We present an experimental implementation of a two-qubit photonic quantum processor fabricated using femtosecond laser writing technology. We employ femtosecond laser writing to create a low-loss reconfigurable photonic chip, implementing precise single-qubit and two-qubit operations. We present a careful characterization of the performance of single- and two-qubit gates. An exemplary application of estimating the ground state energy of an H2 molecule using the variational quantum eigensolver algorithm is demonstrated. Our results highlight the potential of the femtosecond laser writing technology to deliver high quality small-scale quantum photonic processors.

1.
E. R.
MacQuarrie
,
C.
Simon
,
S.
Simmons
, and
E.
Maine
, “
The emerging commercial landscape of quantum computing
,”
Nat. Rev. Phys.
2
,
596
598
(
2020
).
2.
L.
Gyongyosi
and
S.
Imre
, “
A survey on quantum computing technology
,”
Comput. Sci. Rev.
31
,
51
71
(
2019
).
3.
H.-S.
Zhong
,
H.
Wang
,
Y.-H.
Deng
,
M.-C.
Chen
,
L.-C.
Peng
,
Y.-H.
Luo
,
J.
Qin
,
D.
Wu
,
X.
Ding
,
Y.
Hu
,
P.
Hu
,
X.-Y.
Yang
,
W.-J.
Zhang
,
H.
Li
,
Y.
Li
,
X.
Jiang
,
L.
Gan
,
G.
Yang
,
L.
You
,
Z.
Wang
,
L.
Li
,
N.-L.
Liu
,
C.-Y.
Lu
, and
J.-W.
Pan
, “
Quantum computational advantage using photons
,”
Science
370
,
1460
1463
(
2020
).
4.
J. M.
Arrazola
,
V.
Bergholm
,
K.
Brádler
,
T. R.
Bromley
,
M. J.
Collins
,
I.
Dhand
,
A.
Fumagalli
,
T.
Gerrits
,
A.
Goussev
,
L. G.
Helt
,
J.
Hundal
,
T.
Isacsson
,
R. B.
Israel
,
J.
Izaac
,
S.
Jahangiri
,
R.
Janik
,
N.
Killoran
,
S. P.
Kumar
,
J.
Lavoie
,
A. E.
Lita
,
D. H.
Mahler
,
M.
Menotti
,
B.
Morrison
,
S. W.
Nam
,
L.
Neuhaus
,
H. Y.
Qi
,
N.
Quesada
,
A.
Repingon
,
K. K.
Sabapathy
,
M.
Schuld
,
D.
Su
,
J.
Swinarton
,
A.
Száva
,
K.
Tan
,
P.
Tan
,
V. D.
Vaidya
,
Z.
Vernon
,
Z.
Zabaneh
, and
Y.
Zhang
, “
Quantum circuits with many photons on a programmable nanophotonic chip
,”
Nature
591
,
54
60
(
2021
).
5.
T.
Meany
,
M.
Gräfe
,
R.
Heilmann
,
A.
Perez-Leija
,
S.
Gross
,
M. J.
Steel
,
M. J.
Withford
, and
A.
Szameit
, “
Laser written circuits for quantum photonics
,”
Laser Photonics Rev.
9
,
363
384
(
2015
).
6.
S.
Bogdanov
,
M. Y.
Shalaginov
,
A.
Boltasseva
, and
V. M.
Shalaev
, “
Material platforms for integrated quantum photonics
,”
Opt. Mater. Express
7
,
111
132
(
2017
).
7.
F.
Flamini
,
N.
Spagnolo
, and
F.
Sciarrino
, “
Photonic quantum information processing: A review
,”
Rep. Prog. Phys.
82
,
016001
(
2018
).
8.
J.
Wang
,
F.
Sciarrino
,
A.
Laing
, and
M. G.
Thompson
, “
Integrated photonic quantum technologies
,”
Nat. Photonics
14
,
273
284
(
2020
).
9.
A. W.
Elshaari
,
W.
Pernice
,
K.
Srinivasan
,
O.
Benson
, and
V.
Zwiller
, “
Hybrid integrated quantum photonic circuits
,”
Nat. Photonics
14
,
285
298
(
2020
).
10.
J. C.
Adcock
,
J.
Bao
,
Y.
Chi
,
X.
Chen
,
D.
Bacco
,
Q.
Gong
,
L. K.
Oxenløwe
,
J.
Wang
, and
Y.
Ding
, “
Advances in silicon quantum photonics
,”
IEEE J. Sel. Top. Quantum Electron.
27
,
1
24
(
2021
).
11.
S.
Saravi
,
T.
Pertsch
, and
F.
Setzpfandt
, “
Lithium niobate on insulator: An emerging platform for integrated quantum photonics
,”
Adv. Opt. Mater.
9
,
2100789
(
2021
).
12.
P. J.
Shadbolt
,
M. R.
Verde
,
A.
Peruzzo
,
A.
Politi
,
A.
Laing
,
M.
Lobino
,
J. C. F.
Matthews
,
M. G.
Thompson
, and
J. L.
O'Brien
, “
Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit
,”
Nat. Photonics
6
,
45
49
(
2012
).
13.
R.
Santagati
,
J. W.
Silverstone
,
J. L.
O'Brien
,
M. G.
Thompson
,
M. J.
Strain
,
M.
Sorel
,
M. G.
Tanner
,
C. M.
Natarajan
,
R. H.
Hadfield
,
S.
Miki
,
T.
Yamashita
,
H.
Terai
,
M.
Fujiwara
, and
M.
Sasaki
, “
Silicon photonic processor of two-qubit entangling quantum logic
,”
J. Opt.
19
,
8
(
2017
).
14.
X.
Qiang
,
X.
Zhou
,
J.
Wang
,
C. M.
Wilkes
,
T.
Loke
,
S.
O'Gara
,
L.
Kling
,
G. D.
Marshall
,
R.
Santagati
,
T. C.
Ralph
,
J. B.
Wang
,
J. L.
O'Brien
,
M. G.
Thompson
, and
J. C. F.
Matthews
, “
Large-scale silicon quantum photonics implementing arbitrary two-qubit processing
,”
Nat. Photonics
12
,
534
539
(
2018
).
15.
L.-T.
Feng
,
M.
Zhang
,
X.
Xiong
,
D.
Liu
,
Y.-J.
Cheng
,
F.-M.
Jing
,
X.-Z.
Qi
,
Y.
Chen
,
D.-Y.
He
,
G.-P.
Guo
,
G.-C.
Guo
,
D.-X.
Dai
, and
X.-F.
Ren
, “
Transverse mode-encoded quantum gate on a silicon photonic chip
,”
Phys. Rev. Lett.
128
,
060501
(
2022
).
16.
D.
Tan
,
Z.
Wang
,
B.
Xu
, and
J.
Qiu
, “
Photonic circuits written by femtosecond laser in glass: Improved fabrication and recent progress in photonic devices
,”
Adv. Photonics
3
,
024002
(
2021
).
17.
G. D.
Marshall
,
A.
Politi
,
J. C. F.
Matthews
,
P.
Dekker
,
M.
Ams
,
M. J.
Withford
, and
J. L.
O'Brien
, “
Laser written waveguide photonic quantum circuits
,”
Opt. Express
17
,
12546
12554
(
2009
).
18.
L.
Sansoni
,
F.
Sciarrino
,
G.
Vallone
,
P.
Mataloni
,
A.
Crespi
,
R.
Ramponi
, and
R.
Osellame
, “
Polarization entangled state measurement on a chip
,”
Phys. Rev. Lett.
105
,
200503
(
2010
).
19.
A.
Crespi
,
R.
Ramponi
,
R.
Osellame
,
L.
Sansoni
,
I.
Bongioanni
,
F.
