Finally, we realise the decoding circuit and recover the input state with an overall fidelity of |$74.5(6)\%$|, in total with 92 gates. We further implement logical Pauli operations with a fidelity of |$97.2(2)\%$| within the code space. Then, the arbitrary single-qubit errors introduced manually are identified by measuring the stabilisers. The encoded states are prepared with an average fidelity of |$57.1(3)\%$| while with a high fidelity of |$98.6(1)\%$| in the code space. In the experiment, having optimised the encoding circuit, we employ an array of superconducting qubits to realise the code for several typical logical states including the magic state, an indispensable resource for realising non-Clifford gates. To address this challenge, we experimentally realise the code, the so-called smallest perfect code that permits corrections of generic single-qubit errors. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal quantum error-correcting code, with the subsequent verification of all key features including the identification of an arbitrary physical error, the capability for transversal manipulation of the logical state and state decoding. The results show that our machine learning protocol is able to outperform the double threshold protocol across all tests, achieving a final state fidelity comparable to the discrete Bayesian classifier.Quantum error correction is an essential ingredient for universal quantum computing. Based on these real-world imperfections, we generate synthetic measurement signals from which to train the recurrent neural network, and then test its proficiency when implementing active error correction, comparing this with a traditional double threshold scheme and a discrete Bayesian classifier. more » We analyze continuous measurements taken from a superconducting architecture using three transmon qubits to identify three significant practical examples of non-ideal behavior, namely auto-correlation at temporal short lags, transient syndrome dynamics after each bit-flip, and drift in the steady-state syndrome values over the course of many experiments. The algorithm is designed to operate on measurement signals deviating from the ideal behavior in which the mean value corresponds to a code syndrome value and the measurement has white noise. We propose a machine learning algorithm for continuous quantum error correction that is based on the use of a recurrent neural network to identify bit-flip errors from continuous noisy syndrome measurements. « lessĪbstract Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates and ancilla qubits. This leads to lower bounds on the number of qubits required to correct e errors and a formal proof that the classical bounds on the probability of error of e-error-correcting codes applies to e-error-correcting quantum codes, provided that the interaction is dominated by an identity component. A formal definition of independent interactions for qubits is given. We show that the error for entangled states is bounded linearly by the error for pure states. The latter is more appropriate when using codes in a quantum memory or in applications of quantum teleportation to communication. Two notions of fidelity and error for imperfect recovery are introduced, one for pure and the other for entangled states. We relate this definition to four others: the existence of a left inverse of the interaction, more » an explicit representation of the error syndrome using tensor products, perfect recovery of the completely entangled state, and an information theoretic identity. We use them to give a recovery-operator-independent definition of error-correcting codes. The conditions depend only on the behavior of the logical states. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. Quantum error correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |