# Power of Quantum Computation with Few Clean Qubits

@inproceedings{Fujii2016PowerOQ, title={Power of Quantum Computation with Few Clean Qubits}, author={Keisuke Fujii and Hirotada Kobayashi and Tomoyuki Morimae and Harumichi Nishimura and Shuhei Tamate and Seiichiro Tani}, booktitle={International Colloquium on Automata, Languages and Programming}, year={2016} }

This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No initializations of qubits are allowed during the computation, nor intermediate measurements. The main results of this paper are unexpectedly strong error-reducible properties of such quantum computations. It is proved that any problem solvable by a polynomial-time…

## 27 Citations

### Power of one nonclean qubit

- Physics
- 2017

The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed. Although the model is…

### The Power of One Clean Qubit in Communication Complexity

- Computer ScienceMFCS
- 2021

There is a quantum protocol using one clean qubit only and using $O(\log n)$ qubits of communication, such that any classical protocol simulating the acceptance behaviour of the quantum protocol within additive error needs communication $\Omega(n)$.

### 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.

### Verification of Many-Qubit States

- Physics, Computer SciencePhysical Review X
- 2018

This paper shows that a variety of many-qubit quantum states can be verified with only sequential single-qu bit measurements of Pauli operators, and introduces a protocol for verifying ground states of Hamiltonians and proposes an adaptive test of stabilizers.

### How many qubits are needed for quantum computational supremacy?

- Computer ScienceQuantum
- 2020

A quantum computational supremacy argument is refined and it is concluded that Instantaneous Quantum Polynomial-Time circuits with 208 qubits and 500 gates, Quantum Approximate Optimization Algorithm circuits with 420 qu bits and 500 constraints and boson sampling circuits are large enough for the task of producing samples from their output distributions up to constant multiplicative error to be intractable on current technology.

### The battle of clean and dirty qubits in the era of partial error correction

- Physics
- 2022

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each…

### The one clean qubit model without entanglement is classically simulable

- Physics
- 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…

### Space-Bounded Unitary Quantum Computation with Postselection

- MathematicsMFCS
- 2022

Space-bounded computation has been a central topic in classical and quantum complexity theory. In the quantum case, every elementary gate must be unitary. This restriction makes it unclear whether…

### Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy

- Computer ScienceQuantum
- 2018

A promise problem to decide whether output probability distributions of two quantum circuits are far apart or close is defined, and it is shown that PDD-Max is BQP-complete, but if the two circuits are restricted to some types in the second level of the Fourier hierarchy, such as the HC1Q model or the IQP model, PDd-Max has a Merlin-Arthur system with quantum polynomial-time Merlin and classical probabilistic polyn coefficients.

### Additive-error fine-grained quantum supremacy

- Computer ScienceQuantum
- 2020

The additive-error fine-grained quantum supremacy result can be shown for additive- error sampling and should hold for other sub-universal models.

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