Quantum Researchers Combine Surface-Code Correction With IBM’s Heavy-Hex Architecture

Quantum Elements, a three-year-old startup, develops AI-based digital twins that model and simulate quantum computing systems. Its Constellation platform combines AI agents, natural-language capabilities, and simulation tools for tasks including creating and testing quantum software and algorithms, generating code, and building digital twins of quantum systems.

Digital twins allow organizations to study how systems could look, evolve, and behave as they scale without the cost of running equivalent tests on hardware and quantum chips.

In July, Quantum Elements introduced Orbit, a quantum error-suppression tool, through IBM’s Qiskit Functions Catalog. Qiskit Functions provides prebuilt and managed cloud software services intended to streamline quantum research.

Orbit was designed to help researchers, developers, and enterprise quantum teams improve quantum-circuit performance while reducing the time, cost, and workflow complexity associated with error mitigation and suppression. The tool provides access to error-suppression techniques without requiring deep specialization, while also targeting circuit-execution performance, processing overhead, and compilation time.

Applying the Surface Code to a Different QPU Layout

Orbit recently contributed to research that could affect the development of fault-tolerant quantum computers and provide more flexibility in quantum-system design. In a paper published in Nature, researchers from Quantum Elements and the University of Southern California showed that the surface code can scale error correction on a quantum processing unit (QPU) whose physical layout does not use the same grid as the code.

The surface code is a topological quantum error-correction code arranged on a two-dimensional grid. It is considered one of the more practical approaches to building large-scale, fault-tolerant quantum systems. The research demonstrated its use with the heavy-hex architecture of IBM’s Heron quantum processor.

Heron was first released in 2023 and is available in 133-qubit and 156-qubit configurations. The processor is used in IBM System Two and upgraded System One quantum systems.

Heavy-hex arranges qubits on a hexagonal, honeycomb-like lattice. Among other design features, the layout limits crowded connections between neighboring qubits, helping reduce collisions.

“Implementing the surface code on other QPUs with different fixed connectivities is a problem of both fundamental interest and practical importance,” the researchers wrote. “In light of applications, QPU design may be driven by considerations other than optimal surface code performance, for example to avoid frequency crowding affecting crosstalk and gate performance and to reduce the density of circuit elements, easing thermal management in lithographic fabrication.”

Using the surface code with a different physical layout can give engineers more design options. They do not necessarily have to match a processor’s hardware topology directly to the structure of the error-correction code.

Reducing Connectivity and Routing Problems

A central challenge was the reduced connectivity between the surface-code grid and IBM’s heavy-hex architecture. Transferring quantum states between non-neighboring qubits can introduce delays. During these idle periods, noise can cause qubits to lose their quantum states, allowing the number of errors to increase as the code expands.

Mapping the surface code onto IBM’s architecture also required additional routing.

The researchers addressed the mismatch in several ways, including the use of a depth-efficient error-correction code. Surface code and other error-correction methods can require long sequences of gates or measurements. These sequential operations create idle periods in which noise can introduce errors. Depth-efficient codes reduce the number of sequential layers.

They also used dynamical decoupling, which protects qubits from noise, through Quantum Elements’ Orbit Qiskit function. This was combined with SWAP-based embedding on the Heron QPU to map logical qubits onto physical hardware. SWAP-based embedding uses SWAP gates to exchange the quantum states of two qubits.

The approach produced directional subthreshold scaling, an important step in error correction. This method increases the size of the code in a particular direction while reducing a corresponding type of error.

IBM’s Earlier Heavy-Hex Proposal

IBM had proposed using the heavy-hex architecture for its quantum devices five years earlier, when it announced the topology as the foundation for the company’s quantum systems. IBM researchers described the rationale in a report that also discussed the surface code as an example of ongoing error-correction work.

They wrote that the connectivity of other lattices, including square lattices, could be simulated on heavy-hex with constant overhead by adding SWAP operations within appropriately selected unit cells. Vertices in the desired virtual lattice can be associated with groups of vertices in the heavy-hex lattice, allowing nearest-neighbor gates in the virtual lattice to be simulated with additional two-qubit gates.

The researchers also stated that heavy-hex connectivity could be mapped to other standard lattices, such as the square lattice, with constant-cost overhead that would be negligible compared with the cost of encoding.