I am interested in performing a SWAP measurement, namely, measure 2 qubits and project their state onto either the triplet state manifold $\{|00\rangle, |11\rangle, |01\rangle + |10\rangle\}$ or the singlet state $|01\rangle - |10\rangle$ with measurement outcome being +1 in the first case and -1 in the second. The thing is that it needs to be done on a grid of qubits with nearest neighbor coupling only, such as the Sycamore architecture, and the native gateset is CZ + single qubit rotations.

The "canonical" way to do this is a CSWAP with an ancilla as the control prepared in the $|+\rangle$ state and measured in the $X$ basis. However, in this architecture the ancilla is directly connected only one of the qubits and so it is very costly in 2 qubit gates.

My question is: if I have the ability to perform only local gates, namely single qubit gates and 2 qubit gates between nearest neighbor qubits, and I can also measure and perform classically conditioned operations on the qubits, where the condition can be any boolean function of the measured qubits, is there a way to perform this gate using less native gates? It is possible to use more ancillas if needed.


1 Answer 1


Measure SWAP from 7 CNOTs, linear connectivity, ancilla outside:

enter image description here

(Note: improved this to not need any feedback anymore, and to just generally be cleaner.)

  • $\begingroup$ to make sure - the gates that look like 3 qubit gates are a pair of CNOTs from the middle qubit to the 2 outside ones, not a Toffoli with a pair of Hadamards on the top qubit, right? $\endgroup$
    – Lior
    May 2, 2023 at 9:06
  • 1
    $\begingroup$ @Lior right. The image is a link to the quirk circuit to check. $\endgroup$ May 2, 2023 at 15:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.