From the course: Quantum Computing Fundamentals

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Single-qubit gates on multi-qubit states

Single-qubit gates on multi-qubit states

From the course: Quantum Computing Fundamentals

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Single-qubit gates on multi-qubit states

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- We've applied several different single cubic gates in isolation to one qubit at a time. But what if we want to apply one of those gates to a qubit that's part of a multi-qubit system? For example, let's say we have a quantum circuit with two qubits. They're both initialized in the zero basis state, and we want to apply an X gate to one of those qubits. That operation is easy to understand by looking at the circuit diagram, but let's consider how to accomplish that mathematically. The polyX operator is represented as a two-by-two matrix and the initial state vector for our pair of cubits is a four by one matrix. We can't simply multiply the X-Matrix, and state vector like we've been doing in previous videos because the inner dimensions don't match. These two matrices cannot be directly multiplied together. Conceptually, it also makes sense that regular X gate can't be used here because there's nothing to…

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