMs result in an improved scaling of spatial overheads with respect to code distance for all steps of the computation. Finally, we introduce a novel MSC analogue of transversal gates that achieves encoded Clifford gates in small codes by braiding microscopic MZMs. MSC twist defects thus open new paths towards fault-tolerant quantum computation.Comment: 32 pages, 21 figure

Supersymmetry in the Standard Sachdev-Ye-Kitaev Model.

Supersymmetry is a powerful concept in quantum many-body physics. It helps to illuminate ground-state properties of complex quantum systems and gives relations between correlation functions. In this Letter, we show that the Sachdev-Ye-Kitaev model, in its simplest form of Majorana fermions with random four-body interactions, is supersymmetric. In contrast to existing explicitly supersymmetric extensions of the model, the supersymmetry we find requires no relations between couplings. The type of supersymmetry and the structure of the supercharges are entirely set by the number of interacting Majorana modes and are thus fundamentally linked to the model's Altland-Zirnbauer classification. The supersymmetry we uncover has a natural interpretation in terms of a one-dimensional topological phase supporting Sachdev-Ye-Kitaev boundary physics and has consequences away from the ground state, including in q-body dynamical correlation functions

Strong Zero Modes from Geometric Chirality in Quasi-One-Dimensional Mott Insulators.

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include Z_{n} chiral quantum clock models with strong zero modes related to Z_{n} parafermions. Here, we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on n=3 where the Mott insulators are three-leg ladders. We link such ladders to Z_{3} chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the Z_{3} chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature

Strong Zero Modes from Geometric Chirality in Quasi-One-Dimensional Mott Insulators.

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include Zn chiral quantum clock models with strong zero modes related to Zn parafermions. Here we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on n=3 where the Mott insulators are three-leg ladders. We link such ladders to Z3 chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the Z3 chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature

Coherent error threshold for surface codes from Majorana delocalization

Statistical mechanics mappings provide key insights on quantum error correction. However, existing mappings assume incoherent noise, thus ignoring coherent errors due to, e.g., spurious gate rotations. We map the surface code with coherent errors, taken as $X$- or $Z$-rotations (replacing bit or phase flips), to a two-dimensional (2D) Ising model with complex couplings, and further to a 2D Majorana scattering network. Our mappings reveal both commonalities and qualitative differences in correcting coherent and incoherent errors. For both, the error-correcting phase maps, as we explicitly show by linking 2D networks to 1D fermions, to a $\mathbb{Z}_2$-nontrivial 2D insulator. However, beyond a rotation angle $\phi_\text{th}$, instead of a $\mathbb{Z}_2$-trivial insulator as for incoherent errors, coherent errors map to a Majorana metal. This $\phi_\text{th}$ is the theoretically achievable storage threshold. We numerically find $\phi_\text{th}\approx0.14\pi$. The corresponding bit-flip rate $\sin^2(\phi_\text{th})\approx 0.18$ exceeds the known incoherent threshold $p_\text{th}\approx0.11$.Comment: 9 pages, 7 figure