Sciarrino
,
G.
Vallone
, and
P.
Mataloni
, “
Integrated photonic quantum gates for polarization qubits
,”
Nat. Commun.
2
,
566
(
2011
).
20.
G.
Corrielli
,
A.
Crespi
,
R.
Geremia
,
R.
Ramponi
,
L.
Sansoni
,
A.
Santinelli
,
P.
Mataloni
,
F.
Sciarrino
, and
R.
Osellame
, “
Rotated waveplates in integrated waveguide optics
,”
Nat. Commun.
5
,
4249
(
2014
).
21.
R.
Heilmann
,
M.
Gräfe
,
S.
Nolte
, and
A.
Szameit
, “
Arbitrary photonic wave plate operations on chip: Realizing Hadamard, Pauli-X and rotation gates for polarisation qubits
,”
Sci. Rep.
4
,
4118
(
2014
).
22.
A.
Crespi
,
R.
Osellame
,
R.
Ramponi
,
D. J.
Brod
,
E. F.
Galvão
,
N.
Spagnolo
,
C.
Vitelli
,
E.
Maiorino
,
P.
Mataloni
, and
F.
Sciarrino
, “
Integrated multimode interferometers with arbitrary designs for photonic boson sampling
,”
Nat. Photonics
7
,
545
549
(
2013
).
23.
M.
Tillmann
,
B.
Dakić
,
R.
Heilmann
,
S.
Nolte
,
A.
Szameit
, and
P.
Walther
, “
Experimental boson sampling
,”
Nat. Photonics
7
,
540
544
(
2013
).
24.
M.
Gräfe
,
R.
Heilmann
,
A.
Perez-Leija
,
R.
Keil
,
F.
Dreisow
,
M.
Heinrich
,
H.
Moya-Cessa
,
S.
Nolte
,
D. N.
Christodoulides
, and
A.
Szameit
, “
On-chip generation of high-order single-photon w-states
,”
Nat. Photonics
8
,
791
795
(
2014
).
25.
M. A.
Ciampini
,
A.
Orieux
,
S.
Paesani
,
F.
Sciarrino
,
G.
Corrielli
,
A.
Crespi
,
R.
Ramponi
,
R.
Osellame
, and
P.
Mataloni
, “
Path-polarization hyperentangled and cluster states of photons on a chip
,”
Light Sci. Appl.
5
,
e16064
(
2016
).
26.
T.
Meany
,
D. N.
Biggerstaff
,
M. A.
Broome
,
A.
Fedrizzi
,
M.
Delanty
,
M. J.
Steel
,
A.
Gilchrist
,
G. D.
Marshall
,
A. G.
White
, and
M. J.
Withford
, “
Engineering integrated photonics for heralded quantum gates
,”
Sci. Rep.
6
,
25126
(
2016
).
27.
J.
Zeuner
,
A. N.
Sharma
,
M.
Tillmann
,
R.
Heilmann
,
M.
Gräfe
,
A.
Moqanaki
,
A.
Szameit
, and
P.
Walther
, “
Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits
,”
npj Quantum Inf.
4
,
13
(
2018
).
28.
Q.
Zhang
,
M.
Li
,
Y.
Chen
,
X.
Ren
,
R.
Osellame
,
Q.
Gong
, and
Y.
Li
, “
Femtosecond laser direct writing of an integrated path-encoded CNOT quantum gate
,”
Opt. Mater. Express
9
,
2318
2326
(
2019
).
29.
M.
Li
,
Q.
Zhang
,
Y.
Chen
,
X.
Ren
,
Q.
Gong
, and
Y.
Li
, “
Femtosecond laser direct writing of integrated photonic quantum chips for generating path-encoded bell states
,”
Micromachines
11
,
1111
(
2020
).
30.
F.
Flamini
,
L.
Magrini
,
A. S.
Rab
,
N.
Spagnolo
,
V.
D'Ambrosio
,
P.
