Low overhead quantum computation using lattice surgery

TL;DR

This work demonstrates that lattice surgery on the surface code substantially lowers fault-tolerant quantum-computation overhead compared with defects and braids. By reorganizing qubits into rotated logical encodings, enabling compact multi-body measurements, and integrating efficient state distillation, authors show roughly a 4–5x reduction in storage and distillation overhead while maintaining comparable runtime for large-scale algorithms. The results imply that lattice surgery can achieve scalable quantum computation with far fewer physical qubits (e.g., ~$3.7\times 10^5$) for workloads on the order of $10^8$ T gates, marking a practical shift toward lattice-surgery-based architectures. These insights are reinforced by explicit construction of logical operations (XX/ZZ, CNOT, CZ, Hadamard, T/S gates) and a detailed overhead framework, including a distillation scheme and a 3D time-structured layout. Overall, the paper provides a concrete pathway to low-overhead, fault-tolerant quantum computation using lattice surgery on the surface code.

Abstract

When calculating the overhead of a quantum algorithm made fault-tolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7\times 10^5$ physical qubits capable of executing gates with error $p\sim 10^{-3}$. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery.

Figures (25)

• Figure 1: In terms of the code distance $d$, a double-defect logical qubit occupies $25d^2/8$ space to leading order. Each unit of $d$ represents two qubits, a data and measure qubit, so to leading order $12.5d^2$ physical qubits are required.
• Figure 2: a) Distance $d=7$ rotated logical qubit. Dark regions represent X stabilizers, light regions represent Z stabilizers. Each region is associated with a measurement qubit. A data qubit is located at each intersection point of dark lines. b) Proposed layout of rotated logical qubits permitting local operations in parallel and easy movement of collections of logical qubits to the workspace on the left where multi-logical-qubit operations can take place.
• Figure 4: a) Before movement. The product of the $\pm$1 measurement results of the stabilizers marked by blue circles shall be denoted $a$. b) After movement, the new logical operator is related to the old by $a$.
• Figure 5: a) Getting ready to measure the logical operator $X_{12}=X_1X_2$. b) The product of the stabilizers marked by blue circles gives us the eigenvalue of the tensor product of $X$ operators along the red lines. This must then be modified by the current signs of tensor products of operators along these lines to give the actual desired result. This pattern of stabilizers is measured $d$ times. c) After splitting, the eigenvalue of the measurement in green is denoted by $e$, and this and the sign of the $Z_{12}$ operator can be associated with either $Z_1$ or $Z_2$.
• Figure 6: a) Getting ready to measure the logical operator $Z_{12}=Z_1Z_2$. b) The product of the stabilizers marked by blue circles gives us the eigenvalue of the tensor product of $Z$ operators along the green lines. This must then be modified by the current signs of tensor products of operators along these lines to give the actual desired result. This pattern of stabilizers is measured $d$ times. c) After splitting, the eigenvalue of the measurement in red is denoted by $e$, and this and the sign of the $X_{12}$ operator can be associated with either $X_1$ or $X_2$.