Optimize consecutive RZZ gates into a single RZZ gate

[t-imamichi]

What should we add?

Since the fractional gates are available, RZZ can be used as a basis gate.
But, optimization of consecutive RZZ gates does not seem to be enough as follows.
It would be nice to merge them into a single RZZ.

from qiskit import generate_preset_pass_manager, QuantumCircuit

qc = QuantumCircuit(2)
qc.rzz(0.1, 0, 1)
qc.rzz(0.2, 0, 1)

pm = generate_preset_pass_manager(optimization_level=3, basis_gates=["rzz"])
qc2 = pm.run(qc)
print(qc2)

output (both 1.2.4 and main branch)

q_0: ─■─────────■────────
      │ZZ(0.1)  │ZZ(0.2)
q_1: ─■─────────■────────

[melechlapson]

Is this issue limited to the rzz gates and not other gates like ryy rzx etc.?

[t-imamichi]

Not limited to RZZ. But I don't mind RYY and RZX because RZZ becomes a basis gate of devices that supports fractional gates. RYY and RZX are not basis gates of any device.
https://docs.quantum.ibm.com/guides/fractional-gates

[ShellyGarion]

There is a synthesis algorithm TwoQubitControlledUDecomposer that takes a 2q-unitary and synthesizes it using the 2q basis gate RZZGate (with angles in the range [-pi/2, pi/2]. This algorithm has recently been ported to rust in #13139.

Here is an example of the output of this algorithm on the circuit suggested below:

        from qiskit.quantum_info import Operator
        from qiskit.synthesis.two_qubit.two_qubit_decompose import TwoQubitControlledUDecomposer
        unitary = Operator(qc)
        decomposer = TwoQubitControlledUDecomposer(RZZGate)
        qc3 = decomposer(unitary)
        print (qc3)

outputs:

global phase: -π
     ┌─────────┐┌──────────┐                       ┌─────────┐┌──────────┐»
q_0: ┤ Ry(π/2) ├┤ Ry(-π/2) ├─────────────■─────────┤ Ry(π/2) ├┤ Ry(-π/2) ├»
     └┬────────┤├──────────┤┌──────────┐ │ZZ(-0.3) ├─────────┤└┬────────┬┘»
q_1: ─┤ Rz(-π) ├┤ Ry(-π/2) ├┤ Ry(-π/2) ├─■─────────┤ Ry(π/2) ├─┤ Rz(-π) ├─»
      └────────┘└──────────┘└──────────┘           └─────────┘ └────────┘ »
«                 
«q_0: ────────────
«     ┌──────────┐
«q_1: ┤ Ry(-π/2) ├
«     └──────────┘

This algorithm should be added to the unitary synthesis tranpiler pass (#13320).
Then I think that this issues will be solved. Note that the redundant 1q gates should be eliminated by the 1q synthesis transpiler passes.

[ShellyGarion]

Is this issue limited to the rzz gates and not other gates like ryy rzx etc.?

@melechlapson -
Note that the synthesis algorithm TwoQubitControlledUDecomposer suggested above works also for gates like RYY, RZX, RXX etc. that are equivalent to an RZZ up to 1q-unitary gates.

[t-imamichi]

Thank you for your information, @ShellyGarion. I would like to use the algorithm as a transpiler pass. So I wait for #13320.

[t-imamichi]

Thank you, @ShellyGarion. It looks great.
I tried it with ibm_torino, but it could not merge two RZZ as follows.
Do you have any idea to apply the new pass for a real backend with the fractional gates?

from qiskit import QuantumCircuit, __version__, generate_preset_pass_manager
from qiskit_ibm_runtime import QiskitRuntimeService

print(__version__, "\n")
service = QiskitRuntimeService(name="primitives")
backend = service.backend("ibm_torino", use_fractional_gates=True)
target = backend.target

qc = QuantumCircuit(2)
qc.rzz(0.1, 0, 1)
qc.rzz(0.2, 0, 1)

pm = generate_preset_pass_manager(optimization_level=2, target=target)
tqc = pm.run(qc)
print(backend.configuration().basis_gates)
print(tqc.draw(idle_wires=False), "\n")

2.0.0.dev0+f82aa0a

['cz', 'id', 'rx', 'rz', 'rzz', 'sx', 'x']

q_0 -> 87 ─■─────────■────────
           │ZZ(0.1)  │ZZ(0.2)
q_1 -> 88 ─■─────────■────────

I found that the existence of 'cz' in the basis gates prevents the merge as follows.

