Not All Qubits Are Equal! | #quantumcomputers #qubits

Nature isn't classical, and if you want to simulate nature, you'd better make it quantum mechanical. It's a wonderful challenge, but it's far from easy. These words from physicist Richard Feynman capture the essence of why quantum computers were envisioned—to tackle problems that classical computers simply can't handle efficiently. As Feynman saw the potential, John Preskill from Caltech coined the term "quantum supremacy," reminding us of the reality: "We hope to develop quantum computers that will really work and change the world. But we're not there yet. This is a marathon, not a sprint." His words underscore the immense challenges and long-term dedication required to unlock quantum computing's full potential.

To truly simulate nature's complexity and harness quantum power, we must start from the basics. At the heart of quantum computing lies the qubit, the fundamental building block. But what is a qubit, actually? A qubit is short for "quantum bit," and conceptually, it is the quantum counterpart of the classical bit. In classical computing, a bit exists in one of two definite states: 0 or 1, or in other words, on and off. A qubit, in a very counterintuitive manner, can exist in a superposition of both states simultaneously. Imagine a switch that is on and off at the same time in terms of its functionality. That's right; we can't grasp the thought of it, as it has no direct analogy in classical physics. This distinction arises from the principles of quantum mechanics, fundamentally changing how we think about information processing.

Let's briefly visit the basic mathematical foundation of qubits. A qubit is described as a vector in a two-dimensional Hilbert space, a fundamental mathematical structure in quantum mechanics. A qubit can be represented on a Bloch sphere, where its quantum state is a point on the sphere's surface defined by two specific angles. This visualization captures the superposition and phase of the qubit, with states 0 and 1 located at the north and south poles, respectively. Quantum mechanically, the wave function ψ is represented as follows: ψ = α|0⟩ + β|1⟩. Here, |0⟩ and |1⟩ are the basis states in two-dimensional Hilbert space, analogous to the binary states in classical bits. α and β are complex numbers called probability amplitudes, and their squared magnitudes give the probabilities of the qubit being measured in state 0 or 1, respectively. The normalization condition |α|² + |β|² = 1 must always hold. This superposition allows a qubit to encode information that spans the space between states 0 and 1, which is fundamentally different from classical computing.

Regarding the physical nature of a qubit, it is realized by a quantum system that has two well-defined states. There are many physical schemes obtainable and conducive to manipulation, at least at the research and primary system level, some of which are as follows:

Spin systems: The spin of an electron can be up or down, considered to be a qubit.

Photons: A photon's polarization can be horizontal or vertical, establishing the essentials of a qubit.

Trapped ions: The energy levels of artificially trapped ions, such as the ground state and an excited state, are promising candidates.

Superconducting circuits: States of current that flow in different directions can also serve as qubits.

What's remarkable is that these physical systems are inherently quantum, allowing for behaviors like superposition and entanglement. Superposition means that a qubit doesn't merely switch between 0 and 1; rather, it exists along a continuum of probabilities, as represented on the surface of the Bloch sphere. Measuring the qubit forces it to collapse into one of its basis states—either 0 or 1—according to the probabilities |α|² and |β|². Superposition reflects a new kind of reality that blends classical determinism with quantum probabilities.

Entanglement is another profound phenomenon with no classical analog. When two or more qubits are entangled, the state of one qubit is inseparably linked to the state of the others, no matter how far apart they are. Measuring one qubit instantly determines the state of the other, a phenomenon Einstein famously referred to as "spooky action at a distance." Entanglement is the cornerstone of quantum computing, enabling powerful algorithms and phenomena like quantum teleportation.

The power of qubits lies in their ability to process information exponentially more efficiently than classical bits. A classical n-bit system can exist in one of 2ⁿ possible states at any given time, and we only need to know the values of the n bits to recognize the state. In contrast, quantum systems with n qubits can be in a superposition of all 2ⁿ states simultaneously. This property enables massive parallelism in quantum computations.