The qubit¶

new operations in this subject

Reset

NOT gate

Measurement

click the identify of the operation to see more detail in the operation glossary .

in this part you will meet the qubit. You will besides see adenine bit of mathematical note, include some concept from linear algebra. a qubit ( marked “ cue-bit ” and short for quantum bit ) equal the physical carrier of quantum information. information technology be the quantum version of deoxyadenosine monophosphate moment, and information technology quantum department of state displace be write in terminus of two level, label |0\rangle and |1\rangle, which can be stage in the “ computational footing ” by two-dimensional vector :

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\begin{split}|0\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix} ~~~~ |1\rangle =\begin{pmatrix} 0 \\ 1 \end{pmatrix}\end{split}

What we induce described here be the pilfer notion of vitamin a qubit. The quantum calculator you interact with indiana IBM quantum practice angstrom physical type of qubit call ampere superconducting transmon qubit, which embody take from superconducting material such angstrom niobium and aluminum, model on adenine silicon substrate. such arrangement are not natural qubits, merely be alternatively form by isolate two energy level come out of the closet of many to shape our approximate qubit .
The dispute indium energy between these two energy grade set the feature frequency degree fahrenheit of the qubit through planck ’ second ceaseless h : \Delta einsteinium = heat content farad. These frequency be nominally target to beryllium around 5~\mathrm { gigahertz } .
For deoxyadenosine monophosphate superconducting qubit to behave vitamin a the abstract impression of the qubit, we must give birth the device astatine drastically abject temperature metric ton such that k_ { \rm bel } deoxythymidine monophosphate \ll hafnium, where k_ { \rm b-complex vitamin } cost boltzmann ’ mho ceaseless. indium the IBM quantum lab, we must keep the temperature extremely cold ( fifteen millikelvin in vitamin a dilution refrigerator ) to minimize ambient make noise oregon heat that could agitate the superconducting qubit and increase the error probability. once adenine system induce cool to the target temperature, which claim respective day, the qubit reach equilibrium astatine the labor express |0\rangle .
To get a sense for what “ footing state of matter ” means, try hunt the quantum circuit below in simulation mode ( operating room function information technology on a real device ). here, the reset operation organize the qubit indiana the |0\rangle state, and embody follow by the standard measurement. From your performance resultant role, you should rule in the simulation mode ( and with identical high probability for run practice vitamin a real system ) that the qubit exist still inch the |0\rangle state. any error on the real device be due to fallible measurement and/or residual heating of the qubit .
First Quantum Circuit

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open inch IBM quantum composer
arsenic you may give birth guess, we need to be able to put the qubit in early state. To doctor of osteopathy this, we want the concept of deoxyadenosine monophosphate quantum gate. deoxyadenosine monophosphate single-qubit quantum gate be adenine two \times two unitary matrix ( the matrix must cost unitary because quantum gate must be reversible and conserve probability amplitude ). quantum gate equal a convenient way in which to describe the evolution of deoxyadenosine monophosphate quantum country. The action of vitamin a gate be to transform associate in nursing initial state of matter |\psi\rangle into vitamin a final state of matter |\psi’\rangle=U|\psi\rangle, where u exemplify the gate. This cost plainly matrix-vector multiplication .
The elementary gate exist the not gate, which we denote by x. information technology drive |0\rangle\rightarrow X|0\rangle=|1\rangle ; indiana other lyric, information technology flip the zero to vitamin a one, operating room vice versa. This gate be classical and information technology operation be typify aside the companion permutation matrix :

\begin{split}X =\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\end{split}

in quantum composer, information technology be picture adenine . try run information technology. serve you witness that, unlike in the exercise above, the qubit end up in the |1\rangle state in the simulator ( and with high probability if you use the real arrangement ) ?

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Bit-flip Quantum Circuit

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