Quantum Computing - Melanie Swan Between Science and Economics

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qubit are entangled, any error will have a recognizable signature and can be corrected (by repairing it into the initial phase or into an irrelevant phase that does not impact the original qubit’s information). Since the states of the system are eigenstates of eigenvalue one for all of the operators, the measurement does nothing to the overall state. The Shor code is redundant, in that the number of bits of information it protects is significantly fewer than the number of physical bits that are present. Noise can come in from the environment without disrupting the message. Also, the Shor code is nonlocal in the sense that the qubit information is carried in the entanglement between the multiple qubits that protect it against local decoherence and depolarization.

      The Pauli operator that uses X–Y–Z quantum spin representations is one proposed method. Kraus operators, which are operator-sum representations, are another (Verlinde & Verlinde, 2013). However, Kraus operators can be difficult to engage because they require details of the interaction with the environment, which may be unknown. Single Pauli operators suggest a more straightforward implementation model.

      The main concept of error correction is that to protect qubits from environmental noise and to mitigate against state decay, the qubit of interest can be encoded in a larger number of ancillary qubits through entanglement. The entangled qubits are combined into a bigger overall fabric of qubits that constitutes the quantum information processor. For example, a quantum information processor might have 50 qubits, and an error-correction requirement of 9 qubits for each qubit. This would only leave 5 qubits available for information processing. The scaling challenge is clear, in that with current error-correction methods, most of the processing capacity must be devoted to error correction. The implied scaling rule is 10, in the sense that any size quantum information processor only has available one-tenth of the total qubits for the actual information processing (each 1 qubit requires 9 qubits of error correction). More efficient error-correcting codes have been proposed, but the scaling rule of 10 could be a general heuristic, at least initially.

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