What is a Quantum State?

A quantum state is the fundamental mathematical description of a physical system in quantum mechanics. It serves as a complete "container" for all the information that can potentially be known about that system, such as its energy, position, momentum, or spin.

In classical computing, the state of a bit is deterministic—it is either a 0 or a 1. In contrast, a quantum state is probabilistic. Until it is measured, it exists as a superposition of potential outcomes. Think of a classical state like a coin resting on a table (clearly Heads or Tails), while a quantum state is like a coin spinning in mid-air—it embodies the potential for both outcomes simultaneously, defined by a precise probability distribution.

Types of Quantum States in a Quantum System

To accurately describe a quantum system, physicists categorize states into two primary types depending on how much information is known about the system.

• Pure States: A pure state describes a system where we have perfect knowledge of its quantum wavefunction. It is typically represented by a "ket" vector (e.g., $|\psi\rangle$) in Dirac notation. In quantum computing, ideal operations assume we are manipulating pure states.
• Mixed States: In the real world, systems interact with their environment (noise), leading to a loss of information. A mixed state represents a statistical ensemble of pure states—essentially, we know the system is in one of several states, but we don't know which one. Mixed states are described using a density matrix rather than a simple vector.
• Entangled States: When two or more qubits are linked such that the state of one cannot be described independently of the other, they form an entangled state. This correlation is stronger than anything possible in classical physics and is a key resource for quantum algorithms. (See also: Entanglement)

Quantum Phase and Its Role in Computation

One of the most critical components of a quantum state—and one that has no equivalent in classical logic—is the quantum phase.

If we write a qubit's state as $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$, the numbers $\alpha$ and $\beta$ are complex numbers. The relationship between them involves a phase angle. While the probabilities of measuring 0 or 1 depend only on the magnitude of these numbers, the phase controls how states interfere with one another.

"Quantum algorithms work by manipulating the quantum phase to create constructive interference for the correct answer and destructive interference for wrong answers."

Mastering phase control is essential for high-fidelity operations. If the phase drifts randomly due to environmental noise (dephasing), the computation fails. This is why coherence time is such a vital metric for any qubit technology.

Measuring a Quantum State: Quantum State Tomography

A fundamental rule of quantum mechanics is that you cannot observe a quantum state directly without collapsing it. If you measure a qubit in superposition, it snaps to either 0 or 1, destroying the complex quantum information it held.

So, how do researchers verify that they have created the correct state? They use a process called quantum state tomography.

Similar to how a medical CT scan builds a 3D image from many 2D X-rays, quantum state tomography reconstructs the quantum state by repeating the same experiment thousands of times. By measuring the system along different axes (X, Y, and Z bases) across many identical runs, researchers can statistically piece together the full density matrix of the system. This technique is crucial for calibrating hardware and verifying gate fidelity.

(See also: Measurement)

Applications of Quantum States in Quantum Computing

The ability to prepare, manipulate, and read out quantum states enables all quantum applications.

• Simulation: Mapping the quantum state of a molecule onto a quantum computer to predict chemical reaction rates.
• Optimization: Encoding a complex logistics problem into the ground state of a Hamiltonian.
• Cryptography: Using the "no-cloning theorem"—which states you cannot copy an unknown quantum state—to create unhackable communication channels.

Different hardware approaches face different challenges in preserving these states. For instance, superconducting qubits often struggle with short coherence times (states degrade quickly), requiring complex error mitigation.

The QuEra Angle: High-Fidelity States with Neutral Atoms

At QuEra, we utilize neutral atoms (specifically Rubidium) to define our quantum states. This approach offers distinct advantages for state preparation and preservation:

• Nature's Perfection: unlike manufactured circuits where every qubit is slightly different, every Rubidium atom is identical. This allows us to define the quantum state with extreme precision using the atom's internal energy levels (Rydberg states).
• Long Coherence: Neutral atoms are naturally isolated from the environment. They are not coupled to a noisy solid-state chip, allowing their quantum states to persist for very long durations (seconds), which is orders of magnitude longer than many other modalities..

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