# Computing with highly mixed states

@article{Ambainis2006ComputingWH, title={Computing with highly mixed states}, author={Andris Ambainis and Leonard J. Schulman and Umesh V. Vazirani}, journal={J. ACM}, year={2006}, volume={53}, pages={507-531} }

Device initialization is a difficult challenge in some proposed realizations of quantum computers, and as such, must be treated as a computational resource. The degree of initialization can be quantified by k, the number of clean qubits in the initial state of the register. In this article, we show that unless m∈O(k + log n), oblivious (gate-by-gate) simulation of an ideal m-qubit quantum circuit by an n-qubit circuit with k clean qubits is impossible. Effectively, this indicates that there is…

## 39 Citations

### Quantum computing under real-world constraints: efficiency of an ensemble quantum algorithm and fighting decoherence by gate design

- Physics, Computer Science
- 2005

A simple approach to reduce errors in the quantum search algorithm due to a collective decoherence model is investigated, which takes advantage of the freedom inherent in compiling the search algorithm into fundamental gates.

### 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.

### Physical Limits of Heat-Bath Algorithmic Cooling

- PhysicsSIAM J. Comput.
- 2007

A new, efficient initialization procedure for open systems of n-qubit devices that is originally maximally mixed, but is in contact with a heat bath of bias epsilon>>2(-n), can be almost perfectly initialized.

### Normalizer Circuits and Quantum Computation

- Physics, Computer ScienceArXiv
- 2016

An efficient formalism for simulating families of quantum circuits, that are non-universal but comprise important quantum gates such as QFT or CNOT, is developed and used to design new algorithms that provide quantum speedups.

### Studies on the Role of Entanglement in Mixed-state Quantum Computation

- Physics
- 2008

In this thesis, I look at the role of quantum entanglement in mixed-state quantum computation. The model we consider is the DQC1 or `power of one qubit' model. I show that there is minimal bipartite…

### Some Theory and Applications of Probability in Quantum Mechanics

- Computer Science
- 2012

It is proved that quantum states are more difficult to estimate than their classical counterparts by finding optimal estimation strategies, requiring the solution to a difficult optimization problem, are difficult to implement in practise.

### 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.

### On the hardness of distinguishing mixed-state quantum computations

- Computer Science20th Annual IEEE Conference on Computational Complexity (CCC'05)
- 2005

It is proved that the promise problem is complete for the class QIP of problems having quantum interactive proof systems, and is therefore PSPACE-hard.

### Projective Measurement-Based Logic Synthesis of Quantum Circuits

- Computer Science38th International Symposium on Multiple Valued Logic (ismvl 2008)
- 2008

The method to synthesize quantum circuits from examples such that the synthesis process converts the don't knows to the entangled quantum output values which are measurement dependent is demonstrated.

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