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,
*
1
Key Laboratory of Quantum Information, CAS, University of Science and Technology of China,
Hefei 230026, China
2
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
1
, A
2
in two waveguides should obey
d
dL
A
1
¼ð−iβ − γ
1
ÞA
1
− iCA
2
; (1)
d
dL
A
2
¼ð−iβ − γ
2
ÞA
2
− iCA
1
; (2)
where β is the propagation constant, γ
i
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
1671-7694/2017/092701(5) 092701-1 © 2017 Chinese Optics Letters
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