Let fD jg jbe the set of Kraus operators of D. In the Stinespring picture such noise operation acts as the isometry j i Q 7 X i E ij i Q jii E jii Eis an orthonormal basis. A noise operation N() P i E iE y iis correctable if E i2S 8i. operator-algebra quantum error correction 1315, and derive a formula to calculate the value of the spurious.
#Steinspring quantum error correction code
In its original and experimentally implemented form, liquid-state NMR is not generally thought to be scalable: the signal used to read out the result of the quantum computation decays exponentially in the number of qubits in the system and the mixed states produced in these experiments can be shown to possess no quantum entanglement. Given a quantum code we can de ne a linear subspace Sof correctable errors L(C2n). Liquid-state NMR is a testbed for quantum computing ideas in which one uses the internal states of coupled nuclear spins from a molecule as the qubits in a quantum computer. The first experiments that attempted to perform QEC were performed using room-temperature liquid-state NMR. In nonrelativistic systems, the Lieb-Robinson Theorem imposes an emergent speed limit constraining the time needed to perform useful tasks, e.g., preparing a spatially separated Bell pair from unentangled qubits, or teleporting a single qubit. The speed of light sets a strict upper bound on the speed of information transfer in both classical and quantum systems. Friedman, Chao Yin, Yifan Hong, Andrew Lucas. The quantum error correction code must coherently map the 2D space spanned by 0 L and 1 L into the 2D Hilbert spaces required to correct the three types of errors (bit-flip, phase-flip, and a combination of both, which we discuss in the next section) for each of the n physical qubits. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty quantum operations. Locality and error correction in quantum dynamics with measurement. This chapter deals with experimental implementations whose goal is to implement QEC, and not experiments using passive or open-loop methods, which are covered in Chapter 22. Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years. These experiments are all a long way from demonstrating viable QEC, but demonstrate the proof-of-principle methods that will need to be implemented in the future if quantum computation is to be made viable. In this chapter we will survey some of the experiments that have been performed to implement QEC. Further, even if it can be implemented in small laboratory experiments, these experiments need not lead to a technology that is scalable to large quantum computers (where large is defined as “big enough to contemporaneously outperform the best classical computer on some problem”).
Quantum error correction (QEC) is all for naught if it cannot be implemented experimentally in the laboratory.
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