Variational Quantum Eigensolver
Variational Quantum Eigensolver - Related Videos
02:43
Quantum Numbers
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2020
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, etc. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the...
10:00
Gradient Echo Quantum Memory in Warm Atomic Vapor
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Cited by 2 •
2013
The gradient echo memory is a protocol for storing optical quantum states of light in atomic ensembles. Quantum memory is a key element of a quantum repeater, which can extend the range of quantum key distribution. We outline the operation of the scheme when implemented in a 3-level atomic ensemble.
01:14
What is Variation?
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2023
Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of any data set is its variation or spread. In some data sets, the data values are concentrated closely near the mean; in others, the data values are more widely spread out from the mean. The range, standard deviation, standard error, and variance are the different measures of variation. Range: The range is the difference between its maximum and...
02:45
The Quantum-Mechanical Model of an Atom
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2020
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
14:20
Absolute Quantum Yield Measurement of Powder Samples
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Cited by 16 •
2012
In this video we will demonstrate measuring and calculating absolute quantum yield and chromaticity coordinates directly in powder samples using the Hitachi F-7000 Quantum Yield Measuring System.
FAQs
The Hamiltonian assigns an energy to each trial state, and the variational search favors parameter settings that produce lower expectation values. When the Hamiltonian represents a molecule or material, this minimum estimates its ground-state energy. The result therefore depends on whether the prepared trial states can represent a sufficiently accurate approximation of the system’s lowest-energy behavior.
The ansatz determines the family of parameterized trial states that the quantum circuit can prepare. An ansatz that does not represent the relevant ground-state behavior limits the lowest energy the optimization can reach, even if measurements and classical optimization perform well. Consequently, ansatz design is a central accuracy consideration when applying VQE to electronic-structure or materials problems.
The classical optimizer uses measured expectation values to evaluate the current energy and then selects updated circuit parameters for another trial. This creates an iterative exchange between quantum measurement and classical computation. Optimization performance influences whether the search approaches a low-energy solution effectively, so a suitable ansatz alone does not guarantee an accurate final estimate.
A typical workflow begins by selecting a Hamiltonian and a parameterized trial-state circuit. The quantum processor prepares that state and measures the expectation values associated with the Hamiltonian terms. A classical optimizer combines those values into an energy estimate, updates the circuit parameters, and repeats the process until the energy is minimized or the search reaches a satisfactory result.
The energy estimate is assembled from measured expectation values of the Hamiltonian’s individual terms, so unreliable measurements directly affect the quantity being minimized. Poor measurement quality can misrepresent the energy landscape presented to the classical optimizer and influence the final estimate. Careful attention to measurement quality is therefore necessary when interpreting VQE results for molecules or materials.
Engineers may consider VQE for systems whose behavior is difficult to model with conventional methods, particularly electronic structures of molecules and materials. Its hybrid design allows near-term quantum hardware to perform state preparation and measurements while classical computation handles parameter optimization. This makes VQE a framework for investigating engineering-relevant systems without assigning all computational work to the quantum processor.
A successful calculation provides an estimate of the lowest eigenvalue of the selected Hamiltonian, often interpreted as a ground-state energy for a molecule or material. That value can support studies of electronic structure and material behavior. Its credibility must be considered alongside ansatz design, measurement quality, and optimization performance, because each can affect the reported energy.