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Quantum Computing

Quantum Computing with Discord

It has been recognized for a long time that entanglement is essential in quantum computing. Processes such as factorization, searching, teleportation etc. are devised on an entanglement-based algorithm. Clues that entanglement is not absolutely necessary began to trickle in about a decade ago (with the arrival of the 21th century). It was noticed that factorization has been done at room
Quantum Discord temperature, which would destroyed the entanglement in the system. It seems that other quantum process is at work to enable the successful implement of Shor's algorithm (to factorize the number 15 into 5 and 3). Someone suggested quantum discord as the explanation. Discord is an obscure measure of quantum correlations first proposed in 2000. It quantifies the degree of disruption during observation of a system. Macroscopic systems have zero discord because they are not affected by observation. But quantum systems are unavoidably affected, since measurement forces them to settle on one of their many superposition values, so any possible quantum correlations including entanglement, give a positive value for discord. A discord-based

Figure 08d Quantum Discord [view large image]

model called deterministic quantum computation with one quantum bit (DQC1) has been introduced in 1998, in which only one control qubit is protected from the environment with the rest left to their own devices (but all coupled to the control qubit). The task is to evaluate the normalized trace of a unitary matrix.

Figure 08d compares the measured discord DDQC1 (in red dots) and the analytical expression (in solid green) as a function of the degree of protection (purity) for the control qubit ( = 1 is the pure control qubit while = 0 is the completely mixed control qubit). The particular DQC1 circuit has 5 qubits in the unprotected (mixed) state coupled to one control qubit.

Subsequently, using the same discord-based algorithm, the diagonal elements of a 2x2 matrix has been summed up successfully. Although this is a small matrix, the successful run serves as a proof-of-principle.

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