US 2023/0059433 Al

gates becomes the limitation. The maximum number of
qubits that can be supported by photonic links is therefore
inversely proportional to the duty cycle at which each qubit
is driven. The total heat load of a photonic link can be
compared to the cooling power, yielding a maximum num-
ber of physical qubits as a function of duty cycle. Each qubit
is addressed by its own optical fiber and photodiode, and use
typical values for Rabi rate, pulse shaping and coupling rate
to the drive line. In comparison with the photonic link
approach, the total heat load for a regular coaxial approach
is dominated by the passive heat load. In some examples, the
total heat load using a photonic link can be reduced com-
pared to the coaxial approach when operating at duty cycle
of the order of 1%. Although the duty cycle of a gate
sequence must be maximized to avoid the deleterious effects
of decoherence, the rate at which the sequence is repeated
can be reduced without sacrificing fidelity. This could be
advantageous for noisy intermediate-scale quantum compu-
tations, where operating at a smaller overall duty cycle
would allow for an increase in the number of qubits that can
be addressed using photonic links.

[0043] Fault-tolerant quantum computation with a million
qubits will need to run continuously at the highest duty cycle
allowed by the quantum and classical hardware, possibly for
hours or days. Building such a quantum processor will
require both an improvement in cooling power and a reduc-
tion of the heat load. The coaxial approach would require a
reduction of its passive heat load by orders of magnitude,
and microwave multiplexing, thinner coaxial cables, or
superconducting ribbon cables. On the other hand, the
photonic link approach presented herein benefits from any
reduction of its active heat load. As an example, the large
source impedance of a photodiode can be exploited such that
an increase in system impedance decreases the amount of
photocurrent required to deliver a given amount of micro-
wave power. This in turn reduces the required optical power
to drive each qubit, leading to an increase in the maximum
number of physical qubits. Additionally, multiplexing
schemes—such as encoding multiple microwave signals
onto a single optical carrier or the use of short optical
pulses—may likewise provide a path to reduce the required
optical power even further. The ultra-cryogenic photonic
link presented herein comprises scalable platforms for
addressing superconducting qubits. By incorporating high-
speed photodetection with a superconducting qubit at mil-
likelvin temperatures, the photonic link is fully compatible
with quantum coherent qubit operation. The qubits may be
used to measure the noise of the photonic link and show that
the current noise is fundamentally set by the shot noise of the
light, even at extremely low photocurrents. These embodi-
ments highlight the benefits of mature opto-electronic tech-
nology for quantum applications and will only be enhanced
by further optimization of hardware and protocols specifi-
cally tailored for cryogenic operation. Combined with pho-
tonic methods for transmitting the qubit state information to
room temperature on optical fiber, a fully photonic interface
with a superconducting quantum processor is possible. This
promising technology provides a path towards scaling super-
conducting quantum processors to an unprecedented number
of quantum bits, enabling many of the longstanding prom-
ises of the quantum revolution.

[0044] The following paragraphs provide an overview of
various mathematical, operational, and scientific methods
that can be used to operate the photodiode devices described

Feb. 23, 2023

in the preceding figures. Specifically, the mathematical,
operational, and scientific methods relate to the basic theory
for a transmon/cavity system and introduce the notation and
assumptions used.

[0045] A transmon is an anharmonic oscillator of fre-
quency @, and anharmonicity ot. The transmon can be
treated as a two-level system, forming the qubit. It is coupled
to a resonant cavity of frequency @, via the Jaynes-Cum-
mings Hamiltonian represented by equation (1).

ay

hisyG et hed" + hala, + ae)

Hoe

[0046] In Equation (1), g is the strength of the exchange
interaction. When operating in the dispersive regime, the
detuning between the qubit and cavity frequencies is large
compared to the coupling strength, [Al=l0,—,|>>g. pre-
venting any direct energy exchange between the two sys-
tems. In this regime, the Hamiltonian may be represented as
equation (2).

is the so-called dispersive shift. The cavity resonance fre-
quency depends on the qubit state: @.4% or @,.-% for the
qubit respectively in the ground state |g) or excited state le
). Conversely the qubit frequency is shifted by 2x per
photon in the cavity and the qubit frequency can be redefined
as @,=0,+% to absorb the Lamb shift. Importantly, the
dispersive approximation is only valid for small photon
numbers in the cavity, and spurious qubit transitions occur
when approaching the critical photon number n,,,,=A7/4g”.

[0048] The cavity and the qubit are coupled to the envi-
ronment using a single antenna. The cavity linewidth Kk is
dominated by the coupling to the antenna. Due to the
filtering of the cavity, the qubit is only weakly coupled to the
antenna, at a rate [’,.,, much smaller than the intrinsic
relaxation rate [’,,, of the qubit.

