Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session G65: Topological QubitsFocus
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Sponsoring Units: DQI Chair: Alexandre Bourassa, University of Chicago Room: Room 414 |
Tuesday, March 7, 2023 11:30AM - 11:42AM |
G65.00001: Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code Yuri D Lensky, Kostyantyn Kechedzhi, Igor L Aleiner, Eun-Ah Kim Stabilizer codes allow for non-local encoding and processing of quantum information. Deformations of stabilizer surface codes introduce new and non-trivial geometry, in particular leading to emergence of long sought after objects known as projective Ising non-Abelian anyons. Braiding of such anyons is a key ingredient of topological quantum computation. We suggest a simple and systematic approach to construct effective unitary protocols for braiding, manipulation and readout of non-Abelian anyons and preparation of their entangled states. We generalize the surface code to a more generic graph with vertices of degree 2, 3 and 4. Our approach is based on the mapping of the stabilizer code defined on such a graph onto a model of Majorana fermions charged with respect to two emergent gauge fields. One gauge field is akin to the physical magnetic field. The other one is responsible for emergence of the non-Abelian anyonic statistics and has a purely geometric origin. This field arises from assigning certain rules of orientation on the graph known as the Kasteleyn orientation in the statistical theory of dimer coverings. Each 3-degree vertex on the graph carries the flux of this "Kasteleyn" field and hosts a non-Abelian anyon. In our approach all the experimentally relevant operators are unambiguously fixed by locality, unitarity and gauge invariance. We illustrate the power of our method by making specific prescriptions for experiments verifying the non-Abelian statistics. |
Tuesday, March 7, 2023 11:42AM - 11:54AM |
G65.00002: Observation of non-Abelian exchange statistics on a superconducting processor Trond I Andersen, Yuri D Lensky, Kostyantyn Kechedzhi, Ilya K Drozdov, Andreas Bengtsson, Sabrina S Hong, Alexis Morvan, Xiao Mi, Alexander Opremcak, Eun-Ah Kim, Igor Aleiner, Pedram Roushan Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, their experimental observation has remained elusive for decades. Using a superconducting quantum processor, we prepare the ground state of the surface code and manipulate it via unitary operations to form wavefunctions that are described by non-Abelian anyons. By implementing a unitary protocol to move the anyons, we experimentally verify the fusion rules of non-Abelian Ising anyons and braid them to realize their statistics. Building on our technique, we study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work represents a key step towards topological quantum computing. |
Tuesday, March 7, 2023 11:54AM - 12:06PM |
G65.00003: Tunable fermionic error correction Abhijeet Alase, David L Feder, Barry C Sanders, Kevin D Stubbs Majorana-based qubits are promising candidates for realizing topological quantum computers. Developing experimentally feasible schemes for quantum error correction for such qubits is necessary for achieving scalability. In this work, we show that the ground states of the Kitaev chain Hamiltonian, for any parameter values in the topological phase, form an approximate error-correcting code that corrects local fermionic parity-preserving errors. We also show, numerically, that this code has storage time exponentially large in the system size if the errors are caused only due to weak disorder in the system. The stabilizers for our code are constructed using Wannier functions of the modes of the clean system. We analytically prove the exponential localization of such Wannier functions under semi-open boundary conditions. Our work shows that the adverse effects of disorder on the lifetime of Majorana qubits can be alleviated by tuning the stabilizers with respect to the parameters of the clean system. |
Tuesday, March 7, 2023 12:06PM - 12:42PM |
G65.00004: Elements of Majorana-based quantum computing Invited Speaker: Felix von Oppen Majorana bound states have been suggested as building blocks of a topological quantum computer. In this talk, I will discuss theoretical ideas how to implement Majorana-based quantum computing, focusing on Majorana qubits and their readout as well as a possible realization of a universal set of quantum gates. |
