59 research outputs found
Dilemma that cannot be resolved by biased quantum coin flipping
We show that a biased quantum coin flip (QCF) cannot provide the performance
of a black-boxed biased coin flip, if it satisfies some fidelity conditions.
Although such a QCF satisfies the security conditions of a biased coin flip, it
does not realize the ideal functionality, and therefore, does not fulfill the
demands for universally composable security. Moreover, through a comparison
within a small restricted bias range, we show that an arbitrary QCF is
distinguishable from a black-boxed coin flip unless it is unbiased on both
sides of parties against insensitive cheating. We also point out the difficulty
in developing cheat-sensitive quantum bit commitment in terms of the
uncomposability of a QCF.Comment: 5 pages and 1 figure. Accepted versio
The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings
Valiant-Vazirani showed in 1985 that solving NP with the promise that "yes"
instances have only one witness is powerful enough to solve the entire NP class
(under randomized reductions).
We are interested in extending this result to the quantum setting. We prove
extensions to the classes Merlin-Arthur (MA) and
Quantum-Classical-Merlin-Arthur (QCMA). Our results have implications on the
complexity of approximating the ground state energy of a quantum local
Hamiltonian with a unique ground state and an inverse polynomial spectral gap.
We show that the estimation, to within polynomial accuracy, of the ground state
energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized
reductions. This is in strong contrast to the case of constant gapped 1-D
Hamiltonians, which is in NP. Moreover, it shows that unless QCMA can be
reduced to NP by randomized reductions, there is no classical description of
the ground state of every poly-gapped local Hamiltonian which allows the
calculation of expectation values efficiently.
Finally, we discuss a few obstacles towards establishing an analogous result
to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random
projections fail to provide a polynomial gap between two witnesses
The Pursuit For Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings
Valiant-Vazirani showed in 1985 that solving NP with the promise that "yes"
instances have only one witness is powerful enough to solve the entire NP class
(under randomized reductions).
We are interested in extending this result to the quantum setting. We prove
extensions to the classes Merlin-Arthur (MA) and
Quantum-Classical-Merlin-Arthur (QCMA). Our results have implications on the
complexity of approximating the ground state energy of a quantum local
Hamiltonian with a unique ground state and an inverse polynomial spectral gap.
We show that the estimation, to within polynomial accuracy, of the ground state
energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized
reductions. This is in strong contrast to the case of constant gapped 1-D
Hamiltonians, which is in NP. Moreover, it shows that unless QCMA can be
reduced to NP by randomized reductions, there is no classical description of
the ground state of every poly-gapped local Hamiltonian which allows the
calculation of expectation values efficiently.
Finally, we discuss a few obstacles towards establishing an analogous result
to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random
projections fail to provide a polynomial gap between two witnesses
How quantum computers can fail
Abstract We propose and discuss two postulates on the nature of errors in highly correlated noisy physical stochastic systems. The first postulate asserts that errors for a pair of substantially correlated elements are themselves substantially correlated. The second postulate asserts that in a noisy system with many highly correlated elements there will be a strong effect of error synchronization. These postulates appear to be damaging for quantum computers. * Research supported in part by an NSF grant, by an ISF Bikura grant, and by a BSF grant. I am grateful to Dorit Aharonov, Michael Ben-Or, Greg Kuperberg and John Preskill for fruitful discussions and to many colleagues for helpful comments
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