Mataloni
,
F.
Sciarrino
,
T.
Zandrini
,
A.
Crespi
,
R.
Ramponi
, and
R.
Osellame
, “
Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining
,”
Light Sci. Appl.
4
,
e354
(
2015
).
31.
Z.
Chaboyer
,
A.
Stokes
,
J.
Downes
,
M. J.
Steel
, and
M. J.
Withford
, “
Design and fabrication of reconfigurable laser-written waveguide circuits
,”
Opt. Express
25
,
33056
33065
(
2017
).
32.
A.
Crespi
,
M.
Bentivegna
,
I.
Pitsios
,
D.
Rusca
,
D.
Poderini
,
G.
Carvacho
,
V.
D'Ambrosio
,
A.
Cabello
,
F.
Sciarrino
, and
R.
Osellame
, “
Single-photon quantum contextuality on a chip
,”
ACS Photonics
4
,
2807
2812
(
2017
).
33.
I. V.
Dyakonov
,
I. A.
Pogorelov
,
I. B.
Bobrov
,
A. A.
Kalinkin
,
S. S.
Straupe
,
S. P.
Kulik
,
P. V.
Dyakonov
, and
S. A.
Evlashin
, “
Reconfigurable photonics on a glass chip
,”
Phys. Rev. Appl.
10
,
044048
(
2018
).
34.
C.
Pentangelo
,
F.
Ceccarelli
,
S.
Piacentini
,
R.
Albiero
,
E.
Urbinati
,
N.
Di Giano
,
S.
Atzeni
,
A.
Crespi
, and
R.
Osellame
, “
Universal photonic processors fabricated by femtosecond laser writing
,”
Proc. SPIE
12004
,
120040B
(
2022
).
35.
F.
Ceccarelli
,
S.
Atzeni
,
A.
Prencipe
,
R.
Farinaro
, and
R.
Osellame
, “
Thermal phase shifters for femtosecond laser written photonic integrated circuits
,”
J. Lightwave Technol.
37
,
4275
4281
(
2019
).
36.
F.
Ceccarelli
,
S.
Atzeni
,
C.
Pentangelo
,
F.
Pellegatta
,
A.
Crespi
, and
R.
Osellame
, “
Low power reconfigurability and reduced crosstalk in integrated photonic circuits fabricated by femtosecond laser micromachining
,”
Laser Photonics Rev.
14
,
2000024
(
2020
).
37.
F.
Hoch
,
S.
Piacentini
,
T.
Giordani
,
Z.-N.
Tian
,
M.
Iuliano
,
C.
Esposito
,
A.
Camillini
,
G.
Carvacho
,
F.
Ceccarelli
,
N.
Spagnolo
,
A.
Crespi
,
F.
Sciarrino
, and
R.
Osellame
, “
Reconfigurable continuously-coupled 3d photonic circuit for boson sampling experiments
,”
npj Quantum Inf.
8
,
55
(
2022
).
38.
M.
Valeri
,
V.
Cimini
,
S.
Piacentini
,
F.
Ceccarelli
,
E.
Polino
,
F.
Hoch
,
G.
Bizzarri
,
G.
Corrielli
,
N.
Spagnolo
,
R.
Osellame
, and
F.
Sciarrino
, “
Experimental multiparameter quantum metrology in adaptive regime
,” arXiv:2208.14473 (
2022
).
39.
T. C.
Ralph
,
N. K.
Langford
,
T. B.
Bell
, and
A. G.
White
, “
Linear optical controlled-NOT gate in the coincidence basis
,”
Phys. Rev. A
65
,
062324
(
2002
).
40.
A.
Fedrizzi
,
T.
Herbst
,
A.
Poppe
,
T.
Jennewein
, and
A.
Zeilinger
, “
A wavelength-tunable fiber-coupled source of narrowband entangled photons
,”
Opt. Express
15
,
15377
15386
(
2007
).
41.
