Fewer Qubits Maintain Error Correction in Quantum Computers

Aarav Pabla and colleagues at NIST & University of Maryland, have developed a technique to reduce the number of physical qubits needed for hypergraph product codes, while retaining key properties such as code dimension and minimum distance. This reduction in spatial overhead sharply lowers the resource requirements for building practical quantum computers. Their simulations reveal that these reduced codes maintain comparable performance to larger counterparts and remain compatible with essential fault-tolerant operations for logical computation.

Hypergraph product code qubit reduction maintains performance with key savings

Savings of up to 103 physical qubits have been achieved using a new reduction procedure for hypergraph product codes, addressing a major obstacle to building larger quantum computers. Preserving key properties like code dimension and minimum distance enables fewer physical qubits to reliably store quantum information, despite the difficulty of reducing qubit count without compromising performance. This advancement unlocks the potential for more efficient quantum error correction, allowing comparable subthreshold performance to unreduced codes while sharply lessening spatial overhead and maintaining compatibility with essential fault-tolerant operations.

The new qubit reduction procedure applicable to hypergraph product codes now achieves savings of up to 103 physical qubits compared to unreduced versions. Codes with parameters [64, 6]] have been successfully reduced, preserving important code properties including code dimension and minimum distance, vital for reliable quantum information storage. Simulations utilising circuit-level depolarizing noise reveal that these reduced codes maintain comparable subthreshold performance to their unreduced counterparts, indicating no significant loss of error correction capability despite the qubit reduction. Furthermore, compatibility with essential fault-tolerant operations, such as homomorphic measurement gadgets and transversal gates, extends the benefits of this technique to logical computation. However, current simulations focus on relatively small code sizes and do not yet demonstrate the scalability required for truly large-scale, fault-tolerant quantum computers.

Reducing qubit overhead via hypergraph product codes and the trade-offs with fault-tolerance

Quantum error correction promises to underpin fault-tolerant computation, yet demands on physical qubit counts remain a substantial barrier to progress. A reduction in these qubit requirements for hypergraph product codes, a promising architecture built from simpler classical codes, has now been achieved. This gain hinges on maintaining specific code properties, highlighting a tension between minimising qubit overhead and ensuring compatibility with complex, fault-tolerant operations crucial for logical computation.

Acknowledging a trade-off between minimising qubit numbers and maintaining full fault-tolerance is vital for practical quantum computing. Fewer qubits translate to smaller, more achievable quantum processors, as these hypergraph product codes offer a pathway to reduce the substantial physical qubit demands currently hindering progress. Although complex operations may require careful optimisation, the demonstrated preservation of key code properties, like distance and logical basis, means these reduced codes remain viable building blocks for scalable, error-corrected computation.

University College London Quantum AI researchers are refining hypergraph product codes, a new approach to building more compact quantum processors. Derived from classical designs, these codes reduce the number of physical qubits needed for error correction, a critical step towards scalable quantum computation. By restructuring hypergraph product codes from combinations of classical codes, important characteristics like code dimension and minimum distance were preserved during qubit reduction. Maintaining these properties ensures compatibility with fault-tolerant operations, essential for reliable quantum computation, and specifically demonstrates compatibility with complex components like homomorphic measurement gadgets.

The foundation of this work lies in the hypergraph product construction, a method for building quantum error-correcting codes by combining two classical linear codes. This approach leverages the well-understood properties of classical codes to simplify the design and analysis of quantum codes. A paradigmatic example is the surface code, which arises as a hypergraph product of two classical repetition codes. The repetition code simply repeats information multiple times to provide redundancy, and this principle is extended to the quantum realm through the hypergraph product. The code dimension, representing the number of logical qubits encoded, and the minimum distance, indicating the code’s ability to correct errors, are crucial parameters that determine the code’s performance. Maintaining these parameters during qubit reduction is paramount.

The reduction procedure developed by Pabla and colleagues focuses on optimising the connectivity within the hypergraph product code. Hypergraph product codes are defined by a hypergraph, a generalisation of a graph where edges can connect more than two vertices. By carefully restructuring the hypergraph, the researchers were able to eliminate redundant qubits without sacrificing the code’s error-correcting capabilities. This optimisation is not trivial; reducing qubits often leads to a decrease in the minimum distance, thereby reducing the code’s ability to detect and correct errors. The team’s success in preserving both code dimension and minimum distance is a significant achievement. The savings of up to 103 physical qubits for codes with parameters [64, 6]] represent a substantial reduction in resource requirements.

To assess the performance of the reduced codes, the researchers performed simulations using circuit-level depolarizing noise, a realistic model of errors that occur in quantum computers. Depolarizing noise randomly flips the state of a qubit, introducing errors that must be corrected by the quantum error correction code. The simulations demonstrated that the reduced codes maintain comparable subthreshold performance to their unreduced counterparts. ‘Subthreshold’ refers to the regime where the error rate is below a certain threshold, allowing for reliable quantum computation. This indicates that the qubit reduction does not significantly degrade the code’s ability to protect quantum information. The compatibility with fault-tolerant operations, such as homomorphic measurement gadgets, which allow measurements to be performed on encoded qubits without decoding them, and transversal gates, which apply a quantum gate to each physical qubit in a logical qubit, is also crucial. These operations are essential for performing complex quantum computations.

However, it is important to note that the current simulations are limited to relatively small code sizes. Scaling up these codes to the sizes required for truly large-scale, fault-tolerant quantum computers remains a significant challenge. Further research is needed to investigate the scalability of the reduction procedure and to optimise the codes for different types of noise. Nevertheless, this work represents a promising step towards building more efficient and practical quantum computers. The ability to reduce the number of physical qubits required for quantum error correction is a critical step towards overcoming one of the major obstacles to realising the full potential of quantum computation, and the preservation of key code properties ensures that these reduced codes remain viable building blocks for future quantum technologies.

The researchers successfully reduced the number of physical qubits needed for hypergraph product quantum codes while preserving key properties like code dimension and minimum distance. This matters because fewer qubits translate to smaller, potentially more achievable quantum computers. Simulations using depolarizing noise showed the reduced codes, such as changing a $[![610,64,6]!]$ code to $[![441,64,6]!]$, maintained comparable performance to larger codes. The authors indicate these reductions are also compatible with important fault-tolerant operations necessary for complex quantum computations.