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New method eases superconducting’s connectivity issues for quantum error correction

Technical update
New method eases superconducting’s connectivity issues for quantum error correction
Gyorgy Geher
27 March, 2024

A new paper from the Riverlane team introduces the “tangling schedules” method. This technique is the first to enable the measurement of the required long-range stabilisers for logical computation without hardware modification, providing superconducting companies with a realistic route to scale up where they do not need to make significant changes to their existing hardware. 

From superconducting to neutral atoms and many more, there are multiple qubit types. Each one has its own advantages and disadvantages. Superconducting qubits, for example, are essentially tiny circuits. They have fast response times and are based on existing semiconductor technology. But they also have a fixed qubit layout and connectivity. 

Increasing the connectivity of a fixed qubit layout (e.g. superconducting) hardware is a major engineering challenge – but one that’s vital to solve to scale up quantum computers. The crux of the issue is that by increasing the connectivity, we also increase a type of error called crosstalk noise and, thus, make the circuits we run less reliable.  

Instead, it is more realistic to design quantum error correction procedures to improve the connectivity of these fixed layouts.  

Quantum error correction is a set of techniques used to protect the information stored in qubits from errors and decoherence caused by noise. As we scale quantum computers, the errors these machines are prone to also scale – rendering calculations useless unless we can correct them. 

Through quantum error correction, multiple physical qubits are used to encode a single logical qubit, by introducing redundancy which provides protection against errors.  

The surface code is a promising error correction scheme, in part due to the limited requirements it places on the quantum hardware compared to other schemes. However, existing proposals to interact logical qubits still require t­he physical qubits to be connected to one another in a way that is difficult for solid-state quantum hardware – such as superconducting quantum computers.  

In the PRX Quantum paper Tangling schedules eases hardware connectivity requirements for quantum error correction, we present the “tangled schedules” method, which addresses this challenge and removes the need for infeasibly high connectivity, moving the field one step closer to the large-scale quantum error correction required to move past the capabilities of today’s supercomputers.  

Quantum error correction typically works by measuring a set of operators repeatedly via a circuit specifically designed for that purpose. The order in which the two-qubit gates are applied in this circuit, called the scheduling, needs to satisfy a set of rules. 

In our work, we show how breaking one of these scheduling rules can generate entanglement not directly available on the hardware, which we can therefore use to measure long-range or high-weight operators. Our method, which we call “tangling schedules”, operates by simply re-ordering some of the two-qubit gates and making some further simple changes to the circuit to measure a product of operators. 

Crucially, the tangling schedules method does not require a substantial increase in the circuit depth (the count of time steps needed to execute all the gates in a quantum circuit). Therefore, this method does not compromise the fast response times associated with superconducting quantum computers. 

The paper also presents two applications of the tangling schedules method to perform logical computations with the surface code.  Potential interesting future work would be to investigate how the tangling schedules technique could be exploited for other quantum error correction schemes. 

This paper is an important step forward to making fault-tolerant quantum computing possible on restricted connectivity devices. In doing so, we can unlock more error-free quantum operations (QuOps) and reach thresholds such as the MegaQuOp and TeraQuOp sooner – where quantum computers surpass what is possible on classical machines and unlock truly world-changing applications, respectively. With our tangling schedule method, surface codes can run on a connectivity structure that already exists, which is a much more realistic method than expecting hardware companies to catch-up with the theory. 

You can read the full paper here. If you would like to find out more about this patent-pending method, please contact us at 

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