RemoteGates module

QdcEm.RemoteGates — Cat-State Communication and teleportation-based distributed gate library.

M_Unitary

M_Unitary(kappa)

Constructs the unitary operator for a single CM collision step between a system qubit and an environment qubit. Implements the interaction Hamiltonian:

\[\hat{H}_j = \kappa \left( \hat{\sigma}^-_{\mathrm{FQ}} \otimes \hat{\sigma}^+_E + \hat{\sigma}^+_{\mathrm{FQ}} \otimes \hat{\sigma}^-_E \right)\]

The resulting unitary Û_j = exp(−i Ĥ_j) is used to emulate both transduction-induced noise (κ_T) and optical-fiber-induced noise (κ_F).

Parameters

Name	Type	Description
`kappa`	`float`	Coupling constant — either κ_T (transducer) or κ_F (fiber).

Returns UnitaryGate — Qiskit gate implementing exp(−i Ĥ_j).

remote_cx

remote_cx(qc, control, target, CommA, CommB, ENA, ENB,
          creg, creg_index, kappa_Fiber, Steps, kappa_Transductor)

Implements a noisy distributed remote CNOT (CX) gate using the Cat-State Communication (Cat-Comm) protocol with CM noise injection, as described in Section 2.A and Figure 4(a) of the paper.

The noise sequence is: one transducer collision per communication qubit, one initial fiber collision, and Steps additional fiber collisions each preceded by an environment-qubit reset. The corrective feed-forward operations after the mid-circuit measurements complete the Cat-Comm protocol and restore the communication qubits for future use.

Parameters

Name	Type	Description
`qc`	`QuantumCircuit`	Circuit to which operations are appended.
`control`	`Qubit`	Processing qubit in QPU A (control).
`target`	`Qubit`	Processing qubit in QPU B (target).
`CommA` / `CommB`	`Qubit`	Communication qubits in QPU A and QPU B.
`ENA` / `ENB`	`Qubit`	Environment ancillae, reset between collisions to enforce the Markovian assumption.
`creg`	`ClassicalRegister`	Classical register for mid-circuit measurements.
`creg_index`	`int`	Base index into `creg`; two consecutive bits are consumed.
`kappa_Fiber`	`float`	Fiber coupling constant κ_F = √(0.01 · α).
`Steps`	`int`	Number of additional 10 m fiber segments beyond the first.
`kappa_Transductor`	`float`	Transducer coupling constant κ_T (typical value: 0.5).

remote_cz

remote_cz(qc, control, target, CommA, CommB, ENA, ENB,
          creg, creg_index, kappa_Fiber, Steps, kappa_Transductor)

Implements a noisy distributed remote CZ gate using Cat-Comm. The noise model is identical to remote_cx; the local gate applied on CommB–target is a CZ rather than a CNOT.

All parameters are identical to remote_cx.

remote_cp

remote_cp(qc, theta, control, target, CommA, CommB, ENA, ENB,
          creg, creg_index, kappa_Fiber, Steps, kappa_Transductor)

Implements a noisy distributed remote controlled-phase (CP) gate using Cat-Comm. Used as the building block for the distributed QFT.

Additional parameter

Name	Type	Description
`theta`	`float`	Phase rotation angle for the CP gate.

All other parameters are identical to remote_cx.

remote_cx_TP1

remote_cx_TP1(qc, control, target, CommA, CommB, ENA, ENB,
              creg, creg_index, kappa_Fiber, Steps, kappa_Transductor)

Implements a noisy distributed remote CNOT using the single-teleportation (TP1) protocol. Unlike Cat-Comm, TP1 teleports the control qubit’s state to QPU B where the CNOT is applied locally. The teleported state remains on a communication qubit until explicitly reset, which may block resources for subsequent remote operations.

All parameters are identical to remote_cx.

remote_cu

remote_cu(qc, theta, phi, lam, gamma, control, target,
          CommA, CommB, ENA, ENB,
          creg, creg_index, kappa_Fiber, Steps, kappa_Transductor)

Implements a noisy distributed remote controlled-U gate with an arbitrary single-qubit target unitary using Cat-Comm. The CNOT and CZ gates are special cases of this function.

Additional parameters

Name	Type	Description
`theta`, `phi`, `lam`, `gamma`	`float`	Parameters of Qiskit’s `CUGate` defining the single-qubit rotation.

All other parameters are identical to remote_cx.