RESUMO
We study variants of Shor's code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shor's code basis states, we calculate the logical channel applied to the encoded information when subjected to coherent and correlated single qubit idling errors, followed by stabilizer measurement. Changing the signs of the stabilizer generators allows us to change how the coherent errors interfere, leading to a quantum error-correcting code which performs as well as a classical repetition code of equivalent distance against these errors. We demonstrate a factor of 3.78±1.20 improvement of the logical T2^{*} in a distance-3 logical qubit implemented on a trapped-ion quantum computer. Even-distance versions of our Shor-code variants are decoherence-free subspaces and fully robust to identical and independent coherent idling noise.
RESUMO
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system1,2. These extra degrees of freedom enable the detection and correction of errors, but also increase the control complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while controlling the logical qubit, and are essential for realizing error suppression in practice3-6. Although fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. Here we experimentally demonstrate fault-tolerant circuits for the preparation, measurement, rotation and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault-tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6 per cent and a Clifford gate error of 0.3 per cent after offline error correction. In addition, we prepare magic states with fidelities that exceed the distillation threshold7, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant control. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.
RESUMO
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple technique for suppressing systematic coherent errors in low-density parity-check stabilizer codes, which we call stabilizer slicing. The essential idea is to slice low-weight stabilizers into two equally weighted Pauli operators and then apply them by rotating in opposite directions, causing their overrotations to interfere destructively on the logical subspace. With access to native gates generated by three-body Hamiltonians, we can completely eliminate purely coherent overrotation errors, and for overrotation noise of 0.99 unitarity we achieve a 135-fold improvement in the logical error rate of surface-17. For more conventional two-body ion trap gates, we observe an 89-fold improvement for Bacon-Shor-13 with purely coherent errors which should be testable in near-term fault-tolerance experiments. This second scheme takes advantage of the prepared gauge degrees of freedom, and to our knowledge is the first example in which the state of the gauge directly affects the robustness of a code's memory. This Letter demonstrates that coherent noise is preferable to stochastic noise within certain code and gate implementations when the coherence is utilized effectively.
