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arXiv:1911.06755

Monte Carlo studies of modified scalable designs for quantum computation

Guan-Hao Feng, Jingwei Chen, Zhang, Hong-Hao

Published Nov 15, 2019• 0 citations
arXivHTMLPDF

Abstract

As the building blocks of topological quantum computation, Majorana zero modes (MZMs) have attracted tremendous attention in recent years. Scalable mesoscopic island designs with MZMs show great potential in quantum information processing. However, these systems are susceptible to quasi-particle poisoning which would induce various parity-breaking errors. To solve this problem, we modify the mesoscopic islands with gate-tunable valves and non-topological backbones. We study the lifetime of the Majorana qubits on these modified islands which are coupled to local bosonic and fermionic thermal baths. We consider both the parity-breaking and parity-preserving errors, and propose a parity correction scheme. By using Jordan-Wigner transformation, we analyze the probability of logical X and Y errors. The open quantum system is described by the Pauli master equation, and standard Monte Carlo simulations are applied to observe the behavior of the system when the parity correction proposal is implemented. The results demonstrate that (1) our parity correction proposal is effective to most of the parity-breaking errors; (2) the lifetime of the qubit benefits from larger island size before it meets the threshold; (3) small chemical potential $ μ$ on the non-topological backbones and fine tuned paring potential $ Δ$ of the topological bulk segment are required for high probability of correctness. Our results provide an effective error correction scheme for the parity-breaking errors.

DOI
10.48550/arxiv.1911.06755

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As the building blocks of topological quantum computation, Majorana zero modes (MZMs) have attracted tremendous attention in recent years. Scalable mesoscopic island designs with MZMs show great potential in quantum information processing. However, these systems are susceptible to quasi-particle poisoning which would induce various parity-breaking errors. To solve this problem, we modify the mesoscopic islands with gate-tunable valves and non-topological backbones. We study the lifetime of the Majorana qubits on these modified islands which are coupled to local bosonic and fermionic thermal baths. We consider both the parity-breaking and parity-preserving errors, and propose a parity correction scheme. By using Jordan-Wigner transformation, we analyze the probability of logical X and Y errors. The open quantum system is described by the Pauli master equation, and standard Monte Carlo simulations are applied to observe the behavior of the system when the parity correction proposal is implemented. The results demonstrate that (1) our parity correction proposal is effective to most of the parity-breaking errors; (2) the lifetime of the qubit benefits from larger island size before it meets the threshold; (3) small chemical potential μ μμ on the non-topological backbones and fine tuned paring potential Δ ΔΔ of the topological bulk segment are required for high probability of correctness. Our results provide an effective error correction scheme for the parity-breaking errors.
We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological TTT-junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.
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We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy.Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots.Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.
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" – 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 potentially using far fewer resources than in other MSC schemes. All Clifford gates can be implemented on logical qubits by braiding twist defects. We introduce lattice-surgery-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 may result in improved spatial overheads for sufficiently low rates of quasi-particle poisoning. 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.
In the context of quantum computing, error correction remains a pivotal challenge, primarily due to imperfect gate operations and environmental interactions. This study introduces a machine learning-based method to simulate and analyze these errors. Utilizing a minimal scalable 2-Majorana-zero-mode (2-MZM) island model within a one-dimensional p-wave topological superconductor, this research employs a detailed Hamiltonian approach combined with a bosonic thermal bath interaction. The analysis is conducted using the Pauli master equation and Monte Carlo simulations. This work’s novel contribution lies in applying Boosted Decision Tree with Gradient boosting (BDTG) and Multi-Layer Perceptron (MLP) machine learning techniques. These methods, trained on Monte Carlo simulation data, showed proficiency in predicting the evolution of error probabilities in the quantum system. The results indicate a significant potential for machine learning to offer a more efficient alternative for simulating quantum computing errors, thereby contributing to developing more robust quantum computing systems.
Quantum computers are devices that can solve certain problems faster than ordinary, classical computers. The fundamental units of quantum information are qubits, superpositions of two states, a "zero" state and a "one" state. There are various approaches to construct such two-level systems, among others, using superconducting circuits, trapped ions or photons. A common feature of these physical systems is that their coherence times are relatively short compared to the length of useful computations. Superconducting qubits, for instance, are currently the most advanced solid-state qubits, but they decohere after around 100 microseconds, and any information stored in these qubits is lost. On the other hand, useful quantum computations may require quantum information to survive on time scales that are many orders of magnitude longer, as their runtimes can reach several hours or even days. Topological quantum computing is an approach to construct qubits that survive for the entire duration of such a long computation. Topological quantum computing comes in two flavors. The condensed matter approach is to build error-resilient qubits using exotic quasiparticles in topological materials, most prominently Majorana zero modes in topological superconductors. Even though no such qubit has been built to date, the hope is that their coherence times may be significantly longer than the coherence times of currently available solid-state qubits, but are still expected to be too short for large-scale quantum computing. The quantum information approach is to combine many error-prone qubits to build more robust logical qubits using topological error-correcting codes, e.g., surface codes. Even though the first approach is hardware-based and the second approach is software-based, they are deeply related. With Majorana-based qubits, the main logical operations are Majorana fermion parity measurements. By replacing Majorana-based qubits with surface-code patches and parity measurements with lattice-surgery operations, schemes for quantum computation with Majorana-based qubits or with surface codes can be identical. In this thesis, we explore how to construct a large-scale topological fault-tolerant quantum computer that can perform useful quantum computations. Here, topological refers to the nature of the quantum error-correcting code, while the underlying hardware may be based on non-topological qubits, but could also be composed of Majorana-based qubits. We provide a complete picture of such a large-scale device, breaking down large quantum computations into logical qubits and logical operations, describing how these logical operations are performed on the level of physical qubits and physical gates, and finally discussing how these physical qubits can be pieced together in a Majorana-based system using topological superconducting nanowires.