Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical.

- Richard Feynman

Summary

This article delves into quantum computers in basic terms explaining what is it, how it operates and what value does it provide? It aims to be as easy as possible, to understand.

What and Why?

Quantum computers can process information exponentially faster than normal computers because they fundamentally work on a different mechanism than a bit (0 or 1). A classical computer uses a Silicon - semiconductor transistor which can be either conducting (1) or not-conducting (0) depending on our input (electric field we apply, temperature, dopingadding other elements to Silicon, or light exposure).

Carbon, the basic element of life, has a versatile property: its 4 outer shell electrons facilitate easy exchange—capable of either accepting or donating an electron—allowing it to adopt multiple forms. Similarly, silicon straddles a boundary with its semiconductor properties, enabling it to switch between conducting and not-conducting states, thus serving diverse functions.

What is the fundamental factor in Quantum computers which it can hedge on? - Wave nature.

This attribute is complex and not yet fully comprehended. Despite not knowing why it occurs, we can describe how it works with the quantum wave equation, as formulated by the German physicist Schrödinger. The equation allows us to describe this wave nature to our advantage.

How is it better?

It can use multiple states at the same time in parallel. It can be anything in and between 0 and 1 and including both at the same time. So something which involves solving iterations to the magnitude of 2 to the power 300 - classical computers take (10,000 years or more) to solve. Since fundamentally they can solve 1 bit at a time.

With billions of transistors in processor and 1000s of processors in parallel, you can solve really big problems with classical computers. But ...

But how big problems are we talking about?

Picture by a Google Research blog.

"Classically tractable" refers to problems that can be efficiently solved using classical computers, where the required computational resources (time and memory) don't grow exponentially with the size of the problem.

The "number of cycles" on the graph refers to the computational steps a classical computer must perform to complete a specific task.

Process Flow

Let's narrate a story about Alice, a quantum computing researcher, who is using a quantum computer to run the Deutsch algorithm, illustrating the journey from classical input to quantum computation and back to classical interpretation.

Deutsch algorithm: The Deutsch algorithm, a quantum algorithm, tells if a function is constant or balanced by evaluating it only once. A function which has 1 input (with 2 states 0 and 1) and 1 output. It determines whether the output is the same for both inputs (constant) or different (balanced). It is not possible for a normal computer to tell the type of function whether constant or balanced with only 1iterationwhereas quantum computers can do it in 1 step. So, this function is used to prove if there is any benefit of using quantum computer over a normal computer.

1. Classical Input

Alice begins her day at the quantum computing lab, ready to run the Deutsch algorithm. She sits at her workstation, a classical computer equipped with a quantum development environment. Her task is to determine whether a given function is constant or balanced, a problem uniquely suited for quantum advantage.

Alice types in her program, defining the quantum circuit for the Deutsch algorithm. Her classical computer acts as the bridge to the quantum computer, converting her high-level instructions into a sequence of quantum operations.

2. Quantum Realm

Once Alice finalizes her program and runs it, the classical computer sends the instructions to the quantum computer. The command travels through the lab's network, down to the control electronics that interface with the quantum processor.

These control electronics are the gatekeepers, translating Alice's program into precise signals. For superconducting qubits, these are microwave pulses; for ion traps, they are laser beams. These signals journey through waveguides, coaxial cables, or optical fibers, reaching the cold heart of the quantum computer housed in a refrigerator.

Control Electronics

Top Section: The large white cylinder at the top usually houses the interface and the initial stages of cooling. The wires protruding downward are likely coaxial cables that carry microwave signals down to the lower stages where they're needed to control and measure the qubits.

Middle Section with Golden Components: This section often contains the mixing chamber stage, which is one of the coldest parts of the system. The golden color suggests the use of materials with good thermal properties at low temperatures, such as brass or gold-plated copper.

Lower Section with Cables and Wires: This area is closer to where the quantum processor would be located. The cables you see dangling and connecting to various parts are likely involved in delivering control signals to the qubits and reading out their states.

Very Bottom Section: In the center at the bottom, there's a cylinder from which many cables extend. This is likely where the quantum chip resides. It's at the end of the refrigeration cycle and is thus the coldest point, typically just a fraction of a degree above absolute zero (~10 mK).

Why absolute zero?- at this temperature, electrons move freely (superconductivity) without resistance. This is essential to observe the wave nature of electron.

3. Inside the Quantum Processor

Near absolute 0 K, the qubits await their instructions. The first set of signals initiates the quantum gates, manipulating the qubits into a state of superposition.

Superpositionmeans multiple waves can overlap and combine, creating a new wave pattern without altering the original waves.

The qubits, which could be superconducting circuits or trapped ions, vibrate with quantum potential, entangling as dictated by Alice's program.

The wave nature of electron is not a particle but acluster or a cloud. It is described by the equation of probability of finding the electron in space and is called aqubit.

Aqubitis an equivalent of a classical bit, with the unique ability to exist in multiple states (0, 1, or both) simultaneously.

It is described by Schrödinger’s wave equation as we discussed earlier.

A qubit state is represented as |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex probabilities for states |0⟩ and |1⟩.

The oracle function, central to the Deutsch algorithm, is applied. In this quantum realm, the function's nature—constant or balanced—is probed in a single operation.

Oracle functionis an arbitrary function that acts as a black box that evaluates a given function without revealing how the function is implemented.

4. The Measurement: Collapse to Reality

As the final gates are applied, the control system prepares to measure the qubits' states. This act of measurement is a bridge back to the classical world. The quantum information, residing in the delicate balance of superposition, collapses to a definite state—either |0⟩ or |1⟩, constant or balanced.

The readout mechanism detects the qubits' states, translating quantum outcomes into classical bits. These bits travel back through the control electronics, up the electron buses of the classical interface, and onto Alice's screen.

5. Interpretation and Triumph

Back in the warm light of her lab, Alice reviews the results displayed on her classical computer. This journey, from Alice's classical input through the quantum process and back, shows the relationship between classical and quantum computing.