What is a Quantum Computer?

In essence, a quantum computer is a type of computer that utilizes the principles of quantum mechanics to perform specific types of computations more efficiently than traditional computers.

This definition encompasses a lot, so let’s break it down with a straightforward illustration. To clarify what a quantum computer is, it’s essential first to understand how conventional computers operate.

How Conventional Computers Store Information

Traditional computers save data using a series of 0s and 1s. Various forms of information, including numbers, text, and images, can be represented in this binary format. Each individual element in this binary sequence is referred to as a bit, which can either be 0 or 1.

What About Quantum Computers?

Quantum computers, however, do not rely on bits for data storage. Instead, they utilize entities known as qubits. A qubit can be set to 1 or 0, but it can also exist in a state that encompasses both 1 and 0. What does this mean in practice? Let’s clarify with a simple analogy.

A Simple Example

Imagine you are operating a travel agency and need to arrange transportation for three individuals: Alice, Becky, and Chris. You have two taxis at your disposal and need to determine who should ride in which vehicle.

You have the following social dynamics to consider: - Alice and Becky are friends - Alice and Chris are enemies - Becky and Chris are enemies

Your objective is to assign these three individuals to the taxis while achieving two goals: - Maximize the number of friend pairs in the same vehicle - Minimize the number of enemy pairs in the same vehicle

This sets the stage for our problem. Now, let's explore how a conventional computer would tackle this.

Solving the Problem with a Conventional Computer

To solve this issue using a regular computer, you first need to organize the relevant information using bits. Label the taxis as Taxi #0 and Taxi #1. You can represent who gets into which taxi with three bits. For example, setting the bits to 0, 0, and 1 could indicate: - Alice takes Taxi #0 - Becky takes Taxi #0 - Chris takes Taxi #1

With two options for each person, there are 2*2*2 = 8 possible ways to arrange this group into the taxis. Here’s a list of all potential configurations:

A | B | C 0 | 0 | 0 0 | 0 | 1 0 | 1 | 0 0 | 1 | 1 1 | 0 | 0 1 | 0 | 1 1 | 1 | 0 1 | 1 | 1

Using three bits, you can illustrate any combination from this list.

Computing the Score for Each Configuration

Next, how do we determine which configuration is the most optimal? We need a method to compute a score for each arrangement based on how well it meets our goals: - Maximize the number of friend pairs sharing a vehicle - Minimize the number of enemy pairs sharing a vehicle

We define our score as follows:

(score of a configuration) = (number of friend pairs sharing a taxi) - (number of enemy pairs sharing a taxi)

For example, if Alice, Becky, and Chris all ride in Taxi #1 (represented as 111), there is one friend pair (Alice and Becky) and two enemy pairs (Alice and Chris, Becky and Chris), giving a score of 1-2 = -1.

Solving the Problem

To find the optimal configuration with a conventional computer, you would need to evaluate all arrangements to see which achieves the highest score. This could be displayed in a table:

A | B | C | Score 0 | 0 | 0 | -1 0 | 0 | 1 | 1 <--- one of the best solutions 0 | 1 | 0 | -1 0 | 1 | 1 | -1 1 | 0 | 0 | -1 1 | 0 | 1 | -1 1 | 1 | 0 | 1 <--- the other best solution 1 | 1 | 1 | -1

The problem quickly escalates in complexity. With just three individuals, we have 8 configurations to assess. With four individuals, that number doubles to 16, and with n individuals, we would need to evaluate (2^n) configurations. Thus, with 100 individuals, this becomes an astronomical number of combinations, making it impractical for conventional computers to solve.

Solving This Problem with a Quantum Computer

So, how would a quantum computer handle this problem? Let’s revisit the scenario of dividing three people into two taxis. As established, there are 8 potential solutions:

A | B | C 0 | 0 | 0 0 | 0 | 1 0 | 1 | 0 0 | 1 | 1 1 | 0 | 0 1 | 0 | 1 1 | 1 | 0 1 | 1 | 1

Using a conventional computer, we can only evaluate one solution at a time, such as 001. In contrast, with a quantum computer utilizing 3 qubits, we can simultaneously represent all 8 solutions.

This can be conceptualized as creating parallel universes for each qubit. Setting the first qubit to both 0 and 1 generates two worlds. Adding a second qubit doubles this to four worlds, and including a third qubit results in eight parallel worlds, each representing a different configuration.

When computations are applied to these qubits, they occur across all eight worlds concurrently. Therefore, rather than sifting through each potential solution individually, the quantum computer can compute the scores for all configurations simultaneously. In theory, it could identify one of the best solutions in mere milliseconds.

To solve this problem, a quantum computer needs: - All potential solutions encoded as qubits - A function that translates each potential solution into a score, considering friend and enemy pairings

In practice, while quantum computers can theoretically find the best solution each time, operational errors may lead to discovering suboptimal solutions. These errors can become more pronounced with increased complexity, which is why multiple runs may be necessary to select the best result.

How Quantum Computers Scale

Despite these operational challenges, quantum computers do not face the same scaling issues as conventional computers. For three individuals, a single operation is needed. The same applies for four individuals or even 100; the quantum computer computes all (2^n) configurations at once with just one operation.

Thus, although it’s advisable to run the quantum computation multiple times and choose the best outcome, this method is still vastly more efficient than a conventional computer, which would require an astronomical number of computations for the same problem.

Wrapping Up

I extend my gratitude to the team at D-Wave Systems for their thorough explanations. D-Wave has recently introduced a cloud platform for engaging with quantum computers. If you’re a developer eager to explore quantum computing, this is likely the simplest way to start.

Check out Leap at https://cloud.dwavesys.com/leap. You can use it for free to tackle numerous problems, and they offer user-friendly tutorials to help you begin your journey with quantum technology.

In this article, I used the term "regular computer" to signify a non-quantum computer. In the field of quantum computing, such systems are typically referred to as classical computers.