I. L.
Chuang
and
M. A.
Nielsen
, “
Prescription for experimental determination of the dynamics of a quantum black box
,”
J. Mod. Opt.
44
,
2455
2467
(
1997
).
42.
J. B.
Altepeter
,
E. R.
Jeffrey
, and
P. G.
Kwiat
, “
Photonic state tomography
,”
Adv. At., Mol., Opt. Phys.
52
,
105
159
(
2005
).
43.
J. T.
Seeley
,
M. J.
Richard
, and
P. J.
Love
, “
The Bravyi–Kitaev transformation for quantum computation of electronic structure
,”
J. Chem. Phys.
137
,
224109
(
2012
).
44.
A.
Peruzzo
,
J.
McClean
,
P.
Shadbolt
,
M.-H.
Yung
,
X.-Q.
Zhou
,
P. J.
Love
,
A.
Aspuru-Guzik
, and
J. L.
O'Brien
, “
A variational eigenvalue solver on a photonic quantum processor
,”
Nat. Commun.
5
,
4213
(
2014
).
45.
O.
Borzenkova
,
G.
Struchalin
,
A.
Kardashin
,
V.
Krasnikov
,
N.
Skryabin
,
S.
Straupe
,
S.
Kulik
, and
J.
Biamonte
, “
Variational simulation of Schwinger's Hamiltonian with polarization qubits
,”
Appl. Phys. Lett.
118
,
144002
(
2021
).
46.
R.
Heilmann
,
C.
Greganti
,
M.
Gräfe
,
S.
Nolte
,
P.
Walther
, and
A.
Szameit
, “
Tapering of femtosecond laser-written waveguides
,”
Appl. Opt.
57
,
377
381
(
2018
).
47.
V. R.
Bhardwaj
,
P. B.
Corkum
,
D. M.
Rayner
,
C.
Hnatovsky
,
E.
Simova
, and
R. S.
Taylor
, “
Stress in femtosecond-laser-written waveguides in fused silica
,”
Opt. Lett.
29
,
1312
1314
(
2004
).
48.
D.
Tan
,
X.
Sun
,
Q.
Wang
,
P.
Zhou
,
Y.
Liao
, and
J.
Qiu
, “
Fabricating low loss waveguides over a large depth in glass by temperature gradient assisted femtosecond laser writing
,”
Opt. Lett.
45
,
3941
3944
(
2020
).
49.
D.
Tan
,
X.
Sun
,
Z.
Li
, and
J.
Qiu
, “
Effectively writing low propagation and bend loss waveguides in the silica glass by using a femtosecond laser
,”
Opt. Lett.
47
,
4766
4769
(
2022
).
50.
J. F.
Bauters
,
M. J. R.
Heck
,
D. D.
John
,
J. S.
Barton
,
C. M.
Bruinink
,
A.
Leinse
,
R. G.
Heideman
,
D. J.
Blumenthal
, and
J. E.
Bowers
, “
Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding
,”
Opt. Express
19
,
24090
24101
(
2011
).
51.
Z.
Liu
,
Y.
Liao
,
Z.
Fang
,
W.
Chu
, and
Y.
Cheng
, “
Suppression of bend loss in writing of three-dimensional optical waveguides with femtosecond laser pulses
,”
Sci. China: Phys., Mech. Astron.
61
,
70322
(
2018
).
52.
S. M.
Eaton
,
M. L.
Ng
,
R.
Osellame
, and
P. R.
Herman
, “
High refractive index contrast in fused silica waveguides by tightly focused, high-repetition rate femtosecond laser
,”
J. Non-Cryst. Solids
357
,
2387
2391
(
2011
).
53.
T.
Will
,
J.
Guan
,
P. S.
Salter
, and
M. J.
Booth
, “
Trimming laser-written waveguides through overwriting
,”
Opt. Express
28
,
28006
28016
(
2020
).

Supplementary Material

You do not currently have access to this content.