from qiskit import QuantumCircuit, __version__, generate_preset_pass_manager

print(__version__, "\n")

qc = QuantumCircuit(2)
qc.rzz(0.1, 0, 1)
qc.rzz(0.2, 0, 1)

for basis_gates in [["rz", "rzz", "rx"], ["rz", "rzz", "rx", "cz"]]:
    pm = generate_preset_pass_manager(optimization_level=2, basis_gates=basis_gates)
    tqc = pm.run(qc)
    print(basis_gates)
    print(tqc.draw(idle_wires=False), "\n")

2.0.0.dev0+f82aa0a

['rz', 'rzz', 'rx']
global phase: π

q_0: ──────────■──────────────────
     ┌───────┐ │ZZ(-0.3) ┌───────┐
q_1: ┤ Rx(π) ├─■─────────┤ Rx(π) ├
     └───────┘           └───────┘

['rz', 'rzz', 'rx', 'cz']

q_0: ─■─────────■────────
      │ZZ(0.1)  │ZZ(0.2)
q_1: ─■─────────■────────

[ShellyGarion]

Thanks @t-imamichi for checking this! This PR should fix it #13958 (and it will hopefully be merged in time for 2.0).

[t-imamichi]

@ShellyGarion I see #12850 might make a regression. Could you check it?

before #12850 (65d041b)

2.0.0.dev0+65d041b

['rz', 'rzz', 'rx']
global phase: π

q_0: ──────────■──────────────────
     ┌───────┐ │ZZ(-0.3) ┌───────┐
q_1: ┤ Rx(π) ├─■─────────┤ Rx(π) ├
     └───────┘           └───────┘

['rz', 'rzz', 'rx', 'cz']
global phase: π

q_0: ──────────■──────────────────
     ┌───────┐ │ZZ(-0.3) ┌───────┐
q_1: ┤ Rx(π) ├─■─────────┤ Rx(π) ├
     └───────┘           └───────┘

after #12850 (246f5f3)

2.0.0.dev0+246f5f3

['rz', 'rzz', 'rx']
global phase: π

q_0: ──────────■──────────────────
     ┌───────┐ │ZZ(-0.3) ┌───────┐
q_1: ┤ Rx(π) ├─■─────────┤ Rx(π) ├
     └───────┘           └───────┘

['rz', 'rzz', 'rx', 'cz']
global phase: 3π/2
      ┌───────┐                  ┌───────┐                ┌────────┐ ┌────────┐
q_0: ─┤ Rz(π) ├───────────────■──┤ Rx(π) ├─────────────■──┤ Rx(-π) ├─┤ Rz(-π) ├
     ┌┴───────┴─┐┌──────────┐ │ ┌┴───────┴┐┌─────────┐ │ ┌┴────────┴┐├────────┤
q_1: ┤ Rx(-π/2) ├┤ Rz(-π/2) ├─■─┤ Rx(0.3) ├┤ Rz(π/2) ├─■─┤ Rx(-π/2) ├┤ Rz(-π) ├
     └──────────┘└──────────┘   └─────────┘└─────────┘   └──────────┘└────────┘

script

from qiskit import QuantumCircuit, __version__, generate_preset_pass_manager

print(__version__, "\n")

qc = QuantumCircuit(2)
qc.rzz(0.1, 0, 1)
qc.rzz(0.2, 0, 1)

for basis_gates in [["rz", "rzz", "rx"], ["rz", "rzz", "rx", "cz"]]:
    pm = generate_preset_pass_manager(optimization_level=2, basis_gates=basis_gates)
    tqc = pm.run(qc)
    print(basis_gates)
    print(tqc.draw(idle_wires=False), "\n")

[ShellyGarion]

One case that has not been solved yet is the following:

• the circuit has one CZ gate and one RZZ gate
• the target has basis gates containing 'cz' and 'rzz'.

In this case, the circuit would not get consolidated and re-synthesized into a single RZZ gate.
I'm not sure that I have a quick fix for this, but hope that it would be solved in #13419.

       basis_gates = ["rzz", "rx", "rz", "cz"]
        qc = QuantumCircuit(2)
        qc.rzz(0.1, 0, 1)
        qc.cz(0, 1)
        consolidate_pass = ConsolidateBlocks(basis_gates=basis_gates)
        res = consolidate_pass(qc)
        pm = generate_preset_pass_manager(optimization_level=2, basis_gates=basis_gates)
        tqc = pm.run(qc)
        print (res)
        print (tqc)

outputs:

q_0: ─■─────────■─
      │ZZ(0.1)  │ 
q_1: ─■─────────■─
                  
                  
q_0: ─■─────────■─
      │ZZ(0.1)  │ 
q_1: ─■─────────■─

[t-imamichi]

Thank you for your information. I wait for #13419.