![]() We present an infinite family of protocols to distill magic states for $T$-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. ![]() To the best of our knowledge, this approach is the first attempt to prepare general large block stabilizer states free of correlated errors for FTQC in a fault-tolerant and efficient manner. The results support the validity of the protocol when the gate failure rate is reasonably low. Ancilla preparation for the $]$ quantum Golay code is numerically studied in detail through Monte Carlo simulation. At the same time, the yield rate can be boosted from $O(t^)$ to $O(1)$ in practice for an $]$ CSS code. Consequently, the revised protocol is fully fault-tolerant and capable of preparing a large set of stabilizer states sufficient for FTQC using large block codes. In this paper, we show that additional postselection by another classical error-detecting code can be applied to remove almost all correlated errors. It was assumed that the quantum gates in the distillation circuit were perfect however, in reality, noisy quantum gates may introduce correlated errors that are not treatable by the protocol. Previously we have proposed an ancilla distillation protocol for Calderbank-Shor-Steane (CSS) codes by classical error-correcting codes. These ancilla states are usually logical stabilizer states of the data code blocks, which are generally difficult to prepare if the code size is large. A major obstacle is the requirement of a large number of clean ancilla states of different types without correlated errors inside each block. In quantum computation, error correction is just one component of fault-tolerant design.įault-tolerant quantum computation (FTQC) schemes that use multi-qubit large block codes can potentially reduce the resource overhead to a great extent. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). An error set is represented by a set of operators that can multiply the codeword state. No code that stores information can protect against all possible errors instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. In general, codewords of a quantum code are entangled states. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space, without measuring (and hence disturbing) the protected state itself. ![]() This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. Quantum error correction is a set of methods to protect quantum information-that is, quantum states-from unwanted environmental interactions (decoherence) and other forms of noise.
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