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I'm currently learning all about different quantum tools such as qiskit, tket, cirq, Forest SDK and so on. I just want to create a circuit that gets executed given a matrix, because a circuit can be written as a matrix and the other way around. In qiskit, cirq and pyquil (Forest SDK) there is no problem in defining an own gate. I don't find any function in tket which could help with this.

For example I want to define an AND gate. For those who don't know, an AND gate is actually just the CCNOT or CCX Gate. Tket does support the CCX gate but if I want to create maybe an AND Gate with 3 or 4 Qubits (CCCX or CCCCX) Gate the tket framework doesn't help.

Can somebody help me with this? I understand that you can define own gates in Tket but that just include gates that are created from native gates.

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You can define custom gates in tket using CustomGateDef. Here the CustomGate is defined using a circuit which implements the desired unitary instead of the matrix itself. Here is an example for how to do this...

https://cqcl.github.io/pytket/manual/manual_circuit.html#custom-parameterised-gates

If the unitary represents a one, two or three qubit operation it is possible to synthesise a circuit to implement the unitary. See for example https://cqcl.github.io/tket/pytket/api/circuit.html#pytket.circuit.Unitary3qBox

If you're interested in multi-controlled X operations you can add these to your Circuit as a CnX.

from pytket import Circuit, OpType

circ = Circuit(4)
circ.add_gate(OpType.CnX, [0, 1, 2, 3])

You may also wish to check out the ToffoliBox feature which implements an arbitrary permutation of the computational basis states using X and CnX gates.

There is an example in this section of the user manual if you scroll down. https://cqcl.github.io/pytket/manual/manual_circuit.html#boxes

Hope this is helpful.

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  • $\begingroup$ The snippet I showed is for a CCCX gate but you can make as may controls as you like by using a longer list of qubit indices. $\endgroup$
    – Callum
    Dec 5, 2022 at 15:42
  • $\begingroup$ Thank you for the answer. The Problem with CustomeGate is that it needs a circuit which implements the desired matirx. I want to start from a matrix and work my way to the circuit. I had a look at the Unitary Boxes but for my application i want more then just 3 Qubits to work with. Is there any way to go from the matrix (maybe given as a numpy.array) to a circuit. This feature is available in qiskit, cirq and pyquil. $\endgroup$
    – Qubii
    Dec 5, 2022 at 16:16
  • $\begingroup$ Arbitrary unitary synthesis in not implemented in TKET for > 3 qubits. A decision was made not to include this as the algorithms scale badly with respect to two-qubit gate count and runtime. As a workaround you could define your gate in qiskit and convert it to TKET using the qiskit_to_tk function from the pytket-qiskit extension. You may need to supply a method to decompose your new gate first. There are special box types that can be decomposed efficiently for a larger number of qubits. See ToffoliBox and PauliExpBox. Depending on what you are doing these could be useful. $\endgroup$
    – Callum
    Dec 5, 2022 at 17:00
  • $\begingroup$ "A decision was made not to include this as the algorithms scale badly with respect to two-qubit gate count and runtime." I think this is an interesting point, is there any public documentation of this decision? I could not find it along the issues of the tket Github page. $\endgroup$
    – Phil
    Dec 6, 2022 at 15:10
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    $\begingroup$ Sorry I'm not sure I have a great answer to this. I don't think it's discussed explicitly in the documentation. I'm a contributor to TKET so I'll make a note to mention this in our docs. I also recently had another request from someone else asking for the same thing. I think is worth discussing having this as a feature to be used in numerical calculations etc. $\endgroup$
    – Callum
    Dec 9, 2022 at 17:54

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