You’re given three balls that look identical, but one of the balls might have a different weight. The task is not unlike solving a simple logic puzzle. If one of the qubits was different, it would indicate that an error had occurred. Instead, he found a way to tell if the three physical qubits were in the same state as one another. Since measuring a quantum state would destroy the superposition, there wasn’t a straightforward way to check to see whether an error had occurred. The essential power of quantum computation comes from the fact that qubits can exist in a “superposition” of being in a combination of 0 and 1 at the same time.
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Shor’s quantum repeater code couldn’t be exactly the same as the classical version, though. He used three individual “physical” qubits to encode a single qubit of information - the “logical” qubit. If one of the bits is different from the others, the computer can correct the error and continue the calculation. Shor modeled his protocol after the classical repeater code, which involves making copies of each bit of information, then periodically checking those copies against each other.
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So how did Shor crack the conundrums he faced? He used the added complexity of quantum mechanics to his advantage. But at the beginning of October, researchers led by Chris Monroe, a physicist at the University of Maryland, reported that they had demonstrated many of the ingredients necessary to run an error-corrected circuit like Shor’s. “We won’t be able to scale up quantum computers to the degree that they can solve really hard problems without it,” said John Preskill, a physicist at the California Institute of Technology.Īs with quantum computing in general, it’s one thing to develop an error-correcting code, and quite another to implement it in a working machine. Most physicists see it as the only path to building a commandingly powerful quantum computer. W., “ C3, Semi-Clifford and Generalized Semi-Clifford Operations,” Quantum Inf. D., and Kadhe S., “ Synthesis of logical clifford operators via symplectic geometry,” in 2018 IEEE International Symposium on Information Theory (ISIT), 2018, pp. A., “ Reconstruction of multi-user binary subspace chirps,” in 2020 IEEE International Symposium on Information Theory (ISIT), 2020, pp. Pllaha T., Tirkkonen O., and Calderbank R. D., “ Triangularizing matrices over GF(2) by congruence,” Linear and Multilinear Algebra, vol. P., “ Orbits Under Symplectic Transvections II: The Case K = F2,” Proceedings of the London Mathematical Society, vol. P., “ Orbits Under Symplectic Transvections I,” Proceedings of the London Mathematical Society, vol. W., “ Flag fault-tolerant error correction for any stabilizer code,” PRX Quantum, vol. W., “ Quantum Error Correction with Only Two Extra Qubits,” Phys. W., “ Fault-tolerant magic state preparation with flag qubits,” Quantum, vol. E., “ Flag fault-tolerant error correction with arbitrary distance codes,” Quantum, vol. Pllaha T., Rengaswamy N., Tirkkonen O., and Calderbank R., “ Un-Weyling the Clifford Hierarchy,” Quantum, vol. Callan D., “ The generation of Sp(F2) by transvections,” J. Amer-ican Mathematical Society, Providence, R.I., 1978, vol. and Roetteler M., “ Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations,” IEEE Transactions on Information Theory, vol. A., “ Quantum error correction and orthogonal geometry,” Phys. A., “ Quantum error correction via codes over GF(4),” IEEE Trans. Gottesman D., “ Stabilizer codes and quantum error correction,” PhD thesis, California Institute of Technology, 1997.
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