The evaluation of expectation values TrρO for some pure state ρ and Hermitian operator O is of central importance in a variety of quantum algorithms. Near-optimal techniques have been developed in the past and require a number of measurements N approaching the Heisenberg limit N=O1/ϵ as a function of target accuracy ϵ. The use of quantum phase estimation (QPE) requires, however, long circuit depths C=O1/ϵ making its implementation difficult on near-term noisy devices. The more direct strategy of operator averaging is usually preferred as it can be performed using N=O1/ϵ2 measurements and no additional gates aside from those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) to show that the latter strategy can require an overly large number of measurements in order to achieve a prefixed relative target accuracy ϵr. We propose to overcome this problem using a single step of QPE and classical postprocessing. This approach leads to a circuit depth C=Oϵμ (with μ≥0) and to a number of measurements N=O1/ϵ2+ν for 0

Short-depth circuits for efficient expectation-value estimation / Roggero, A.; Baroni, A.. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - 101:2(2020), pp. 022328.1-022328.19. [10.1103/PhysRevA.101.022328]

Short-depth circuits for efficient expectation-value estimation

Roggero A.;
2020

Abstract

The evaluation of expectation values TrρO for some pure state ρ and Hermitian operator O is of central importance in a variety of quantum algorithms. Near-optimal techniques have been developed in the past and require a number of measurements N approaching the Heisenberg limit N=O1/ϵ as a function of target accuracy ϵ. The use of quantum phase estimation (QPE) requires, however, long circuit depths C=O1/ϵ making its implementation difficult on near-term noisy devices. The more direct strategy of operator averaging is usually preferred as it can be performed using N=O1/ϵ2 measurements and no additional gates aside from those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) to show that the latter strategy can require an overly large number of measurements in order to achieve a prefixed relative target accuracy ϵr. We propose to overcome this problem using a single step of QPE and classical postprocessing. This approach leads to a circuit depth C=Oϵμ (with μ≥0) and to a number of measurements N=O1/ϵ2+ν for 0
2
Roggero, A.; Baroni, A.
Short-depth circuits for efficient expectation-value estimation / Roggero, A.; Baroni, A.. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - 101:2(2020), pp. 022328.1-022328.19. [10.1103/PhysRevA.101.022328]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/312946
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