# 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…

## 398 Citations

### Contextuality Supplies the Magic for Quantum Computation

- Computer Science2015 IEEE International Symposium on Multiple-Valued Logic
- 2015

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

- Computer Science, PhysicsNew Journal of Physics
- 2019

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

- PhilosophyProceedings 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

- Computer Science
- 2018

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.

- PhysicsPhysical review letters
- 2019

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

- Physics
- 2017

— 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

- Computer Science
- 2022

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

- Computer ScienceNew Journal of Physics
- 2018

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

- Physics
- 2022

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’

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2018

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

- Physics
- 2009

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)

- Physics
- 2005

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

- Computer Science, PhysicsNature
- 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

- Physics
- 2013

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

- Computer Science, Physics
- 2010

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

- PhysicsEntropy
- 2013

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

- Physics, Computer ScienceNature
- 2013

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

- Physics, PhilosophyProceedings 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.

- PhysicsPhysical review letters
- 2008

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.…