How many ancilla qubits to use with Multiple-Control Toffoli (mct) gate in Qiskit?

Question

The Multiple-Control Toffoli (mct) gate takes as input: 1. a register containing the control qubits, 2. the target qubits and 3. a register containing ancilla qubits.

I don't know how many ancilla qubits I need to pass in for a number of $n$ controll qubits. I've seen examples and used mct gates with 4 control qubits and 2 ancillas so I know the number of ancillas is not $n-1$ like suggested in this answer

Is there a strict dependency meaning for 10 control qubits you need 5 ancillas or does the implementation adapt to the number or ancillas that are passed in?

score 4 · Accepted Answer · answered Oct 12 '19 at 14:33

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I found out the number of ancillas is minimum $n-2$.

I found this line in the Qiskit source code of mct:

if len(ancillary_qubits) < len(control_qubits) - 2:
    raise AquaError('Insufficient number of ancillary qubits.')

answered Oct 12 '19 at 14:33

Sorin Bolos

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Im new to QC so this may be a trivial question; Why use more than one ancilla? Im using the mct gate for my 6 qubit grover's algorithm circuit and the gate works just fine with just 1 ancilla... unless I am doing something wrong. Thanks in advance. – James Bian Jun 22 '21 at 13:40
In Qiskit, it seems fine even if I don't specify any ancilla qubit. For example, Minh Pham's answer (see below) doesn't cause an error. – LearnerAL Jan 04 '22 at 23:34

Minh Pham · Answer 2 · 2021-06-22T14:04:44.560

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You don't need to use any ancillas at all. Just add in the controls as a list and a target and you should be good.

Take this as an example of 9 control bits

edited Jun 22 '21 at 14:04

answered Jun 21 '21 at 18:18

Minh Pham

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8

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It forces you to put in atleast 1 ancilla when the control gate gets bigger than 5. – James Bian Jun 22 '21 at 13:39

How many ancilla qubits to use with Multiple-Control Toffoli (mct) gate in Qiskit?

2 Answers2