Quantum LDPC Codes Enable Addressable Gate-Based Computation on Individual Logical Qubits

Quantum computation promises revolutionary advances, but building practical machines demands overcoming the challenge of maintaining reliable operations as systems grow in complexity. Laura Pecorari, Francesco Paolo Guerci, and Hugo Perrin, alongside colleagues at the University of Strasbourg and CNRS, now present a significant step towards scalable quantum computation by demonstrating addressable logical operations using quantum low-density parity-check (LDPC) codes. Their research overcomes limitations of previous methods, which typically apply operations to all logical qubits simultaneously, by introducing a protocol that enables individual qubit control. This achievement, enabled by leveraging transversal operations and teleportation, unlocks the potential for a complete set of logical Clifford gates and, crucially, paves the way towards universal, fully addressable quantum computation when combined with existing techniques for generating the necessary quantum resources.

Quantum error correction is a demanding process, requiring significant resources to protect fragile quantum information. Scientists are exploring high-rate quantum low-density parity-check (LDPC) codes as a means to reduce this overhead, but realising practical, fault-tolerant computation with these codes remains a central challenge. Researchers have now introduced a new protocol for addressable quantum computation using these codes, achieving a significant breakthrough in the field.

Hybrid Error Correction with BS and LDPC Codes

Scientists have combined surface codes, known as BS codes, with La-cross codes, a type of LDPC code, to create a hybrid error correction scheme. This approach leverages the strengths of both codes, offering a balance between error correction capability and qubit overhead. The team demonstrates a method for performing logical operations on encoded qubits without disrupting the quantum information they hold, a crucial step towards building complex quantum circuits. This is achieved through transversal gates, which act on the encoded qubits in a specific way that avoids introducing new errors. The simulations employ detectors to identify errors and a technique called backpropagation to track them through the circuit.

By carefully designing these detectors and utilising artificial stabilizers, the team improves the accuracy of the decoding process. The researchers evaluate the performance of the scheme by measuring the logical error rate, which represents the probability of an error occurring on the encoded qubit. The simulations consider various sources of noise, including errors after two-qubit gates, measurements, and resets, providing a realistic assessment of the scheme’s performance. The team prioritises finding the shortest representations of logical operators to minimise overhead and optimise performance.

La-Cross Codes Enable Constant-Time Logical Operations

Researchers have demonstrated a protocol for performing addressable quantum computation using La-cross codes, achieving constant time overhead for logical operations. This means the time required to perform an operation on an encoded qubit does not increase with the complexity of the code, a significant advantage for scaling up quantum computations. The team focused on manipulating logical operators, which represent errors that must be corrected, within the La-cross code. They discovered that the shortest logical operators align along single rows or columns of the code’s lattice structure. For La-cross codes with open boundaries, the team demonstrated the ability to translate logical operators by multiplying them with specific stabilizers, effectively shifting their position without altering their length.

This ability to translate logical operators is crucial for performing operations on individual qubits. Importantly, the team proved that even when logical operators extend beyond the code distance, it is always possible to find multiple equivalent representations, ensuring fault tolerance. This work paves the way for integrating this protocol with techniques for generating the necessary quantum resources, potentially achieving universal, gate-based, and fully addressable quantum computation.

Addressable Qubit Control with LDPC Codes

Scientists have developed a new gate-based protocol for performing addressable quantum computation using high-rate quantum LDPC codes, avoiding the complexities of other techniques. This protocol enables constant-time overhead for logical operations, meaning the time required to perform an operation does not increase with the size of the code. The team demonstrates the ability to perform Clifford and non-Clifford operations on individual logical qubits encoded within these codes, leveraging transversal operations and teleportation via an auxiliary Bacon-Shor code. This approach offers a comparable or improved spacetime overhead when compared to existing methods.

The researchers successfully implemented an overcomplete logical Clifford gate set and validated the protocol through numerical simulations, demonstrating its potential for universal, gate-based, and fully addressable computation. Importantly, the protocol is hardware-agnostic, making it suitable for implementation on various qubit platforms, including Rydberg atom and trapped-ion systems. While employing state-of-the-art decoding algorithms, the authors acknowledge the need for faster decoding methods to enable deeper quantum computations. Future research will focus on extending the protocol to other LDPC code families and developing more efficient decoding methods to further enhance its practicality and scalability.