Cartan sub-algebra approach to efficient measurements of quantum
observables
- URL: http://arxiv.org/abs/2007.01234v4
- Date: Tue, 21 Sep 2021 01:40:46 GMT
- Title: Cartan sub-algebra approach to efficient measurements of quantum
observables
- Authors: Tzu-Ching Yen and Artur F. Izmaylov
- Abstract summary: We provide a unified Lie algebra for developing efficient measurement schemes for quantum observables.
The framework is based on two elements: 1) embedding the observable operator in a Lie algebra and 2) transforming Lie algebra elements into those of a Cartan sub-algebra.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: An arbitrary operator corresponding to a physical observable cannot be
measured in a single measurement on currently available quantum hardware. To
obtain the expectation value of the observable, one needs to partition its
operator to measurable fragments. However, the observable and its fragments
generally do not share any eigenstates, and thus the number of measurements
needed to obtain the expectation value of the observable can grow rapidly even
when the wavefunction prepared is close to an eigenstate of the observable. We
provide a unified Lie algebraic framework for developing efficient measurement
schemes for quantum observables, it is based on two elements: 1) embedding the
observable operator in a Lie algebra and 2) transforming Lie algebra elements
into those of a Cartan sub-algebra (CSA) using unitary operators. The CSA plays
the central role because all its elements are mutually commutative and thus can
be measured simultaneously. We illustrate the framework on measuring
expectation values of Hamiltonians appearing in the Variational Quantum
Eigensolver approach to quantum chemistry. The CSA approach puts many recently
proposed methods for the measurement optimization within a single framework,
and allows one not only to reduce the number of measurable fragments but also
the total number of measurements.
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