Fault-tolerant quantum computation with a neutral atom processor (2411.11822v3)

Abstract: Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical error rates required for valuable algorithms. However, it requires flexible control of high-fidelity operations performed on large numbers of qubits. We demonstrate fault-tolerant quantum computation on a quantum processor with 256 qubits, each an individual neutral Ytterbium atom. The operations are designed so that key error sources convert to atom loss, which can be detected by imaging. Full connectivity is enabled by atom movement. We demonstrate the entanglement of 24 logical qubits encoded into 48 atoms, at once catching errors and correcting for, on average 1.8, lost atoms. We also implement the Bernstein-Vazirani algorithm with up to 28 logical qubits encoded into 112 atoms, showing better-than-physical error rates. In both cases, "erasure conversion," changing errors into a form that can be detected independently from qubit state, improves circuit performance. These results begin to clear a path for achieving scientific quantum advantage with a programmable neutral atom quantum processor.

• The paper encodes 24 logical qubits using a distance-two [4,2,2] code, achieving a combined X and Z basis error rate of about 26.6% that outperforms unencoded qubits.
• The paper implements the Bernstein-Vazirani algorithm with up to 28 logical qubits, demonstrating reduced error rates and improved scalability over physical qubit operations.
• The paper validates fault-tolerant gate operations through repeated syndrome extraction and a distance-three Bacon-Shor code, marking a significant step toward robust quantum computation.

Logical Computation Demonstrated with a Neutral Atom Quantum Processor

In the paper "Logical computation demonstrated with a neutral atom quantum processor," the authors showcase a series of experiments that underline the potential of neutral atom quantum processors for reliable quantum computation. The paper harnesses the power of 256 qubits, each represented by an individual Ytterbium atom, to perform logical operations with quantum error correction (QEC) and fault-tolerance features. These operations demonstrate how logical qubits encoded in quantum error-correcting codes can outperform computations directly on physical qubits.

Key Contributions

1. Encoded Logical Qubits and Error Detection:
   • The authors demonstrated entanglement among 24 logical qubits using a distance-two $[4,2,2]$ code. This setup enables the simultaneous detection of errors and correction of qubit losses. The encoded cat states achieved a total $X$ basis plus $Z$ basis error rate of about 26.6%, indicating a meaningful entanglement, surpassing physical qubit baseline performance.
2. Bernstein-Vazirani Algorithm Implementation:
   • The team implemented the Bernstein-Vazirani algorithm with up to 28 logical qubits encoded using the $[4,1,2]$ code. By encoding logical qubits this way, they achieved lower error rates than those of the unencoded qubits. This represents one of the largest implementations of this algorithm with encoded qubits to date.
3. Fault-Tolerant Gates with Repeated Syndromes:
   • Implementing Gottesman’s proposal for fault tolerance, the paper demonstrates the use of repeated syndrome extraction across encoded qubits for logical gates. These gates include transversal operations such as CNOT, CZ, and Hadamard, which enhance fault tolerance by allowing error detection between computational steps.
4. Distance-Three Bacon-Shor Code for Error and Loss Correction:
   • A significant achievement showcased is the implementation of a distance-three $[9,1,3]$ Bacon-Shor code, demonstrating the correction of both qubit loss and errors. This marks a step towards achieving a quantum error correction and loss tolerance in future large-scale quantum processors.

Implications and Future Directions

The implications of deploying such technologies are threefold:

• Practical Quantum Computing: The demonstrations highlight the systematic transition from error-prone physical qubits to much reliable logical qubits, paving the way for practical applications using quantum computing, especially where high precision is vital.
• Scalability and Connectivity: The use of neutral atoms offers nearly all-to-all connectivity, advantageous for implementing non-local QEC codes that can be configured for higher efficiency and requiring fewer qubits.
• Logical Qubits as a Baseline Metric: The logical qubit performance now becomes a new baseline metric for evaluating the power of quantum systems, focusing on error rates and fidelity improvement.

Conclusion

The paper’s confluence of encoding strategies, fault-tolerant operational schemes, and the versatility of a neutral atom quantum processor exemplifies progress towards robust quantum computation. Continuous improvements in fidelity of quantum gates, combined with advanced error correction techniques, are anticipated to support more sophisticated quantum algorithms. Such advances are crucial as the quantum computing field edges closer to achieving scientific and industrial quantum advantage.