Tuesday, March 7, 2023 12:42PM - 12:54PM |
G65.00005: Quantum Computing with Two-dimensional Conformal Field Theories Elias Kokkas, Aaron Bagheri, Zhenghan Wang, George Siopsis Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of two-dimensional conformal field theories to fault-tolerant quantum computation based on the coset SU(2)1k /SU(2)k. We calculate higher-dimensional braiding matrices by considering conformal blocks involving 2N anyons, and search for gapped states that can be built from these conformal blocks. We introduce a gapped wavefunction that generalizes the Moore-Read state which is based on the critical Ising model, and show that our generalization leads to universal quantum computing. |
Tuesday, March 7, 2023 12:54PM - 1:06PM |
G65.00006: Induced superconductivity in thin films of cadmium arsenide Arman Rashidi, Robert Kealhofer, Alexander C Lygo, Victor Huang, Susanne Stemmer Topological superconductors can host non-Abelian quasiparticles that have profound implications for fault-tolerant quantum computing. Hybrid structures between topological insulators and superconductors are an attractive route towards a topological superconductor. Here, we report on induced superconductivity in Josephson junctions fabricated on the surface of thin films of cadmium arsenide (Cd3As2), which are tuned into different topological and trivial states, respectively, including a two-dimensional (2D) topological insulator (TI). The junctions are in a short junction limit with no hysteresis in their current-voltage characteristic and exhibit a 20 µeV induced superconducting gap. The measured superconducting quantum interference (SQI) pattern for mesa-isolated junctions fabricated on a film that is in a 2D TI state deviates from a Fraunhofer pattern that is expected for a junction with a bulk-dominated superconducting transport. Measurements of the SQI in Josephson junction and superconducting quantum interference (SQUID) device geometries, respectively allows us to separate the contribution of bulk and edge electronic states and determine current-phase relations of the junctions. We utilize electrostatic gating to tune the films into the gap of the insulating states and demonstrate gate-tuning between the bulk- and edge-dominated transport regimes. |
Tuesday, March 7, 2023 1:06PM - 1:18PM |
G65.00007: Probing Majorana States in S-TI-S Josephson Junctions by Resonator and Transmon Measurements Drew G Wild, Guang Yue, Xiong Yao, Deepti Jain, Jisoo Moon, Seongshik Oh, Dale J Van Harlingen The observation of Majorana zero modes and their non-abelian statistics is critical to the development of topologically-protected quantum computers. Lateral S-TI-S Josephson junctions made from depositing s-wave superconductors on a topological insulator substrate are predicted to host localized Majorana zero modes in a weak vertical magnetic field. The critical current and hence inductive energy of such a junction is thought to be partially dependent on the parity of Majorana pairs in the junction, with experimental evidence suggestive but thus far inconclusive. To make a more definitive test, we are creating quantum circuits incorporating S-TI-S junctions to probe for parity sensitivity in the inductive energy via microwave resonator and transmon experiments. |
Tuesday, March 7, 2023 1:18PM - 1:30PM |
G65.00008: Electronic structure of the InSb-CdTe-αSn interface: using CdTe as a barrier Malcolm J Jardine, Sergey M Frolov, Noa Marom, Derek Dardzinski, Maituo Yu, An-Hsi Chen, Aaron N Engel, Chris J Palmstrom, Yu-Hao Chang, Moira Hocevar Understanding the effects of interfacing materials is pivotal to the design of semiconductor, spintronic, and quantum devices. We study the InSb-CdTe-αSn interface via density functional theory (DFT). |
Tuesday, March 7, 2023 1:30PM - 1:42PM |
G65.00009: Superconducting quantum effects in Ge-Si core-shell nanowires Joost Ridderbos, Zhen Wu, Ang Li, Erik P. A. M. Bakkers, Chuan Li, Alexander Brinkman, Floris Zwanenburg Ge-Si core-shell nanowires feature one-dimensional confinement, low disorder and strong ‘first order’ Rashba spin-orbit interaction (SOI) [1]. These wires can therefore be utilised to realize various advanced applications such as an (Andreev) spin-qubit and a long-range quantum bus based on strong spin-photon coupling. Additionally, when combined with an s-wave superconductor and a sufficiently large Zeeman field - or in the case of double nanowires a sufficiently large crossed-Andreev excitation gap [2] - Ge-Si nanowires should undergo a topological phase transition that hosts Majorana fermions [3]. |
