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Add equivalences from CR<Pauli> to R<Paulis> #9507

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Feb 1, 2023
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Add equivalences from CR<Pauli> to R<Paulis> #9507

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27321f0
ensure equivalences work to RZX
Cryoris Feb 1, 2023
bda6d8b
Merge branch 'main' into crx-equivalences
mergify[bot] Feb 1, 2023
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135 changes: 135 additions & 0 deletions qiskit/circuit/library/standard_gates/equivalence_library.py
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Original file line number Diff line number Diff line change
Expand Up @@ -235,6 +235,33 @@
crx_to_srycx.append(inst, qargs, cargs)
_sel.add_equivalence(CRXGate(theta), crx_to_srycx)

# CRX in terms of one RXX
# ┌───┐ ┌────────────┐┌───┐
# q_0: ────■──── q_0: ───┤ H ├───┤0 ├┤ H ├
# ┌───┴───┐ ≡ ┌──┴───┴──┐│ Rxx(-ϴ/2) │└───┘
# q_1: ┤ Rx(ϴ) ├ q_1: ┤ Rx(ϴ/2) ├┤1 ├─────
# └───────┘ └─────────┘└────────────┘
theta = Parameter("theta")
crx_to_rxx = QuantumCircuit(2)
crx_to_rxx.h(0)
crx_to_rxx.rx(theta / 2, 1)
crx_to_rxx.rxx(-theta / 2, 0, 1)
crx_to_rxx.h(0)
_sel.add_equivalence(CRXGate(theta), crx_to_rxx)

# CRX to CRZ
#
# q_0: ────■──── q_0: ─────────■─────────
# ┌───┴───┐ ≡ ┌───┐┌───┴───┐┌───┐
# q_1: ┤ Rx(ϴ) ├ q_1: ┤ H ├┤ Rz(ϴ) ├┤ H ├
# └───────┘ └───┘└───────┘└───┘
theta = Parameter("theta")
crx_to_crz = QuantumCircuit(2)
crx_to_crz.h(1)
crx_to_crz.crz(theta, 0, 1)
crx_to_crz.h(1)
_sel.add_equivalence(CRXGate(theta), crx_to_crz)

# RXXGate
#
# ┌─────────┐ ┌───┐ ┌───┐
Expand All @@ -257,6 +284,20 @@
def_rxx.append(inst, qargs, cargs)
_sel.add_equivalence(RXXGate(theta), def_rxx)

# RXX to RZX
# ┌─────────┐ ┌───┐┌─────────┐┌───┐
# q_0: ┤0 ├ q_0: ┤ H ├┤0 ├┤ H ├
# │ Rxx(ϴ) │ ≡ └───┘│ Rzx(ϴ) │└───┘
# q_1: ┤1 ├ q_1: ─────┤1 ├─────
# └─────────┘ └─────────┘
theta = Parameter("theta")
rxx_to_rzx = QuantumCircuit(2)
rxx_to_rzx.h(0)
rxx_to_rzx.rzx(theta, 0, 1)
rxx_to_rzx.h(0)
_sel.add_equivalence(RXXGate(theta), rxx_to_rzx)
Comment on lines +287 to +298
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If this is correct then I don't like our naming convention for RZXGate - to me, that reads as a ZX bitstring interaction, i.e. the Z is on qubit 1. But whatever, even if it mattered what I thought, the ship's long since sailed.

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@Cryoris Cryoris Feb 1, 2023 •
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Tbh I never know which order it is and just end up trying until it fits 😅 but I agree that RZX should implement e^{i theta * ZX} and in our tensor order that would be Z on q_1..

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@jakelishman jakelishman Feb 1, 2023 •
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I think the argument is that it implements what our documentation calls $Z \otimes X$, where I think there's some conflation of the general tensor product $\otimes$ with the Kronecker product ordering we use to make concrete matrix representations.

But anyway, the ship's sailed, and it's unrelated to this PR!

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Ah - Wikipedia explains:

the Kronecker product, sometimes denoted by $\otimes$

as opposed to:

the tensor product $V\otimes W$

I've never used \otimes to refer to the Kronecker product, and wasn't aware that was something people did - to me, it's always meant the arbitrary tensor product, which isn't tied to any particular representation of linear algebra.



# RXX to RZZ
q = QuantumRegister(2, "q")
theta = Parameter("theta")
Expand Down Expand Up @@ -321,6 +362,49 @@
def_cry.append(inst, qargs, cargs)
_sel.add_equivalence(CRYGate(theta), def_cry)

# CRY to CRZ
#
# q_0: ────■──── q_0: ───────────────■────────────────
# ┌───┴───┐ ≡ ┌─────────┐┌───┴───┐┌──────────┐
# q_1: ┤ Ry(ϴ) ├ q_1: ┤ Rx(π/2) ├┤ Rz(ϴ) ├┤ Rx(-π/2) ├
# └───────┘ └─────────┘└───────┘└──────────┘
theta = Parameter("theta")
cry_to_crz = QuantumCircuit(2)
cry_to_crz.rx(pi / 2, 1)
cry_to_crz.crz(theta, 0, 1)
cry_to_crz.rx(-pi / 2, 1)
_sel.add_equivalence(CRYGate(theta), cry_to_crz)

