Quantum computing circuit for qubits equality

Comp Sci
Thread starter Hill
Start date Oct 18, 2023
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Circuit Computing Quantum

Oct 18, 2023

Hill

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Homework Statement: How can the circuit shown below be used to measure the qubits b0 and b1 for equality without learning anything else about the state of b0 and b1? (Hint: you are free to choose any initial state on the register consisting of qubits a0 and a1.)

Relevant Equations: Cnot = |0⟩⟨0|⊗I + |1⟩⟨1| ⊗X

This is the given circuit:

I think to add another Cnot on the right with a1 as control and a0 as target, to set initial states of a0 an a1 both |0⟩, and to measure the a0. If a0=|0⟩ then b0=b1, and vice versa.
Is it correct?

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Oct 21, 2023

Hill

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This question has been answered. It does not need to stay in the list of unanswered threads.

1. What is a quantum computing circuit?

A quantum computing circuit is a set of instructions and operations performed on a series of qubits (quantum bits) in order to carry out a specific computational task. These circuits are designed to take advantage of the principles of quantum mechanics, such as superposition and entanglement, to solve problems that are difficult or impossible for classical computers to solve efficiently.

2. How does a quantum computing circuit work?

A quantum computing circuit works by manipulating the state of qubits using quantum gates, which are analogous to classical logic gates. These gates can perform operations such as flipping the state of a qubit or entangling multiple qubits. By stringing together a series of gates in a specific sequence, a quantum computing circuit can perform calculations and solve complex problems.

3. What is the purpose of a qubit in a quantum computing circuit?

A qubit, or quantum bit, is the basic unit of information in a quantum computing circuit. Unlike classical bits, which can only exist in a state of 0 or 1, a qubit can exist in a state of 0, 1, or a superposition of both states. This allows for exponentially more information to be processed and manipulated in a quantum computing circuit, making it more powerful than classical computing.

4. How is the equality of qubits determined in a quantum computing circuit?

In a quantum computing circuit for qubits equality, the equality of qubits is determined by comparing the states of two or more qubits. This is achieved by using quantum gates, such as the CNOT gate, to entangle the qubits and then measuring their states. If the qubits are in the same state, they will collapse to the same measurement result, indicating equality.

5. What are the potential applications of a quantum computing circuit for qubits equality?

A quantum computing circuit for qubits equality has potential applications in fields such as cryptography, optimization, and simulation. By being able to efficiently compare and manipulate the states of qubits, it could be used to develop more secure encryption methods, solve complex optimization problems, and simulate quantum systems that are difficult to study using classical computers.