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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 parametrised gates in pytket 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 taken from the user manual.

from pytket.circuit import Circuit, CustomGateDef
from sympy import symbols

a, b = symbols("a b")
def_circ = Circuit(2)
def_circ.CZ(0, 1)
def_circ.Rx(a, 1)
def_circ.CZ(0, 1)
def_circ.Rx(-a, 1)
def_circ.Rz(b, 0)

gate_def = CustomGateDef.define("MyCRx", def_circ, [a])

Its also possible to define a custom subroutine from a circuit using CircBox. The Custom parameterised gates shown above are useful when you want to define a parametrised gate in terms of lower level gates which you can then use repeatedly with different parameter values.

If the unitary represents a one, two or three qubit operation it is possible to synthesise a circuit to implement the unitary. See the manual section on unitary synthesis.

If you're interested in multi-controlled X operations you can add these to your Circuit as a CnX. You can have as many controls as you like. Here the we pass in the qubit indices as a list with the last element being the target qubit.

from pytket import Circuit, OpType

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

You may also wish to check out the ToffoliBox feature which implements an arbitrary permutation of the computational basis states using either {X, CnX} gates or a sequence of multiplexor operations.

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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