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3.2.2 The Quantum Bit (Qubit)
In this section, get ready to meet the qubit. We will start to use a bit of mathematical notation, including some concepts from linear algebra.
A qubit is a quantum system consisting of two levels, labeled |0⟩ and |1⟩ (here we are using Dirac's bra-ket notation) and is represented by a two-dimensional vector space over the complex numbers C2 . This means that a qubit takes two complex numbers to fully describe it. The computational (or standard) basis corresponds to the two levels |0⟩ and |1⟩ , and corresponds to the following vectors
The qubit does not always have to be in just |0⟩ or |1⟩ but can be in any quantum state, denoted |ψ⟩ , which can be any superposition |ψ⟩=α|0⟩+β|1⟩ , of the basis vectors. The superposition quantities α and β are complex numbers; together they obey |α|2+|β|2=1 .
Interesting things happen when quantum systems are measured, or observed. Quantum measurement is described by the Born rule. In particular, if a qubit that is in some state |ψ⟩ is measured in the standard basis, the result 0 is obtained with probability |α|2 and the result 1 is obtained with the complementary probability |β|2 . A point of fascination is that a quantum measurement takes any superposition state of the qubit, and projects it to either the state |0⟩ or the state |1⟩ with a probability determined from the parameters of the superposition.
What we have described here is the abstract notation of a qubit. The prototype quantum computer you can use here in the IBM Quantum Experience uses a type of qubit called a superconducting transmon qubit, which is made from superconducting materials such as niobium and aluminum, patterned on a silicon substrate.
Physically, for this superconducting qubit to behave as the abstract notion of the qubit, we actually need to cool down the device considerably. In fact, in the IBM Quantum Lab, we are able to keep the temperature cold enough (15 milliKelvin in a dilution refrigerator) that there is no ambient noise or heat to excite the superconducting qubit; after our system has gotten cold enough (for a few days), the superconducting qubit reaches equilibrium down to the ground state |0⟩ .
To get a sense for what this ground state of a qubit means, try running the first score file below in a simulation mode (or look at some real cached runs). Here, the qubit is initially prepared in the ground state |0⟩ , then is followed by the standard measure. From your execution results, you should find in the ideal case, and with very high probability for the cached runs, that the qubit is still in the ground state. In the actual experiment runs, you can observe that there is some error, with some shots giving a |1⟩ instead, which is due to imperfect measurements and some residual heating of the qubit.
The output for every score you run will be in the My Scores tab. Click the little bar graph icon next to the time stamp for your quantum score to see the results (if the results are not yet ready, or if there has been an error, you will see a yellow or red symbol on the bar graph icon). This will take you to the Results screen, where you can see the latest results.
We run the above exercise, and use the actual quantum computer, the result is return in the link of an email to me,
and it looks like this:
Executed on: May 14, 2016 5:38:11 PM
Results date: May 14, 2016 5:38:27 PM
Number of shots: 1024
Distribution
Distribution
Device Calibration
Device Calibration
Date Calibration: 2016-05-14 00:05
Fridge Temperature: 0.014405 Kelvin
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