Noise Model

The QdcEm noise model is based on the Collisional Model (CM) framework. This page describes the physical assumptions, mathematical formulation, and circuit-level implementation of the CM within the QdcEm gate primitives.

Physical motivation

In a real Quantum Data Center, QPUs communicate via quantum channels that traverse a microwave-to-optical transducer and an optical fiber link. Each stage introduces decoherence:

  • Transducer noise arises from imperfect microwave-to-optical conversion, modelled by coupling constant κT.

  • Fiber noise arises from photon loss along the optical fiber, modelled by coupling constant κF = √(0.01 · α), where α is the fiber attenuation coefficient (km-1).

Interaction Hamiltonian

Each collision step between the flying qubit (FQ) and a single environment ancilla E is governed by:

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

This is an excitation-exchange (amplitude-damping) interaction. The corresponding unitary for a single collision step is:

\[\hat{U}_j = \exp\!\left(-i\hat{H}_j\right)\]

This unitary is computed numerically via QuTiP’s expm() routine and wrapped as a Qiskit UnitaryGate by M_Unitary(kappa).

Channel noise sequence

For every remote gate, noise is injected in three stages:

  1. Bell pair generation. CommA and CommB are prepared in the state |Φ+⟩ = (|00⟩ + |11⟩)/√2.

  2. Transducer collisions. One CM collision at strength κT is applied to each communication qubit. The environment qubit is reset to |0⟩ after each collision to enforce the Markovian (memoryless) assumption.

  3. Fiber collisions. One initial CM collision at strength κF is applied per side, followed by Steps further collisions — each preceded by an environment-qubit reset. Each collision models a 10 m fiber segment, so the total channel distance is D = 10 · (1 + Steps) metres.

Supported fiber grades

ITU-T Grade

Attenuation α (km-1)

κF

G-652-D

0.0415

0.02037

G-654-E

0.0392

0.01980

G-655-D

0.0507

0.02252

Numerical reference

0.0415

0.02037

Implementation

from QdcEm.RemoteGates import M_Unitary

# Construct the CM unitary for kappa_T = 0.5
U_T = M_Unitary(kappa=0.5)

# Append to a circuit: one collision between CommA and ENA
qc.append(U_T, [CommA, ENA])
qc.reset(ENA)   # enforce the Markovian assumption