Contextuality supplies the ‘magic’ for quantum computation

@article{Howard2014ContextualityST,
  title={Contextuality supplies the ‘magic’ for quantum computation},
  author={Mark Howard and Joel J. Wallman and Victor Veitch and Joseph Emerson},
  journal={Nature},
  year={2014},
  volume={510},
  pages={351-355}
}
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple ‘hidden… 

Contextuality Supplies the Magic for Quantum Computation

It is established that quantum contextuality, a generalization of nonlocality identified by Bell and Kochen-Specker almost 50 years ago, is a critical resource for quantum speed-up within the leading model for fault-tolerant quantum computation, known as magic state distillation (MSD).

Quantifying the magic of quantum channels

A resource theory for magic quantum channels is developed to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits, and two efficiently computable magic measures for quantum channels are introduced.

Logical paradoxes in quantum computation

  • Nadish de Silva
  • Philosophy
    Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
  • 2018
The precise features of quantum theory enabling quantum computational power are unclear. Contextuality---the denial of a notion of classical physical reality---has emerged as a promising hypothesis:

Contextuality bounds the efficiency of classical simulation of quantum processes

It is found that the presence of contextuality demands that the minimum number of classical bits of memory required to simulate a multi-qubit system must scale quadratically in the number of qubits; notably, this is the same scaling as the Gottesman-Knill algorithm.

Contextuality and the Single-Qubit Stabilizer Subtheory.

It is proved that generalized contextuality is present even within the simplest subset of quantum operations, the so-called single-qubit stabilizer theory, which offers no computational advantage and was previously believed to be completely noncontextual.

Spekkens ’ toy model and contextuality as a resource in quantum computation

— Spekkens’ toy model (SM) is a non-contextual hidden-variable model made to support the epistemic view of quantum theory, where quantum states are states of partial knowledge about a deeper

Hierarchies of resources for measurement-based quantum computation

This work identifies which Boolean functions can be computed in non-adaptive MBQC, with local operations contained within a finite level in the Clifford hierarchy, and compute the minimal number of qubits required to compute a given Boolean function.

Contextuality as a resource for measurement-based quantum computation beyond qubits

This work identifies precisely that strong non-locality is necessary in a qudit measurement-based computation (MBC) that evaluates high-degree polynomial functions with only linear control and introduces the concept of local universality, which places a bound on the space of output functions accessible under the constraint of single-qudit measurements.

Scalable measures of magic for quantum computers

Magic characterizes the degree of non-stabilizerness of quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic

Coherence makes quantum systems ‘magical’

This work argues on the similar spirit that quantum coherence is the fundamental resource when it comes to the creation of magic and unifies the two strands of modern development in quantum technology under the common underpinning of existence of quantum superposition.
...

References

SHOWING 1-10 OF 49 REFERENCES

Measurement-based quantum computation

Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation

Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.

Quantum computing with realistically noisy devices

  • E. Knill
  • Computer Science, Physics
    Nature
  • 2005
This work reports a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent, and shows that non-trivial quantum computations at EPG’s of as low as one per cent could be implemented.

The resource theory of stabilizer quantum computation

A resource theory, analogous to the theory of entanglement, is developed that is relevant for fault-tolerant stabilizer computation and introduces two quantitative measures for the amount of non-stabilizer resource, including the sum of the negative entries of the discrete Wigner representation of a quantum state.

Nonlocality and communication complexity

The area of quantum communication complexity is reviewed, and it is shown how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science.

Quantum Contextuality with Stabilizer States

This work applies the graph-theoretical contextuality formalism of Cabello, Severini and Winter to sets of stabilizer states, with particular attention to the effect of generalizing two- level qubit systems to odd prime d-level qudit systems.

Classical command of quantum systems

A scheme is described that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics, and makes it possible to test whether a claimed quantum computer is truly quantum.

Quantum theory, the Church–Turing principle and the universal quantum computer

  • D. Deutsch
  • Physics, Philosophy
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1985
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible

Quantum discord and the power of one qubit.

We use quantum discord to characterize the correlations present in the model called deterministic quantum computation with one quantum bit (DQC1), introduced by Knill and Laflamme [Phys. Rev. Lett.

A quantum computer only needs one universe