Optimal quantum measurements of expectation values of observables

By Emanuel Knill, G. Ortiz, Rolando D. Somma. 2006

203 citations recorded by the source corpus.

of A or on their tail distribution. These algorithms are particu larly useful for simulating quantum systems on quantum computers because they enable efficient measurement of observables and correlation functions. Our algorithms are based on a method for efficiently measuring the complex overlap of |ψi and U |ψi , where U is an implementable unitary operator. We explicitly consider the issue of confidence level s in measuring observables and overlaps and show that, as expected, confidence levels can be improved exponentially with linear overhead. We further show that the algorithms given here can typically be parallelized with minimal increase in resource usage.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c1cf01d3c4fd685aa2cb7836209f3a593d6270af

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum machine learning: a classical perspective (2017, methodology): “A number of other algorithms accelerate classical Monte Carlo methods applied to the estimation of quantities such as expectation values and partition functions, which play a major role in physics [9,96,101].”
Simulating chemistry using quantum computers. (2010, unknown): “An algorithm for the expectation values of observables has been proposed that can get arbitrarily close to the Heisenberg limit (72).”
Amplitude estimation without phase estimation (2019, background): “, in chemistry [7, 8], finance [9, 10], and machine learning [11– 14].”
Polynomial-time quantum algorithm for the simulation of chemical dynamics (2008, methodology): “However, it is possible to achieve a convergence of 1/M, which is the ultimate limit of quantum metrology (35), by using techniques such as amplitude estimation (36, 37).”
Elucidating reaction mechanisms on quantum computers (2016, methodology): “[47] Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma, “Simulating hamiltonian dynamics with a truncated taylor series,” Physical review letters 114, 090502 (2015).”
Barren plateaus in quantum neural network training landscapes (2018, background): “On a quantum device, the cost of estimating the gradient scales as O(1/ ) [36].”
Quantum speedup of Monte Carlo methods (2015, background): “The related problem of quantum estimation of expectation values of observables, an important task in the simulation of quantum systems, has been studied by Knill, Ortiz and Somma [36].”