A [[30,6,5]] code may allow quantum experiments to scale up faster

Naoyuki Kanomata of RIKEN Center for Quantum Computing and Toshiba Corporation and Hayato Goto have developed a new encoder for the [[30,6,5]] symplectic double code, a quantum error correction method offering a high encoding rate of 20%. This compactness, combined with an efficient method for preparing encoded states, addresses a key limitation of many high-rate codes. The researchers’ encoder reduces resource overheads while maintaining low logical error rates by detecting errors with as few auxiliary qubits as possible. This work demonstrates that efficient and reliable logical state preparation is achievable for a compact, high-rate code, offering a potential step toward near-term experiments in fault-tolerant quantum computing. Fault-Tolerant Encoding with Goto’s Minimum-Overhead Verification A newly proposed encoder for a [[30,6,5]] symplectic double code reduces the number of quantum gates needed to prepare encoded states to 67, a significant decrease from the initial 108 gates required by standard methods. The [[30,6,5]] code itself offers a higher encoding rate, 20 percent, than alternative quantum low-density parity-check (qLDPC) codes like the bivariate bicycle code, which achieves approximately 17 percent, while maintaining comparable error correction capabilities. This increased efficiency stems from the code’s ability to encode six logical qubits into 30 physical qubits, a more compact arrangement than many existing high-rate codes. The development of this code addresses a growing need for codes that can balance high encoding rates with the practical constraints of near-term quantum hardware, where qubit counts and gate fidelities remain limited. Previous investigations into symplectic double codes had largely focused on smaller distances, up to a value of 3, but this work extends the analysis to a code distance of 5, demonstrating improved error correction potential. The encoder’s efficiency gains are achieved through an optimization technique applied to the initial plus-state encoder design. This method strategically identifies opportunities to consolidate CNOT gates, reducing the total gate count from 108 to 67 without compromising the integrity of the encoded state. The method works by examining column vectors within the stabilizer matrix HZ′, looking for instances where two vectors share multiple overlapping ‘1’ values; these overlaps allow for the replacement of multiple CNOT gates with a single, more efficient operation. The method involves optimizing CNOT gates to reduce the overall number required for encoding, an important step towards minimizing resource overhead. Beyond the plus-state encoder, the team also developed an arbitrary-state encoder capable of injecting any quantum state into the code space. This capability is essential for universal quantum computation, as it allows for the encoding of diverse quantum algorithms and data. Combined with basic fault-tolerant operations, this supports universal quantum computation. Numerical simulations, conducted using a circuit-level noise model, confirm the reliability and effectiveness of the proposed encoder. These simulations demonstrate that the encoder can maintain low logical error rates even with a reduced number of gates, validating its potential for practical implementation. The [[30,6,5]] code is defined by a specific stabilizer matrix, H = (HX| H_Z), where HX and HZ are binary matrices that dictate the code’s error correction properties. The symplectic orthogonality condition, (HX HZ)(HZ H_X)^T, ensures the commutativity of the stabilizers, a fundamental requirement for a valid quantum code. The logical Pauli operators, which represent the fundamental building blocks of quantum computation, are derived from the stabilizer matrix and must satisfy specific commutation and orthogonality conditions to ensure correct operation within the encoded space. These logical operators, denoted as MX and MZ, are essential for performing quantum gates on the encoded qubits. The researchers highlight the potential for performing Clifford operations fault-tolerantly using transversal gates, a technique that simplifies the implementation of quantum algorithms. Transversal gates apply the same gate to each physical qubit in a logical qubit, reducing the complexity of error correction.

The team also details how transversal physical Hadamard gates, combined with physical SWAP gates, can be used to implement logical Hadamard gates, a key component of many quantum algorithms. The construction of the plus-state encoder begins with converting the matrix HZ′ using Gaussian elimination to a form where the left part is the identity matrix. This transformation allows for the preparation of the first 12 physical qubits in the eigenstate of Z, while the remaining 18 qubits are initialized in a superposition state using Hadamard gates. Physical CNOT gates are then applied, corresponding to the rows of HZ′, to entangle the qubits and create the encoded state. The resulting state is a simultaneous eigenstate with eigenvalue +1 for all Z stabilizers, X stabilizers and logical X operators, representing the logical all-plus state. The zero-state encoder is constructed in a similar manner, using the matrix HX′ and the overlap method to minimize the number of CNOT gates. However, the researchers found that the logical all-zero state obtained from the zero-state encoder exhibited lower performance than the logical all-plus state obtained from the plus-state encoder under the circuit-level noise model. This finding suggests that the plus-state encoder may be more robust to noise and more suitable for practical implementation. The performance difference between the two encoders highlights the importance of careful optimization and characterization in the design of fault-tolerant quantum codes.

The team’s evaluation with a circuit-level noise model provided valuable insights into the resilience of the proposed method. The researchers believe that this code could play a significant role in overcoming the limitations of current quantum hardware and enabling the development of more powerful and reliable quantum computers. The potential for early experimental realization is a key advantage of this approach, as it allows for the validation of theoretical predictions and the refinement of encoding techniques.

The team’s work offers a potential pathway toward scaling up quantum computations with reduced resource overheads. Source: https://www.science.org/doi/abs/10.1126/sciadv.aec4142 More like thisQuantum Computing NewsAtom Computing Says it secures $100 million to build fault-tolerant quantum computersQuantum Computing NewsQuantum computer Jiuzhang 4.0 takes World Internet Conference’s leading tech awardQuantum Error CorrectionA shifted operating point prevents controller stall in quantum error correctionQuantum Error CorrectionResearchers Bound Quantum Error Weight at Node Degree Plus TwoStay currentSee today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals. Tags: