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Supplementary Information: Difference between revisions
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This shows that for a pair of C-Z entangled qubits, if the second qubit is in |+i state (not an eigen value of Z) then one can teleport (transfer) the first qubit state operated by any unitary gate U to the second qubit by performing operations only on the first qubit and measuring it. Next, we would need to make certain Pauli corrections (in this case Xm) to obtain U |ψi. In other words, we can say the operated state is teleported to the second qubit by a rotated basis measurement of the first qubit with additional Pauli corrections. | This shows that for a pair of C-Z entangled qubits, if the second qubit is in |+i state (not an eigen value of Z) then one can teleport (transfer) the first qubit state operated by any unitary gate U to the second qubit by performing operations only on the first qubit and measuring it. Next, we would need to make certain Pauli corrections (in this case Xm) to obtain U |ψi. In other words, we can say the operated state is teleported to the second qubit by a rotated basis measurement of the first qubit with additional Pauli corrections. | ||
===Graph states=== | ===Graph states=== | ||
The above operation can also be viewed as a graph state with two nodes and one edge. The qubit 1 is measured in a rotated basis HZ(θ), thus leaving qubit 2 in desired state and Pauli Correction Xs1HZ(θ1)|ψi, where s1 is the measurement outcome of qubit 1.[[Supplementary Information#3|Figure 3]]<br/> | |||
<div id="3"> | <div id="3"> | ||
[[File:Graph States for Single Qubit States.jpg|center|thumb|1000px|Figure 3: Graph State for Single Qubit Gates]]</div> | [[File:Graph States for Single Qubit States.jpg|center|thumb|1000px|Figure 3: Graph State for Single Qubit Gates]]</div> | ||
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[[File:Gate Teleportation for Multiple Qubit Gates.jpg|center|thumb|500px|Figure 4: Gate Teleporation for Multiple Single Qubit Gates]]</div> | [[File:Gate Teleportation for Multiple Qubit Gates.jpg|center|thumb|500px|Figure 4: Gate Teleporation for Multiple Single Qubit Gates]]</div> | ||
The measurement on qubit 1 will operate Xs1HZ(θ1)|ψi⊗I on qubits 2 and 3. If qubit 2 when measured in the given basis yields outcome s2, qubit 3 results in the following state Xs2HZ(θ2)Xs1HZ(θ1)|ψi. Using the relation we shift all the Pauli corrections to one end i.e. qubit 3 becomes Xs2Zs1HZ(±θ2)HZ(θ1)|ψi{equation missing}(Zs1H = HXs1). This method of computation requires sequential measurement of states i.e. all the states should not be measured simultaneously. As outcome of qubit 1 can be used to choose sign of ±θ2. This technique is also known as adaptive measurement. With each measurement, the qubits before the one measured at present have been destroyed by measurement. It is a feed-forward mechanism, hence known as one way quantum computation.<br/> | The measurement on qubit 1 will operate Xs1HZ(θ1)|ψi⊗I on qubits 2 and 3. If qubit 2 when measured in the given basis yields outcome s2, qubit 3 results in the following state Xs2HZ(θ2)Xs1HZ(θ1)|ψi. Using the relation we shift all the Pauli corrections to one end i.e. qubit 3 becomes Xs2Zs1HZ(±θ2)HZ(θ1)|ψi{equation missing}(Zs1H = HXs1). This method of computation requires sequential measurement of states i.e. all the states should not be measured simultaneously. As outcome of qubit 1 can be used to choose sign of ±θ2. This technique is also known as adaptive measurement. With each measurement, the qubits before the one measured at present have been destroyed by measurement. It is a feed-forward mechanism, hence known as one way quantum computation.<br/> | ||
===Cluster States=== | ===Cluster States=== | ||
In case of multi-qubit quatum circuits, one needs a 2-dimensional graph state. Cluster State is a square lattice used as substrate for such computation. All the nodes are in |+i entangled by C-Z indicated by the edges. It is known to be universal i.e. it can simulate any quatum gate.<br/> | In case of multi-qubit quatum circuits, one needs a 2-dimensional graph state. Cluster State is a square lattice used as substrate for such computation. All the nodes are in |+i entangled by C-Z indicated by the edges. It is known to be universal i.e. it can simulate any quatum gate.<br/> | ||