The Effect of Mixture Preparation on Fuel Economy

Harrow, G.

doi:10.1007/978-1-349-03418-5_6

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The total error is ǫ = kǫn, where limn→∞ ǫn = 0. The RSP method in [46] can be improved [51] to prepare n states from an ensemble E with n χ (tr AA ′ E ) + o(n) cbits and nS(ρB) + o(n) ≤ n log M0 ebits where ρB is the average reduced density matrix of the ensemble as seen from Bob, so that M ≤ M t 0 . Putting all these parameters into Eq.…”

Section: A Linear Bound In Communication Cost For Distillationmentioning

confidence: 99%

On the capacities of bipartite hamiltonians and unitary gates

Bennett

Harrow

Leung

et al. 2003

IEEE Trans. Inform. Theory

158

282

View full text Add to dashboard Cite

Abstract-We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted one-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions.

show abstract

Section: A Linear Bound In Communication Cost For Distillationmentioning

confidence: 99%

On the capacities of bipartite hamiltonians and unitary gates

Bennett

Harrow

Leung

et al. 2003

IEEE Trans. Inform. Theory

158

282

View full text Add to dashboard Cite

show abstract

“…Quantum algorithms aim to provide complexity polynomial in n, an exponential speedup over the classical methods. It is shown in [7] that the lower bound for scaling of the complexity of quantum algorithms in κ and ϵ is Ω(poly(n)κ log(1/ϵ)). That shows that the optimal scaling is linear in κ when aiming for the exponential quantum speedup in n, as opposed to the √ κ classical complexity.…”

Section: Introductionmentioning

confidence: 99%

Optimal Scaling Quantum Linear-Systems Solver via Discrete Adiabatic Theorem

Costa

Sanders

et al. 2022

PRX Quantum

View full text Add to dashboard Cite

The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number κ and the allowable error ϵ [PRX Quantum 3, 0403003 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,500 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is over an order of magnitude more efficient than using a randomised approach from [arXiv: 2305.11352] that claimed to be more efficient.

show abstract

The Effect of Mixture Preparation on Fuel Economy

Cited by 2 publications

References 13 publications

On the capacities of bipartite hamiltonians and unitary gates

On the capacities of bipartite hamiltonians and unitary gates

Optimal Scaling Quantum Linear-Systems Solver via Discrete Adiabatic Theorem

Contact Info

Product

Resources

About