Power of One Bit of Quantum Information

  title={Power of One Bit of Quantum Information},
  author={Emanuel Knill and Raymond Laflamme},
  journal={Physical Review Letters},
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 state is a highly mixed state and the answer is determined by measuring the expectation of {sigma}{sub z} on the first bit with bounded sensitivity? This is the situation in high temperature ensemble quantum computation. We show that in this model it is possible to perform interesting physics… 

Computing with highly mixed states

It is shown that unless m∈O(k + log n), oblivious (gate-by-gate) simulation of an ideal m-qubit quantum circuit by an n-qu bit circuit with k clean qubits is impossible, this indicates that there is no avoiding physical initialization of a quantity of qubits proportional to that required by the best ideal quantum circuit.

Are Quantum Computing Models Realistic

The commonly used circuit model of quantum computing leaves out the problems of imprecision in the initial state preparation, particle statistics, and error correction, so the question if a hierarchy of quantum-type computing models exists is speculated.

Quantum Algorithm for Fidelity Estimation

This paper proposes a quantum algorithm that solves this problem in poly(log N , r, 1 /ε ) time, where r is the lower rank of ρ and σ , and ε is the desired precision, provided that the purifications ofπ and ρ are prepared by quantum oracles.

Computational Complexity of Some Quantum Theories in $1+1$ Dimensions

It is proved that additive approximation to single amplitudes of these models can be obtained by the one-clean-qubit model, if no initial superpositions are allowed, and it is shown that conditioned on infinite polynomial hierarchy assumption it is hard to sample from the output distribution ofThese models on a classical randomized computer.

Negative quasi-probability as a resource for quantum computation

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speed-up and, in particular, for fault-tolerant quantum

Blindness and Verification of Quantum Computation with One Pure Qubit

This paper presents the adaptation of Encoding via blindness to the one pure qubit model, and presents the first feasible scheme for the verification of delegated one purequbit model of quantum computing.

Eliminating intermediate measurements in space-bounded Quantum computation

This work exhibits a procedure to eliminate all intermediate measurements that is simultaneously space efficient and time efficient, and shows that the definition of a space-bounded quantum complexity class is robust to allowing or forbidding intermediate measurements.

Quantum computers

The latest developments for each of the leading approaches to quantum computation are described and the major challenges for the future are explained.

Verified Delegated Quantum Computing with One Pure Qubit

This paper presents the adaptation of this approach to the one pure qubit model, and presents the rst feasible scheme for the verication of delegated one purequbit model of quantum computing.

General description of discriminating quantum operations

It is shown that, employing the theory of operator fidelity, it can not only verify some previous results to discriminate unitary operations, but also exhibit a more general discrimination condition.




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