Multiple-particle interference and quantum error correction

TLDR

Multiple‑particle interference, informed by classical error‑correcting code theory, motivates error‑correction strategies for quantum communication channels and quantum computers. The authors present quantum‑regime error‑correcting methods and evaluate their limitations. They show that encoding K logical qubits into n physical qubits can correct arbitrary decoherence of x qubits when K/n exceeds 1‑2H(2x/n) and is below 1‑2H(x/n), yielding exponential decoherence suppression with only polynomial resource growth, enabling fault‑tolerant quantum computation and secure quantum communication.

Abstract

The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer. Methods of error correction in the quantum regime are presented, and their limitations assessed. A quantum channel can recover from arbitrary decoherence of x qubits if K bits of quantum information are encoded using n quantum bits, where K/n can be greater than 1-2 H(2x/n), but must be less than 1 - 2 H(x/n). This implies exponential reduction of decoherence with only a polynomial increase in the computing resources required. Therefore quantum computation can be made free of errors in the presence of physically realistic levels of decoherence. The methods also allow isolation of quantum communication from noise and evesdropping (quantum privacy amplification).