How to synthesize quantum circuits?

In summary, the conversation discusses how to synthesize a quantum circuit, specifically for performing the exclusive or operation on three qubits. The speaker mentions that they can write the matrix form of the circuit but are unsure how to translate it into a list of gates. They suggest using a controlled not gate with a as the control and another controlled not gate with b as the control to achieve the desired operation. The speaker also recommends using a quantum computing textbook or a circuit simulator like Quirk for further guidance.
  • #1
nashed
58
5
I wonder if anyone can explain how to actually synthesis a quantum circuit, what I mean by this is that given some requirements, I am able to write the matrix form of the circuit needed, but I have no idea how to turn that into a list of gates.

For example:
Build a circuit that performs the exclusive or operation on three qubits $$ |abc\rangle \rightarrow |ab\rangle\otimes|a\oplus b\oplus c\rangle $$ looking at a truth table for the circuit I can see that when a and b are the same then c is conserved, otherwise c is flipped so I can deduce that if I connect c to a controlled not where a is the control and another controlled not where b is the control I get the desired operation.
That said if I try and write the matrix form of the circuit I have no idea how to manipulate it so it looks like the repeated application of controlled not gates.

BTW this is not a homework question but I am not sure this is the correct forum either so feel free to tell me and I"ll delete the post.
 
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  • #2
This kind of information is covered in quantum computing textbooks, and those might be your best bet.

Other than that, you could try reading this blog post about cutting down a NOT with many controls into single-control NOTs and single-qubit operations.

You will probably also find my drag-and-drop quantum circuit simulator Quirk very useful. For example, I bet the truth table you have looks quite a lot like the grid on the right:

Screenshot from 2017-02-27 15:32:56.png
 

1. What is a quantum circuit?

A quantum circuit is a sequence of quantum operations, also known as quantum gates, that are applied to a set of quantum bits (qubits) to perform a specific quantum computation.

2. How do I synthesize a quantum circuit?

To synthesize a quantum circuit, you first need to define the problem you want to solve and determine the required number of qubits. Then, you can use a quantum programming language such as Qiskit or Cirq to write the circuit using different quantum gates.

3. What are the key principles of quantum circuit synthesis?

The key principles of quantum circuit synthesis include minimizing the number of quantum gates, optimizing the gate sequence to reduce errors and increase efficiency, and taking into account the physical constraints of the quantum hardware being used.

4. Is there a standard way to synthesize quantum circuits?

There is no universal standard for synthesizing quantum circuits, as it depends on the specific problem and available resources. However, there are various algorithms and techniques, such as gate decomposition and gate cancellation, that are commonly used in quantum circuit synthesis.

5. How can I test the effectiveness of a synthesized quantum circuit?

To test the effectiveness of a synthesized quantum circuit, you can use quantum simulators or actual quantum hardware to run the circuit and compare the results to the expected outcome. Additionally, you can use metrics such as gate count and success rate to evaluate the efficiency and accuracy of the circuit.

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