Quantum gates

Key takeaways:

• Quantum gates are the fundamental building blocks of quantum computing. They manipulate qubits, which can exist in multiple states simultaneously, unlike classical bits.

• Quantum gates are represented by unitary matrices. These matrices describe the transformations that gates apply to qubits.

• Quantum gates can create superpositions of states and entangle qubits. These properties allow for unique computational capabilities that are not possible with classical computers.

Quantum gates or quantum logic gates are fundamental components in quantum computing, analogous to classical logic gates in traditional computing. However, there is a great difference between the way quantum gates and traditional logical gates operate.

Traditional logic gates

Classical logic gates are building blocks of traditional digital circuits. These circuits process classical bits, which can be in one of two states: 0 or 1. Classical gates manipulate these bits according to specific logical operations, such as AND, OR, NOT, etc. Some common classical gates are:

1. AND Gate: Outputs 1 only if both inputs are 1.

2. OR Gate: Outputs 1 if at least one input is 1.

3. NOT Gate: Outputs the inverse of its input.

4. NOR Gate: Outputs 1 if neither of its inputs is 1; otherwise, outputs of 0 (false).

5. NAND Gate: Outputs the inverse of an AND operation.

Quantum logic gates

Instead of operating on bits, quantum gates operate on quantum bits known as “qubits.” Qubits can exist in superpositions of 0 and 1 and can be entangled with other qubits. Quantum gates enable the manipulation and transformation of qubits according to the principles of quantum mechanics. Here are some key aspects of quantum gates:

Unitary transformations

Unitary matrices are used to represent quantum gates. This preserves the normalization of quantum states. The unitary matrices represent transformations that can be applied to qubits, changing their states according to the principles of quantum mechanics. Here’s the representation of a simple quantum gate as a unitary matrix:

Superposition and entanglement

As discussed above, qubits can be entangled with other qubits. Hence, quantum gates can create superpositions of states and exploit entanglement between qubits. Here’s the representation of a qubit in a superposition state and two entangled qubits:

Probabilistic nature

Quantum logic gates have a probabilistic nature until a measurement is made. The probabilistic nature of quantum gates is their ability to manipulate qubits in ways that involve uncertainty in outcomes, which are determined by probabilities instead of definite states. Here is the representation of the probabilistic nature of quantum computation:

Examples of quantum gates

Here are some examples of common quantum gates used in quantum computing:

Hadamard gate (H)

The Hadamard gate in quantum computing transforms a qubit from definite states |0⟩ or |1⟩ into combinations of both with equal probability. It operates on a single qubit represented by a Hadamard matrix (H).

Pauli-X gate (X)

Pauli-X gate (X) is analogous to the classical NOT gate. It flips the state of a qubit from |0⟩ to |1⟩ and vice versa.

Test yourself

Before moving on to the conclusion, test your understanding:

Conclusion

Quantum gates are the foundational components of quantum computing, enabling the manipulation and transformation of qubits according to the principles of quantum mechanics. Unlike classical logic gates, which operate on classical bits with definite states of 0 and 1, quantum gates work with qubits that can exist in superpositions of states and can be entangled with each other. Quantum gates perform unitary transformations on quantum states, allowing for complex computations to be executed in parallel.