# CRY to CRZ
#
# q_0: ────■──── q_0: ────────────────────■─────────────────────
# ┌───┴───┐ ≡ ┌───┐┌─────────┐┌───┴───┐┌──────────┐┌───┐
# q_1: ┤ Ry(ϴ) ├ q_1: ┤ H ├┤ Rz(π/2) ├┤ Rx(ϴ) ├┤ Rz(-π/2) ├┤ H ├
# └───────┘ └───┘└─────────┘└───────┘└──────────┘└───┘
theta = Parameter("theta")
cry_to_crx = QuantumCircuit(2)
cry_to_crx.h(1)
cry_to_crx.rz(pi / 2, 1)
cry_to_crx.crx(theta, 0, 1)
cry_to_crx.rz(-pi / 2, 1)
cry_to_crx.h(1)
_sel.add_equivalence(CRYGate(theta), cry_to_crx)

# CRY to RZZ
#
# q_0: ────■──── q_0: ────────────────────────■───────────────────
# ┌───┴───┐ ≡ ┌─────┐┌─────────┐┌───┐ │ZZ(-ϴ/2) ┌───┐┌───┐
# q_1: ┤ Ry(ϴ) ├ q_1: ┤ Sdg ├┤ Rx(ϴ/2) ├┤ H ├─■─────────┤ H ├┤ S ├
# └───────┘ └─────┘└─────────┘└───┘ └───┘└───┘
cry_to_rzz = QuantumCircuit(2)
cry_to_rzz.sdg(1)
cry_to_rzz.rx(theta / 2, 1)
cry_to_rzz.h(1)
cry_to_rzz.rzz(-theta / 2, 0, 1)
cry_to_rzz.h(1)
cry_to_rzz.s(1)
_sel.add_equivalence(CRYGate(theta), cry_to_rzz)

# RYYGate
#
# ┌─────────┐ ┌─────────┐ ┌──────────┐
Expand Down Expand Up @@ -398,6 +482,44 @@
def_crz.append(inst, qargs, cargs)
_sel.add_equivalence(CRZGate(theta), def_crz)

# CRZ to CRY
#
# q_0: ────■──── q_0: ────────────────■───────────────
# ┌───┴───┐ ≡ ┌──────────┐┌───┴───┐┌─────────┐
# q_1: ┤ Rz(ϴ) ├ q_1: ┤ Rx(-π/2) ├┤ Ry(ϴ) ├┤ Rx(π/2) ├
# └───────┘ └──────────┘└───────┘└─────────┘
theta = Parameter("theta")
crz_to_cry = QuantumCircuit(2)
crz_to_cry.rx(-pi / 2, 1)
crz_to_cry.cry(theta, 0, 1)
crz_to_cry.rx(pi / 2, 1)
_sel.add_equivalence(CRZGate(theta), crz_to_cry)

# CRZ to CRX
#
# q_0: ────■──── q_0: ─────────■─────────
# ┌───┴───┐ ≡ ┌───┐┌───┴───┐┌───┐
# q_1: ┤ Rz(ϴ) ├ q_1: ┤ H ├┤ Rx(ϴ) ├┤ H ├
# └───────┘ └───┘└───────┘└───┘
theta = Parameter("theta")
crz_to_crx = QuantumCircuit(2)
crz_to_crx.h(1)
crz_to_crx.crx(theta, 0, 1)
crz_to_crx.h(1)
_sel.add_equivalence(CRZGate(theta), crz_to_crx)

# CRZ to RZZ
#
# q_0: ────■──── q_0: ────────────■────────
# ┌───┴───┐ ≡ ┌─────────┐ │ZZ(-ϴ/2)
# q_1: ┤ Rz(ϴ) ├ q_1: ┤ Rz(ϴ/2) ├─■────────
# └───────┘ └─────────┘
theta = Parameter("theta")
crz_to_rzz = QuantumCircuit(2)
crz_to_rzz.rz(theta / 2, 1)
crz_to_rzz.rzz(-theta / 2, 0, 1)
_sel.add_equivalence(CRZGate(theta), crz_to_rzz)

# RZZGate
#
# q_0: ─■───── q_0: ──■─────────────■──
Expand Down Expand Up @@ -429,6 +551,19 @@
rzz_to_rxx.append(inst, qargs, cargs)
_sel.add_equivalence(RZZGate(theta), rzz_to_rxx)

# RZZ to RZX
# ┌─────────┐
# q_0: ─■───── q_0: ─────┤0 ├─────
# │ZZ(ϴ) ≡ ┌───┐│ Rzx(ϴ) │┌───┐
# q_1: ─■───── q_1: ┤ H ├┤1 ├┤ H ├
# └───┘└─────────┘└───┘
theta = Parameter("theta")
rzz_to_rzx = QuantumCircuit(2)
rzz_to_rzx.h(1)
rzz_to_rzx.rzx(theta, 0, 1)
rzz_to_rzx.h(1)
_sel.add_equivalence(RZZGate(theta), rzz_to_rzx)

# RZZ to RYY
q = QuantumRegister(2, "q")
theta = Parameter("theta")
Expand Down
18 changes: 18 additions & 0 deletions releasenotes/notes/crx-equivalences-cc9e5c98bb73fd49.yaml
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Original file line number Diff line number Diff line change
@@ -0,0 +1,18 @@
---
features:
- |
Equivalences between the controlled Pauli rotations and translations to two-Pauli rotations
are now available in the equivalence library for Qiskit standard gates. This allows,
for example, to translate a :class:`.CRZGate` to a :class:`.RZZGate` plus :class:`.RZGate`
or a :class:`.CRYGate` to a single :class:`.RZXGate` plus single qubit gates::

from qiskit.circuit import QuantumCircuit
from qiskit.compiler import transpile

angle = 0.123
circuit = QuantumCircuit(2)
circuit.cry(angle, 0, 1)

basis = ["id", "sx", "x", "rz", "rzx"]
transpiled = transpile(circuit, basis_gates=basis)
print(transpiled.draw())