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International Conference on Information and Communication Technology Convergence (ICTC)

Limited Connectivity Quantum Architectures: Enhancing Surface Code Implementation Through Routing Qubits

Sungyeon Kook, Yujin Kang, Jun Heo

Published Oct 16, 2024• 1 citation
Publisher

Abstract

In quantum computer architectures, low connectivity poses a major challenge in implementing efficient error correction codes such as surface codes that require high connectivity degrade when direct interaction between qubits is limited, making accurate error correction and reliable computation difficult. To implement surface codes with distances of 2 and 3 in quantum computer structures with limited connectivity, we analyze resources by the number of qubits and by the number of CNOT gates, suggesting a way to expand connectivity using routing qubits and SWAP gates.

DOI
10.1109/ictc62082.2024.10826661

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In quantum computer architectures, low connectivity poses a major challenge in implementing efficient error correction codes such as surface codes that require high connectivity degrade when direct interaction between qubits is limited, making accurate error correction and reliable computation difficult. To implement surface codes with distances of 2 and 3 in quantum computer structures with limited connectivity, we analyze resources by the number of qubits and by the number of CNOT gates, suggesting a way to expand connectivity using routing qubits and SWAP gates.
In near-term quantum computing devices, connectivity between qubits remain limited by architectural constraints. A computational circuit with given connectivity requirements necessary for multiqubit gates has to be embedded within physical hardware with fixed connectivity. Long-distance gates have to be done by first routing the relevant qubits together. The simplest routing strategy involves the use of gates to swap the information carried by two unconnected qubits to connected ones. Ideal gates just permute the qubits; real gates, however, have the added possibilities of causing simultaneous errors on the qubits involved and spreading errors across the circuit. A general swap scheme thus changes the error-propagation properties of a circuit, including those necessary for fault-tolerant functioning of a circuit. Here, we present a simple strategy to design the swap scheme needed to embed an arbitrary circuit onto a physical hardware with constrained connectivity, in a manner that preserves the fault-tolerant properties of the abstract circuit. Our approach is generally applicable, and works on any circuit, including ones that carry out logical operations and error correction. The embedded circuit will, of course, be noisier, compared to a native implementation of the abstract circuit, but we show in the examples of embedding surface codes on heavy-hexagonal and hexagonal lattices that the deterioration is not severe. This then offers a straightforward solution to implementing circuits with fault-tolerance properties on current hardware.
Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum circuits for quantum computers implementing surface codes. Optimal or near-optimal compilation is critical for both efficiency and correctness. The compilation problem requires (1) mapping circuit qubits to the device qubits and (2) routing execution paths between interacting qubits. We solve this problem efficiently and near-optimally with a novel algorithm that exploits the dependency structure of circuit operations to formulate discrete optimization problems that can be approximated via simulated annealing, a classic and simple algorithm. Our extensive evaluation shows that our approach is powerful and flexible for compiling realistic workloads.
Qubit shuttling has become an indispensable ingredient for scaling leading quantum computing platforms, including semiconductor spin, neutral-atom, and trapped-ion qubits, enabling both crosstalk reduction and tighter integration of control hardware. Cai et al. (2023) proposed a scalable architecture that employs short-range shuttling to realize effective three-dimensional connectivity on a strictly two-dimensional device. Building on recent advances in quantum error correction, we show that this architecture enables the native implementation of folded surface codes on 2D hardware, reducing the runtime of all single-qubit logical Clifford gates and logical CNOTs within subsets of qubits from O(d)\mathcal{O}(d)O(d) in conventional surface code lattice surgery to constant time. We present explicit protocols for these operations and demonstrate that access to a transversal SSS gate reduces the spacetime volume of 8T-to-CCZ magic-state distillation by more than an order of magnitude compared with standard 2D lattice surgery approaches. Finally, we introduce a new "virtual-stack" layout that more efficiently exploits the quasi-three-dimensional structure of the architecture, enabling efficient multilayer routing on these two-dimensional devices.
Efforts are being made to develop quantum processors beyond planar connectivity and quantum error correction codes suitable for 3-dimensional structures. In this study, we propose 3-dimensional architectures of logical data qubits and logical ancilla qubits based on surface codes using lattice surgery in situations where 3-dimensional nearest-neighbor connectivity between physical qubits is guaranteed. We also propose a method for performing CNOT operations on the proposed architecture. We present a physical qubit structure that stacks 2-dimensional physical qubit layers and adds several additional physical qubits for lattice surgery between adjacent layers. Our design permits the fast transversal application of CNOT operations between logical qubits in a nearest-neighbor relationship on adjacent layers, which is three times faster than the speed of standard lattice surgery CNOTs. Our design also permits the performance of CNOT operations between logical qubits that are far from each other using fast SWAP operations with transversal CNOT and lattice surgery. To demonstrate the advantages of our architecture, we present the required number of qubits and time for benchmark circuits on the proposed architecture and compare the required qubits and time on the checkerboard architecture and row-type architecture which are a 2-dimensional architectures to show the advantages of our architecture.
Computer architectures which exploit quantum mechanical effects can solve computing tasks that are otherwise impossible to perform. A quantum computer operates on a number of small quantum mechanical systems, known as quantum bits, or qubits. Since these systems are realized on the scale of atoms, they are very prone to errors. Errors occur when the environment interacts with the qubits, a process called decoherence. It is widely accepted that it will not be possible to shield qubits completely from the outside world. If one were to perform a quantum computation on the qubits directly, then after a short period of time the information present in the qubits would be lost. To counter decoherence the state of a qubit can be encoded into multiple physical ones. This is called a quantum error correcting code. Performing quantum error correction allows one to extend the life time of the encoded qubit arbitrarily, assuming that the rate of errors remains below a certain threshold value. The use of quantum codes creates an overhead in resources, as for every logical qubit many more physical qubits are needed. The resource overhead for fault-tolerance is problematic, since realizing qubits will be costly, and in the early stages of building quantum computers the number of physical qubits will be limited. The currently favored coding architecture is the toric code and its variant the surface code in which the physical qubits are put on a square grid in which interactions are only between nearest neighbors. In this thesis we will explore quantum codes in which qubits interact as if they were nearest neighbors in more exotic spaces. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and enumerate all quantum codes derived from them which have less than 10.000 physical qubits. For codes that are extremal in a certain sense we perform numerical simulations to determine the value of their threshold. Furthermore, we give evidence that these codes can be used for more overhead efficient storage as compared to the surface code by orders of magnitude. We also show how to read and write the encoded qubits while keeping their connectivity low. In the second part we consider codes in which qubits are layed-out according to a four- dimensional geometry. Such codes allow for much simpler decoding schemes compared to codes which are two-dimensional. In particular, measurements do not necessarily have to be repeated to obtain reliable information about the error and the classical hardware performing the error correction is greatly simplified. We perform numerical simulations to analyze the performance of these codes using decoders based on local updates. We also introduce a novel decoder based on techniques from machine learning and image recognition to decode four-dimensional codes.
Two primary challenges stand in the way of practical large-scale quantum computation, namely achieving sufficiently low error rate quantum gates and implementing interesting quantum algorithms with a physically reasonable number of qubits. In this work we address the second challenge, presenting a new technique, bridge compression, which enables remarkably low volume structures to be found that implement complex computations in the surface code. The surface code has a number of highly desirable properties, including the ability to achieve arbitrarily reliable computation given sufficient qubits and quantum gate error rates below approximately 1%, and the use of only a 2-D array of qubits with nearest neighbor interactions. As such, our compression technique is of great practical relevance.