In order to understand how computers work, we looked at bits. We then used logic gates (AND, OR, NOT) to build circuits, which in turn make up the computer you are using currently. In the first module, we were introduced to spin-qubits via the Stern-Gerlach experiment. Now, we will use similar concepts and using quantum logic gates to build quantum circuits, which in turn would make up your quantum computer. In other words, a quantum logic gate is used to manipulate quantum information (the quantum state of a qubit or a collection of qubits) to enable us to perform tasks that require using concepts of superposition and measurement.
In this section, we will
1.Understand what effect gates can have on qubits
2.Build quantum circuits with one and two qubits
The tools we will use to conduct our experiments will be Scratch (as used in Stern-Gerlach experiment from a previous module) and IBM Circuit Composer.
Simulating Circuits using Scratch
In the first module, we saw how we could use magnets and blockers to do measurements on quantum spins. Drawing pictures of magnets, sources, and blockers all the time gets a bit tiring, so we'll introduce a different picture to describe the same thing. The new picture is called a quantum circuit.
There are three parts of a quantum circuit.
1. Wires. Wires carry qubits from place to place.
2. Gates. Gates do things to qubits.
3.Measurements. These measure qubits, just like the magnets and blockers in the Stern-Gerlach 3.
experiment.
There are three parts of a quantum circuit. Wires. Wires carry qubits from place to place. Gates. Gates do things to qubits. Measurements. These measure qubits, just like the magnets and blockers in the Stern-Gerlach experiment.
We will again put our experimentalist hat on and explore what different gates do to the spin-qubits we saw in the Stern-Gerlach experiment. In this activity you'll be exploring quantum circuits in your small groups. The purpose of this activity is to deduce by experimentation how application of each gate changes the state of the qubit.
You will use the "One Qubit Circuit": https://scratch.mit.edu/projects/41217589https://scratch.mit.edu/projects/412175897/7/ project in Scratch to build your circuits. Using the simulations, you will solve a series of challenges on the following page, which will give you an idea about how quantum circuits work.
The circuit builder has three types of gates that you can use:
X gates
Z gates
H gates
Our first challenge will get you familiar with these different gates you have available to you. Use the Scratch simulator - https://scratch.mit.edu/projects/412175897/ - that we have built for you.
Simulating Circuits Using IBM Circuit Composer
Now that we are more familiar with basic quantum gates, we will learn a more advanced tool called the IBM Circuit Composer. For this, you should have created an account with the IBM Quantum Experience. The tools provided here will be used to build, execute and analyze quantum circuits.
In the two videos that follow, you will learn:
Basics of IBM Circuit Composer to help you get started
Creating a one-qubit superposition circuit, executing the circuit on a simulator and analyze the results
Now we will use the IBM Circuit Composer to solve the circuit challenge problems. Additionally, we will also try using the standard notation, called the Dirac notation or the ket notation, more often. Here are the basics of Dirac Notation:
|0⟩ instead of spin-up qubit
|1⟩ instead of spin-down qubit
Superposition state of |0⟩ and plus |1⟩ instead of spin-right qubit
Superposition state of |0⟩ and minus |1⟩ instead of spin-right qubit
Important Note: The Q-sphere representation on IBM Circuit Composer is not related to spin direction. It simply shows what outcomes are possible after applying a measurement gate (same as the up-down measurement magnet in the Scratch simulations).
One-qubit Operations at a Glance
Dirac notation recap:
|0⟩ instead of spin-up qubit
|1⟩ instead of spin-down qubit
Superposition state of |0⟩ and plus |1⟩ instead of spin-right qubit
Superposition state of |0⟩ and minus |1⟩ instead of spin-left qubit
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