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ETRI Journal

A multilayered Pauli tracking architecture for lattice surgery‐based logical qubits

Jinho On, Chei‐Yol Kim, Soo‐Cheol Oh, Sangmin Lee, Gyu‐Il Cha

Published Nov 2, 2022• 5 citations
Publisher

Abstract

Abstract In quantum computing, the use of Pauli frames through software traces of classical computers improves computation efficiency. In previous studies, error correction and Pauli operation tracking have been performed simultaneously using integrated Pauli frames in the physical layer. In such a complex processing structure, the number of simultaneous operations processed in the physical layer exponentially increases as the distance of the surface code encoding logical qubit increases. This study proposes a Pauli frame management architecture partitioned into two layers for a lattice surgery‐based surface code and describes its structure and operation rules. To evaluate the effectiveness of our method, we generated a random circuit according to the gate ratios constituting the commonly known quantum circuits and compared the generated circuit with the existing Pauli frame and our method. Simulations show a decrease of about 5% over traditional methods. In the case of experiments that only increase the code distance of the logical qubit, it can be seen that the effect of reducing the physical operation through the logical Pauli frame becomes more important.

DOI
10.4218/etrij.2022-0037

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•Feb 1, 2026•0 citations
Abstract In quantum computing, the use of Pauli frames through software traces of classical computers improves computation efficiency. In previous studies, error correction and Pauli operation tracking have been performed simultaneously using integrated Pauli frames in the physical layer. In such a complex processing structure, the number of simultaneous operations processed in the physical layer exponentially increases as the distance of the surface code encoding logical qubit increases. This study proposes a Pauli frame management architecture partitioned into two layers for a lattice surgery‐based surface code and describes its structure and operation rules. To evaluate the effectiveness of our method, we generated a random circuit according to the gate ratios constituting the commonly known quantum circuits and compared the generated circuit with the existing Pauli frame and our method. Simulations show a decrease of about 5% over traditional methods. In the case of experiments that only increase the code distance of the logical qubit, it can be seen that the effect of reducing the physical operation through the logical Pauli frame becomes more important.
The Pauli frame mechanism allows Pauli gates to be tracked in classical electronics and can relax the timing constraints for error syndrome measurement and error decoding. When building a quantum computer, such a mechanism may be beneficial, and the goal of this paper is not only to study the working principles of a Pauli frame but also to quantify its potential effect on the logical error rate. To this purpose, we implemented and simulated the Pauli frame module which, in principle, can be directly mapped into a hardware implementation. Simulation of a surface code 17 logical qubit has shown that a Pauli frame can reduce the error rate of a logical qubit up to 70% compared to the same logical qubit without Pauli frame when the decoding time equals the error correction time, and maximum parallelism can be obtained.
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.
Abstract Quantum error correction is likely to be key in obtaining near term quantum advantage. We propose a novel method for providing multiple logical qubits in the correction of quantum errors using classical computers. The core idea of our work is built upon two main pillars: dividing the Hilbert space into reduced Hilbert spaces with individual logical qubits and synthesizing the reduced Hilbert spaces through a mathematical collaborating between classical bits and logical quantum states. We demonstrate that our method supports at least 20 logical qubits in a surface code with a code distance of 3. Furthermore, we generate entangled states of multiple logical qubits from lattice surgery-based surface codes using only physical qubit operations. This approach enables classical computers to support a larger number of logical qubits using less memory and perform faster simulations.
Abstract Quantum error correction is needed for quantum computers to be capable of executing algorithms using hundreds of logical qubits in a fault-tolerant manner. Recent experiments have progressed towards this by demonstrating sufficiently low error rates for state preservation of a single logical qubit. However, quantum computation algorithms also require that these logical qubits can be entangled and that gate operations can be performed on them. Lattice surgery is a technique that offers a practical approach for implementing such gates, particularly in planar quantum processor layouts. Here we demonstrate lattice surgery between two distance-three repetition-code qubits by splitting a single distance-three surface-code qubit. Using a quantum circuit that is fault-tolerant for bit-flip errors, we achieve an improvement in the value of the decoded Z Z logical two-qubit observable compared with a similar non-encoded circuit. We therefore demonstrate the functional building blocks needed for lattice-surgery operations on larger-distance codes based on superconducting circuits.
Low-overhead quantum error-correction schemes are essential for enabling quantum computation on registers containing multiple logical qubits. For planar architectures with limited nearest-neighbor qubit connectivity, the surface code has emerged as the leading paradigm. Recent theoretical and experimental work has shown that a physical-qubit connectivity of degree three is sufficient to implement fault-tolerant quantum error correction. In this work, we study lattice surgery in the context of such trivalent architectures and introduce scalable circuit constructions to implement it. Compared with the four-valent measurement scheme, the trivalent lattice-surgery protocol reduces the required resources by O(d)\mathcal{O}(d)O(d) qubits out of a total qubit count of O(d2)\mathcal{O}(d^2)O(d2) and by O(d)\mathcal{O}(d)O(d) two-qubit gates out of a total two-qubit gate count of O(d3)\mathcal{O}(d^3)O(d3). We benchmark the logical fidelity of both lattice-surgery schemes in terms of experimentally realistic simulations targeting an implementation with a fluxonium qubit based architecture and find a potential improvement of up to ≈25%\approx25\%≈25% for distance-three. These results open a way for scalable planar trivalent qubit architectures to host a surface-code-based logical quantum processor.
Quantum error correction is needed for quantum computers to be capable of executing algorithms using hundreds of logical qubits in a fault-tolerant manner. Recent experiments have progressed towards this by demonstrating sufficiently low error rates for state preservation of a single logical qubit. However, quantum computation algorithms also require that these logical qubits can be entangled and that gate operations can be performed on them. Lattice surgery is a technique that offers a practical approach for implementing such gates, particularly in planar quantum processor layouts. Here we demonstrate lattice surgery between two distance-three repetition-code qubits by splitting a single distance-three surface-code qubit. Using a quantum circuit that is fault-tolerant for bit-flip errors, we achieve an improvement in the value of the decoded ZZ logical two-qubit observable compared with a similar non-encoded circuit. We therefore demonstrate the functional building blocks needed for lattice-surgery operations on larger-distance codes based on superconducting circuits.