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Exploring Quantum Computing with Qiskit

These step-by-step instructions will guide you through running your first quantum program on a real quantum computer. The only pre-requisite is an account on the IBM Quantum Experience (http://ibm.co/iqx).

Landing page

Below is an example of the page you'll see upon logging in to the IBM Quantum Experience website. In the middle are large buttons for launching the composer (for programming with a GUI) and notebooks (for programming with Qiskit); if a list of recent items appears instead of these buttons, the quick-access toolbar mentioned below can be used instead. Toward the bottom, you'll find lists of pending and completed jobs. On the right you'll find a list of quantum backends (i.e. real quantum devices or quantum simulators) to which you have access. Finally on the left you'll find a vertical toolbar for quick access to various resources.

Starting a Qiskit notebook

Click the "Qiskit Notebooks" icon from the landing page or the quick-access toolbar, which will take you to the page shown below:

This page provides four options: load a pre-loaded tutorial notebook, create a new notebook from scratch, import a notebook from your computer, or load a previously saved notebook. Click "New Notebook" to create your own notebook from scratch.

A new notebook will load. As shown below, the first cell is already populated with code that loads some useful tools, so you're not working completely from scratch.

The [*] on the left denotes that this cell is actively running; it is set to run automatically upon loading the notebook, and should take about 10 seconds. When it completes, the [*] will be replaced by a [1], where 1 indicates that this is the first cell that has been run in this notebook session.

Writing your first quantum program

Our first quantum program will demonstrate the idea of superposition, one of the fundamental properties of the quantum world that is harnessed in quantum computing. Simply put, a quantum bit in a superposition state is neither 0 or 1 (which henceforth we will write as |0> or |1> to reflect the fact that we are referring to quantum states, not just the numbers 0 and 1), but some simultaneous combination of these states, which in the language of quantum physics can be expressed as a|0> + b|1>, where a and b are complex numbers. When a superposition state is measured, it collapses to either |0> (with probability |a|^2) or |1> (with probability |b|^2). From this, you can infer that we must have |a|^2 + |b|^2 = 1.

To demonstrate superposition, we'll build a quantum circuit, which is a series of operations (typically called gates) to be applied to a collection of quantum bits, along with a set of classical bits for storing the results of measurements. The code below defines a quantum circuit with 1 quantum bit and 1 classical bit. Type it in the blank cell just below the first one and hit Shift+Enter to run the cell.

qc = QuantumCircuit(1,1)

There are various ways to prepare a superposition state, but one of the simplest and certainly the most common is to start with a qubit in the |0> state (which is where all qubits are automatically initialized on IBM Quantum backends) and apply a Hadamard gate. This takes a qubit from |0> to the equal-weighted superposition state with a = b = sqrt(2), also referred to as the |+> state. More generally, it rotates a qubit's state 180 degrees around the axis equidistant between the X and Z axes of the Bloch sphere. To insert this gate into our quantum circuit, type the code below into a new cell and run it (the '0' refers to qubit index 0):

qc.h(0)

To see the effect of this gate on our qubit, we'll need to measure it. Use the line below to insert a measurement instruction that takes the result of measuring qubit 0 and stores it in bit 0 of the classical bit register:

qc.measure([0],[0])

Congratulations: you have now written a (very simple) quantum program! You can view it as a quantum score:

qc.draw()

Running your first quantum program

We are now ready to run our circuit on a backend, i.e. a real quantum device or a simulator. Since the real quantum devices sometimes have long queues, we'll want to find the least busy one:

from qiskit.providers.ibmq import least_busy
real_device = least_busy(provider.backends(simulator=False))
backend

This should display an interactive widget showing some properties of the least-busy real quantum device.

We can now launch a job to run our circuit. Since we are not expecting a definite result, we should have our job run the circuit many times in order to gather statistics, so we'll call for 1,000 shots.

job1 = execute(qc, backend=real_device, shots=1000)

We can get a pop-up widget for tracking the status of our jobs:

%qiskit_job_watcher

When the job finishes, we can plot a histogram of the results:

res1 = job1.result()
plot_histogram(res1.get_counts())

Assuming the qubit is well-behaved, we should observe roughly equal counts of |0> and |1>.

Follow-up exercise: what do you expect to observe if you add a second Hadamard gate to your circuit prior to the measurement? Think about it and then try it (results not shown here).

Writing your second quantum program: demonstrating entanglement with Bell states

Now that you've started to wrap your mind around superposition, it's time to explore entanglement, a quantum phenomenon so counter-intuitive that Einstein famously referred to its consequences as "spooky action at a distance." In the context of quantum computing, an entangled state can be thought of as a correlated superposition state involving multiple qubits. The simplest such states are the two-qubit states known as Bell states in honor of the physicist John Bell. Preparing a Bell state is remarkably simple: put one qubit in a superposition state (e.g. using a Hadamard gate) and then use it as the control qubit in a controlled-NOT (CNOT) gate.

Familiar from classical computing, the CNOT gate acts on two bits labeled control and target, and has the effect of flipping the state of the target bit if and only if the control bit is a 1. Applied to qubits, this DOES NOT mean we measure the state of the control qubit to collapse it to |0> or |1> and then choose whether to flip the target qubit accordingly; that would merely be a classical operation done with qubits. Instead, we apply a pulse sequence that performs this operation without measuring or otherwise causing any other disturbance to the quantum states.

The implementation of CNOT gates involves some detailed physics, but fortunately the user need not worry about the details. The code below defines a circuit that prepares a Bell state and then measures both qubits to check for the expected correlations (note that CNOT is written as cx):

qc2 = QuantumCircuit(2,2)
qc2.h(0)
qc2.cx(0,1)
qc2.measure([0,1],[0,1])

Interpreting the Bell state measurement results

The code below plots the results of a job that runs 1,000 shots of the Bell state circuit:

job2 = execute(qc2,backend=backend,shots=1000)
res2 = job2.result()
plot_histogram(res2.get_counts())

Ideally the only observed outcomes would be ones with both qubits |0> or both qubits |1>, reflecting the correlated behavior expected from entangled states. Any observations of the other two possible outcomes indicate errors due to imperfections in the gates or measurements.

While this is an important result, it doesn't fully capture the surprising features of entangled states. Think about what you would expect to happen if you apply a Hadamard gate to both qubits just prior to the measurement. Now try it (result not shown).

Conclusion

The exercise above can be thought of as the equivalent of a "Hello world" program for a quantum computer. Writing and running quantum algorithms designed to solve real-world problems requires a more developed understanding of these principles and various techniques for harnessing them, but the concepts and paradigms explored here form the hull upon which the rest of the ship gets built. Welcome aboard!