Quantum Computers Edge Closer with Fewer Hardware Connections Needed

Kun Liu and colleagues at Yale University present a new hardware-software co-design employing a 2D toric network to address limitations caused by restricted qubit connectivity. The architecture reduces the need for long-range couplers from linear to square root scaling and enables high-fidelity, low-latency two-qubit gates via dual-rail qubits and native gate operations. Circuit-level simulations incorporating realistic noise demonstrate a logical error rate of 3.06% for a bivariate bicycle code, representing a 2.6-fold improvement over previously reported experimental results and paving the way for practical, low-overhead fault-tolerant quantum computation.

Reduced qubit connectivity achieves sharp gains in quantum error correction

Error rates dropped to 3.06% for a bivariate bicycle (BB) code, a 2.6-fold improvement over existing experimental results and surpassing a key threshold for practical quantum error correction. Previously, achieving such low error rates demanded a linear scaling of long-range connections between qubits, hindering scalability. This new design reduces that requirement to a square root scaling, denoted as O(√n). A two-dimensional toric network of oscillators forms the basis of this advance, effectively acting as a reconfigurable communication fabric between qubits.

The challenge in building scalable quantum computers lies significantly in mitigating the effects of noise and decoherence, which introduce errors into quantum computations. Quantum error correction (QEC) is crucial for overcoming these limitations, but implementing QEC requires complex codes and substantial overhead in terms of qubits and operations. Bivariate bicycle (BB) codes are a promising class of quantum low-density parity-check (LDPC) codes, offering advantages such as high encoding rates and large code distances compared to more established codes like surface codes. The code distance is a critical parameter, determining the number of physical qubits required to protect a single logical qubit and its ability to correct errors. However, a major impediment to realising BB codes is the need for numerous long-range connections between qubits, particularly for performing stabilizer measurements, the core process in detecting and correcting errors. These long-range connections are difficult to implement on current quantum hardware platforms, such as those based on superconducting circuits, which are limited by physical connectivity and introduce significant signal delays and errors.

The architecture enables efficient routing and execution of long-range two-qubit gates, vital for maintaining code distance and minimising syndrome extraction cycle duration, paving the way for larger, more reliable quantum computations. Circuit-level simulations, informed by realistic noise modelling of experimental hardware, validated the achieved logical error rate of 3.06%. The system utilises a two-dimensional network of oscillators as a reconfigurable communication fabric, reducing the need for long-range connections from a linear scaling, O(n), to a square root scaling, O(√n). Incorporating dual-rail qubits and native gates, including Swap-Wait-Swap gates, enables high-fidelity and low-latency execution of important two-qubit operations, and minimises the duration of syndrome extraction. The reduction in scaling from O(n) to O(√n) is particularly significant as it dramatically reduces the complexity of the control wiring and the number of required couplers as the number of qubits (n) increases. This simplification is essential for building larger, more practical quantum processors. While these figures currently represent performance in simulation, they do not yet demonstrate sustained, low error rates in a fully fabricated and operating quantum processor.

Reducing qubit connectivity via oscillator networks enables scalable quantum architectures

Ever more sophisticated architectures are demanded as researchers build quantum computers, with attention now focused on streamlining the connections between individual qubits. Bivariate bicycle codes promise efficient encoding, but their reliance on numerous long-range links has presented a significant hurdle in superconducting systems. This new design, utilising a two-dimensional network of oscillators, offers a compelling solution, though it introduces a reliance on ‘dual-rail’ qubits, a technique for representing quantum information that requires careful calibration and control.

The concept of dual-rail encoding involves representing each logical qubit using two physical qubits, allowing for the detection and correction of certain types of errors. While effective, it doubles the qubit overhead and necessitates precise control over both physical qubits to maintain coherence and fidelity. The oscillators within the 2D network act as intermediaries, facilitating communication between qubits that are not directly connected. By dynamically routing signals through these oscillators, the architecture effectively shortens the path length for long-range interactions, reducing the impact of signal degradation and latency. The oscillators themselves are carefully designed and calibrated to minimise their contribution to the overall error rate.

The requirement for dual-rail qubits and precise calibration introduces complexity to any quantum system. However, an architectural simplification is achieved through a reduction in long-range connections from a linear relationship to a square root relationship, enabling a move towards scalable, practical quantum computers. Validating this approach and highlighting its potential for future development is a 2.6× reduction in logical error rate, compared to existing experimental results. The simulations employed realistic noise models derived from characterisation of superconducting qubit devices, including parameters such as decoherence times (T1 and T2) and gate error rates. These models were used to accurately predict the performance of the BB code under realistic operating conditions.

Integrating hardware and software design, specifically for bivariate bicycle codes, clarifies a new method for quantum computation. By employing a two-dimensional network of oscillators, the architecture minimises the need for direct, long-range connections between qubits, a key obstacle to scaling up quantum processors. This improvement opens questions regarding the optimisation of decoders for dual-rail qubit systems and the potential for further gains in error correction performance. Future research will likely focus on exploring different oscillator network topologies, optimising the control sequences for the dual-rail qubits, and developing more sophisticated decoding algorithms to further reduce the logical error rate and improve the overall performance of the quantum computer. The demonstrated reduction in connectivity requirements represents a significant step towards building fault-tolerant quantum computers capable of tackling complex computational problems.

The research demonstrated a new hardware-software co-design utilising a 2D network of oscillators to reduce the number of long-range connections needed for bivariate bicycle codes. This is important because it addresses a key limitation in scaling up quantum computers with current hardware. Simulations using a [[18, 4, 4]] code achieved a logical error rate of 3.06% per logical qubit per cycle, representing a 2.6× reduction compared to previous results. The authors intend to explore oscillator network topologies and decoding algorithms to further improve performance and reduce the logical error rate.