Tuesday, March 7, 2023 1:42PM - 1:54PM |
G65.00010: Extrinsic spin-orbit coupling in hybrid nanowires with micromagnet arrays Michael P Hynes, Declan Burke, Alexandros Vekris, Jesper Nygard, Kristof Moors, Will R Branford, Malcolm R Connolly, Mark R Buitelaar Arrays of anti-aligned micromagnets have been proposed as a way to generate rotating magnetic fields which can induce both an extrinsic spin-orbit coupling and Zeeman splitting in superconducting-semiconductor nanowires. This technique has the potential to widen the range of materials that can host Majorana modes to include low-disorder materials like carbon nanotubes or silicon nanowires, as well as enhance the topological protection available in existing materials by adding to their intrinsic spin-orbit coupling. We demonstrate the preparation of micromagnet arrays into the anti-aligned micromagnetic configuration using a sequence of externally applied magnetic fields. Measurements using bias spectroscopy show micromagnetic configuration dependence in a hybrid nanowire superconducting island . Low bias features of the superconducting island are consistent with the presence of a subgap state in the nanowire with a 25µeV difference in subgap state energy between anti-aligned and aligned micromagnetic configurations. |
Tuesday, March 7, 2023 1:54PM - 2:06PM |
G65.00011: Qubit resource states for measurement-based quantum teleportation beyond the Haldane phase David L Feder, Zhuohao Liu, Emma C Johnson All currently known resource states for measurement-based quantum computation possess symmetry protected topological order (STPO), known as Haldane-phase states, but it is not clear if this is a necessary or sufficient condition. This work investigates the ability of one-dimensional qubit states to perform universal and deterministic measurement-based quantum gate teleportation (MBQT) in correlation space, within the framework of matrix product states with bond dimension four, without making any assumptions about SPTO. Several families of resource states are identified and expressed analytically that permit MBQT of both single-qubit and two-qubit gates. We find examples of states without SPTO that are able to perform MBQT, and examples of Haldane-phase states that are unable to do so, even via infinitesimal gates. The results reveal a complex relationship between SPTO and MBQT for qubits. |
Tuesday, March 7, 2023 2:06PM - 2:18PM |
G65.00012: Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation Campbell McLauchlan, Benjamin Béri Majorana zero modes (MZMs) could offer a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations for computation (e.g., braids) pose significant challenges. We introduce fermion-parity-based computation (FPBC): a measurement-based scheme, modeled on Pauli-based computation, that uses efficient classical processing to "virtually" increase the number of available MZMs. Furthermore, given a suitable input state, FPBC operates without the need to perform any transformations such as braids. This could greatly reduce the resource cost of implementing fermionic circuits. However, FPBC requires all MZM parity operators to be measurable, a requirement that conflicts with constraints in previously proposed MZM hardware. We thus introduce a novel design in which all such operators are directly measurable in a single shot, and which is hence well suited to FPBC. |
Tuesday, March 7, 2023 2:18PM - 2:30PM |
G65.00013: Non-Abelian holonomy in a chaotic Majorana billiard Max Geier, Svend Krøjer, Felix von Oppen, Karsten Flensberg, Piet Brouwer A ``Majorana billiard'' consists of a chaotic cavity coupled to a topological superconductor via tunneling contacts. In the limit of zero transmission, each of these contacts hosts a Majorana zero mode. Close to a cavity resonance and at a finite contact transparency, the resonant mode couples the Majorana modes, but a ground state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the cavity exceeds five. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold can be achieved. We characterize the corresponding non-Abelian holonomy using random matrix theory and discuss measurable signatures of the non-Abelian time-evolution. |
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