# The one clean qubit model without entanglement is classically simulable

@article{Yoganathan2019TheOC, title={The one clean qubit model without entanglement is classically simulable}, author={Mithuna Yoganathan and Chris Cade}, journal={arXiv: Quantum Physics}, year={2019} }

Entanglement has been shown to be necessary for pure state quantum computation to have an advantage over classical computation. However, it remains open whether entanglement is necessary for quantum computers that use mixed states to also have an advantage. The one clean qubit model is a form of quantum computer in which the input is the maximally mixed state plus one pure qubit. Previous work has shown that there is a limited amount of entanglement present in these computations, despite the…

## 2 Citations

Measurement-Based Quantum Correlations for Quantum Information Processing

- PhysicsScientific Reports
- 2020

It is shown that MbQCs exist more generally than entanglement and discord in optimal assisted quantum state discrimination and in a deterministic quantum computation with a single qubit.

## References

SHOWING 1-10 OF 16 REFERENCES

Role of entanglement and correlations in mixed-state quantum computation

- Physics
- 2007

In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum…

On the hardness of classically simulating the one clean qubit model

- PhysicsPhysical review letters
- 2014

This Letter introduces a slightly modified version of DQC1, which it is shown that DZC1(k) cannot be classically efficiently simulated for any k≥3 unless the polynomial hierarchy collapses at the third level.

Efficient classical simulation of slightly entangled quantum computations.

- Computer Science, PhysicsPhysical review letters
- 2003

The results imply that a necessary condition for an exponential computational speedup is that the amount of entanglement increases with the size n of the computation, and provide an explicit lower bound on the required growth.

On the role of entanglement in quantum-computational speed-up

- Physics, Computer ScienceProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2003

It is argued that it is nevertheless misleading to view entanglement as a key resource for quantum‐computational power, as it is necessary for any quantum algorithm to offer an exponential speed‐up over classical computation.

Entanglement and the power of one qubit

- Physics
- 2005

The ``power of one qubit'' refers to a computational model that has access to only one pure bit of quantum information, along with $n$ qubits in the totally mixed state. This model, though not as…

Power of Quantum Computation with Few Clean Qubits

- Mathematics, PhysicsICALP
- 2016

It is proved that the TRACE ESTIMATION problem defined with fixed constant threshold parameters is complete for the classes of problems solvable by polynomial-time quantum computations with completeness 2/3 and soundness 1/3 using logarithmically many clean qubits and just one clean qubit.

Hardness of classically sampling one clean qubit model with constant total variation distance error

- Computer ScienceArXiv
- 2017

It is shown that it is indeed possible to improve the multiplicative error hardness result to a constant total variation distance error one like other sub-universal quantum computing models such as the IQP model, the Boson Sampled model, and the Fourier Sampling model if the authors accept a modified version of the average case hardness conjecture.

Estimating Jones polynomials is a complete problem for one clean qubit

- MathematicsQuantum Inf. Comput.
- 2008

It is shown that evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is a complete problem for the one clean qubit complexity class.

Power of One Bit of Quantum Information

- Physics
- 1998

In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial…

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

- Computer Science, MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2010

The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.