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commit d0206bb777ab0604829b81f3cc7ea9694e949792
Author: Trevor Grant <[email protected]>
AuthorDate: Tue Jan 16 14:12:04 2024 -0600

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+# Quantum Gate Explanations
+
+## NOT Gate (X-Gate)
+The NOT gate, represented by the X-gate, is a fundamental quantum gate used to 
flip the state of a qubit. It is often referred to as a bit-flip gate. When 
applied to a qubit in the |0⟩ state, it changes it to the |1⟩ state, and vice 
versa. Mathematically, if |ψ⟩ represents the qubit's state, applying the X-gate 
results in X|ψ⟩ = |¬ψ⟩.
+
+## Hadamard Gate (H-Gate)
+The Hadamard gate, denoted as the H-gate, is used to create superposition 
states. When applied to a qubit in the |0⟩ state, it transforms it into an 
equal superposition of |0⟩ and |1⟩ states. Mathematically, H|0⟩ = (|0⟩ + |1⟩) / 
√2. It's a crucial gate in quantum algorithms like Grover's and quantum 
teleportation.
+
+## CNOT Gate (Controlled-X Gate)
+The CNOT gate, or controlled-X gate, is an entangling gate that acts on two 
qubits: a control qubit and a target qubit. If the control qubit is in the |1⟩ 
state, it applies the X-gate to the target qubit; otherwise, it does nothing. 
It creates entanglement between the two qubits and is essential in building 
quantum circuits for various applications.
+
+## Toffoli Gate (Controlled-Controlled-X Gate)
+The Toffoli gate is a three-qubit gate that acts as a controlled-controlled-X 
gate. It applies the X-gate to the target qubit only if both control qubits are 
in the |1⟩ state. It is used in quantum computing for implementing reversible 
classical logic operations.
+
+## SWAP Gate
+The SWAP gate exchanges the states of two qubits. When applied, it swaps the 
state of the first qubit with the state of the second qubit. This gate is 
fundamental in quantum algorithms and quantum error correction codes.
+
+## Pauli X Gate (X-Gate)
+The Pauli X gate is another name for the NOT gate, as mentioned earlier. It 
flips the state of a qubit, changing |0⟩ to |1⟩ and vice versa. It's named 
after Wolfgang Pauli, a pioneer in quantum physics.
+
+## Pauli Y Gate (Y-Gate)
+The Pauli Y gate is a quantum gate that introduces complex phase shifts along 
with a bit-flip operation. It can be thought of as a combination of bit-flip 
and phase-flip gates. Mathematically, it is represented as Y|0⟩ = i|1⟩ and Y|1⟩ 
= -i|0⟩. It's essential in quantum error correction and quantum algorithms.
+
+## Pauli Z Gate (Z-Gate)
+The Pauli Z gate is a gate that introduces a phase flip without changing the 
qubit's state. It leaves |0⟩ unchanged and transforms |1⟩ to -|1⟩. 
Mathematically, Z|0⟩ = |0⟩ and Z|1⟩ = -|1⟩. It's used for measuring the phase 
of a qubit.
+
+These quantum gates are fundamental building blocks in quantum computing, 
enabling the manipulation and transformation of qubit states to perform various 
quantum algorithms and computations.
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+![QuMat Logo](images/mascot.png)
+
+# QuMat
+
+QuMat is a POC of a high level Python library for intefacing with multiple 
+quantum computing backends. It is designed to be easy to use and to abstract 
+the particularities of each backend, so that you may 'write once, run 
+anywhere.' Like the Java of quantum computing, but Java is the new COBOL so 
+we're trying to distance ourselves from that comparison :P
+
+Check out [basic gates](basic_gates.md) for a quick introduction to the 
+basic gates which are basically all that exist right now (and even those 
+only exist for `qiskit`).
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