# Measurement of a Hydrogen qubit?

• Julian Blair
In summary, the conversation discusses measuring a 2 state hydrogen atom that is in a superimposed state. It is clarified that in quantum mechanics, the state of a system is not an observable and that observables are represented by hermitian operators. The energy eigenfunctions of a hydrogen atom are infinite, making it not a two state system. The conversation then discusses the possibility of measuring the probabilities of the qubit being in either state |0> or state |1>, which would require multiple measurements to arrive at an estimation.
Julian Blair
Given a 2 state hydrogen atom in a superimposed state, how does one measure it for either of its two states?

I don't think your question is well posed. In quantum mechanics the state of a system is not an "observable". The observables (the quantities that you measure in experiments) are represented by hermitian operators that act on the states of the system.

The energy eigenfunctions of a hydrogen atom are infinite - its not a two state system.

Thanks
Bill

OK, let me explain a bit better. The ground and 1st excited states of an Hydrogen atom are often given as an example of a qubit for use in quantum computing. The energies of these states are definitely eigenstates of the Hamiltonian. My question has to do with an Hydrogen qubit in a superimposed state comprising both the ground and 1st excited state. If this qubit has been altered via a quantum algorithm, then one would like to measure the probabilities that it is in state |0> or state |1>. How could this be done?
Of course this measurement would have to be re-done multiple times to arrive at an estimation of the probabilities.

## 1. What is a hydrogen qubit?

A hydrogen qubit is a unit of quantum information that is represented by the state of a hydrogen atom. It has two possible states, known as the ground state and the excited state, which can be manipulated and measured to store and process quantum information.

## 2. How is a hydrogen qubit measured?

A hydrogen qubit can be measured using techniques such as spectroscopy, which involves shining light on the atom and analyzing the resulting spectrum. The energy levels of the atom can also be measured using techniques like nuclear magnetic resonance (NMR) or electron spin resonance (ESR).

## 3. What are the advantages of using a hydrogen qubit?

Hydrogen qubits have longer coherence times, meaning they can retain quantum information for longer periods of time without being affected by external factors. They also have a larger energy gap between their ground and excited states, making them less susceptible to noise and errors.

## 4. How are hydrogen qubits used in quantum computing?

Hydrogen qubits are used in quantum computing to perform operations and calculations on quantum information. They can be manipulated and measured to perform tasks such as storing and transferring quantum states, implementing quantum algorithms, and performing quantum error correction.

## 5. What are the challenges in measuring hydrogen qubits?

One of the main challenges in measuring hydrogen qubits is the precise control and manipulation of the hydrogen atom. This requires advanced technology and techniques, as well as a highly controlled environment to minimize external interference. Additionally, the measurement process itself can be complex and may require sophisticated equipment and analysis methods.

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