Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations

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Abstract

Algorithms such as quantum factoring1 and quantum search2 illustrate the great theoretical promise of quantum computers; but the practical implementation of such devices will require careful consideration of the minimum resource requirements, together with the development of procedures to overcome inevitable residual imperfections in physical systems3,4,5. Many designs have been proposed, but none allow a large quantum computer to be built in the near future6. Moreover, the known protocols for constructing reliable quantum computers from unreliable components can be complicated, often requiring many operations to produce a desired transformation3,4,5,7,8. Here we show how a single technique—a generalization of quantum teleportation9—reduces resource requirements for quantum computers and unifies known protocols for fault-tolerant quantum computation. We show that single quantum bit (qubit) operations, Bell-basis measurements and certain entangled quantum states such as Greenberger–Horne–Zeilinger (GHZ) states10—all of which are within the reach of current technology—are sufficient to construct a universal quantum computer. We also present systematic constructions for an infinite class of reliable quantum gates that make the design of fault-tolerant quantum computers much more straightforward and methodical.

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Figure 1: Quantum circuit for teleportation.
Figure 2: Quantum circuit for teleporting two qubits through a controlled-NOT gate.
Figure 3: Quantum circuit to create the |χ〉 state.
Figure 4: Quantum circuit to perform U in a fault-tolerant manner using quantum teleportation.

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Acknowledgements

We thank C. Bennett for suggesting the concept of “quantum sofrware” to us, and R. Jozsa for pointing out an error in an early version of this manuscript. We also thank J. Kempe, D. Leung, and D. Bacon for helpful discussions. This work was supported in part by DARPA under the NMRQC initiative.

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Correspondence to Isaac L. Chuang.

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Gottesman, D., Chuang, I. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999) doi:10.1038/46503

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