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Effect of unbalanced and common losses in quantum

photonic integrated circuits

Ming Li (李明)

1,2

, Changling Zou (邹长铃)

1,2

, Guangcan Guo (郭光灿)

1,2

and Xifeng Ren (任希锋)

1,2,

Key Laboratory of Quantum Information, CAS, University of Science and Technology of China,

Hefei 230026, China

Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and

Technology of China, Hefei 230026, China

*Corresponding author: renxf@ustc.edu.cn

Received March 16, 2017; accepted May 23, 2017; posted online June 16, 2017

Loss is inevitable for the optical system due to the absorption of materials, scattering caused by the defects, and

surface roughness. In quantum optical circuits, the loss can not only reduce the intensity of the signal, but also

affect the performance of quantum operations. In this work, we divide losses into unbalanced linear losses and

shared common losses, and provide a detailed analysis on how loss affects the integrated linear optical quantum

gates. It is found that the orthogonality of eigenmodes and the unitary phase relation of the coupled waveguide

modes are destroyed by the loss. As a result, the fidelity of single- and two-qubit operations decreases signifi-

cantly as the shared loss becomes comparable to the coupling strength. Our results are important for the

investigation of large-scale photonic integrated quantum information processes.

OCIS codes: 270.0270, 130.0130.

doi: 10.3788/COL201715.092701.

Photonic integra ted circuits (PICs)

[1]

have been developed

for the increasing complexity of both classical and quan-

tum information processing, which is demanding on

scalability, stability, and high-quality interference. By in-

tegrating the waveguides and controlling their coupling on

a chip, basic optical elements

[2]

in bulk optics can be real-

ized on-chip with high quality, such as a beam splitter

(BS), phase shifter, and polarization beam splitter

(PBS)

[3,4]

. Recently, a quantum C-NOT gate, quantum

walk, and Boson sampling have been performed on a single

chip, based on silica-on-silicon waveguides

[5,6]

, laser direct

writing waveguides

[7,8]

, and plasmonic waveguides

[9,10]

There remains challenges in integrating optical devices

with good performance, and the errors due to experimen-

tal imperfection will be amplified when cascading many

basic integrated devices together for future quantum com-

puting, simulation, and communication.

Among various imperfections, loss is inevitable that is

generated from both the essential absorption of materials

and the technical problems in fabrication. The effect of

loss in bulk optics has been studied in earlier years

[11,12]

When dealing with integrated circuits, many basic optical

components are integrated together, and more complex

structures should attract our attention. Genera lly, there

are off-chip insertion losses and on-chip waveguide losses.

Usually, people summarize these linear losses and combine

them with the inefficiency of detectors. Since quantum

processes can be realized via post selection, which claims

success when detecting the photons in the desired manner,

so linear quantum computation can still be performed

with those imperfections, and the only influence is the

low success probability.

In this Letter, we studied the general loss model in the

on-chip BS devices and its effects on the gate fidelities. We

found that when there is an unbalanced loss (UBL) or a

shared common loss (CL) channel in the BS, there will be

significant errors that will affect the performance of the

optical quantum processing.

For an ideal linear process supported by a quantum PIC,

the relation between the input and output field can be de-

scribed by a unitary matrix. It has been demonstrated that

any unitary matrix can be decomposed to the product of

two level matrices

[13]

, which meanwhile can be further de-

composed to phase shifters and BSs

[14]

.Figure1(a) shows

a sketch picture of a directional coupler, the physical reali-

zation of a BS, where two waveguides approach each other

and exchange energy. For simplicity, we only focus on the

uniform coupling regime, whose properties can be analyzed

by solving the eigenmodes of the coupled waveguide at the

cross section. In the weak coupling regime, two waveguides

couple with each other through tunneling, which can be

quantitatively described by the coupling rate C.According

to the coupled mode theory, the dynamics of photon am-

plitude A

, A

in two waveguides should obey

¼ð−iβ − γ

ÞA

− iCA

; (1)

¼ð−iβ − γ

ÞA

− iCA

; (2)

where β is the propagation constant, γ

is the damping

rate, and L is the distance along the propagation direc-

tion. The coupled equations can also be expressed in

vector form

COL 15(9), 092701(2017) CHINESE OPTICS LETTERS September 10, 2017

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