[0049] The qubit is readout by driving the cavity with an
input microwave field of amplitude o,,, and frequency @,. In
the steady state, the resulting coherent state, 0, ., depends on

the qubit state |g) or le), following the Equation (3):
i 3)
(os -ect0+ Sige =i °

[0050] The output field, o,,,,=\KO, OF, acquires a qubit
state dependent phase shift


US 2023/0059433 Al

Feb. 23, 2023 Sheet 4 of 7

Patent Application Publication

vSYyNOH
zip eno TOP LNSWNOUIANS OINSDOAHO
NOWSNVELL
Ly ALIAWO.
+—@® |_ INVNOSSH Ce
rn
i 90F
——)
x YOLOSLaG
oly Tt U Or -OLOHd
area alr yNnaSTNd
ya1dNoo Anoavay
SOP HAL
N—Awolndo
iad SiN
aI “inodvaY
¥. 60v SNM POP
ity “WIXvOO YOLVANELLLY
YHOLOaL3q
Ol 4
Elp HOLVESNAD 60p
3S1Nd SAYG.UENO >| aod
80 HOLVEEINSD __
3SMd LNOGVSH, w Z0P HaSV1 MO



US 2023/0059433 Al

be taken to imply that the terminology is being redefined
herein to be restricted to any specific characteristics, fea-
tures, or aspects of the technology with which that termi-
nology is associated. In general, the terms used in the
following claims should not be construed to limit the tech-
nology to the specific examples disclosed in the specifica-
tion, unless the above Detailed Description section explicitly
defines such terms. Accordingly, the actual scope of the
technology encompasses not only the disclosed examples,
but also all equivalent ways of practicing or implementing
the technology under the claims.

[0080] To reduce the number of claims, certain aspects of
the technology are presented below in certain claim forms,
but the applicant contemplates the various aspects of the
technology in any number of claim forms. Any claims
intended to be treated under 35 U.S.C. § 112(f) will begin
with the words “means for” but use of the term “for” in any
other context is not intended to invoke treatment under 35
US.C. § 112(f). Accordingly, the applicant reserves the right
to pursue additional claims after filing this application to
pursue such additional claim forms, in either this application
or in a continuing application.

What is claimed is:

1. A method for delivering electric signals into a cryo-
genic environment comprising an optical link, the method
comprising:

generating an optical signal external to the cryogenic

environment;

routing the optical signal into the cryogenic environment;

in the cryogenic environment, converting the optical

signal to an electrical signal; and

routing the electric signal to a target in the cryogenic

environment.

2. The method of claim 1 further comprising sending the
electric signal to control circuitry of a superconducting
qubit

3. The method of claim 1 further comprising sending the
electric signal to readout circuitry of a superconducting
qubit.

4. The method of claim 3 further comp!

routing the electric signal to the target in a readout cavity

in the cryogenic environment;

producing a readout signal; and

routing the readout signal out of the cryogenic environ-

ment

5. The method of claim 1 wherein generating the optical
signal comprises encoding one or more microwave pulses
‘onto the optical signal

6. The method of claim 5 wherein converting the optical
signal to the electrical signal comprises reconstituting the
one or more microwave pulses into the electrical signal.

7. The method of 1 wherein the optical link comprises at
least one of a guided optics link or a free space optics link.

8. The method of claim 1 wherein routing the optical
signal into the cryogenic environment comprises routing the
optical signal to a photodetector in the cryogenic environ-
ment.

Feb. 23, 2023

9. The method of claim 8 wherein converting the optical
signal to the electrical signal in the cryogenic environment
comprises the photodetector converting the optical signal to
the electrical signal.

10. The method of claim 8 wherein routing the optical
signal into the cryogenic environment comprises simultane-
ously routing multiple optical signals over the optical link to
multiple photodetectors in the cryogenic environment.

11. A cryogenic signal delivery system comprising:

a signal source external to the cryogenic environment,

wherein the signal source generates an electrical signal;
an Flectric-to-Optical (F/O) converter external to the

cryogenic environment, wherein the F/O converter

converts the electrical signal to an optical signal;

an optical link that carries the optical signal into the

cryogenic environment; and

an Optical-to-Electric (O/E) converter in the cryogenic

environment, wherein the O/E converter converts the
optical signal to another electrical signal and delivers
the other electrical signal to a target in the cryogenic
environment.

12. The cryogenic signal delivery system of claim 11
wherein the optical link comprises a guided optics link.

13. The cryogenic signal delivery system of claim 11
wherein the optical link comprises a free space optics link.

14. The cryogenic signal delivery system of claim 11
wherein the O/E converter comprises an electro-optical
device configured to convert the optical signal to the other
electrical signal using one or more of a photoelectric effect,
a piezoelectric effect, a Pockel effect, or another non-linear
optical property.

15. The cryogenic signal delivery system of claim 11
wherein the E/O converter comprises a laser configured to
generate the optical signal.

16. The cryogenic signal delivery system of claim 15
further comprising a modulator external to the cryogenic
environment, wherein the modulator encodes one or more
microwave pulses onto the optical signal.

17. The cryogenic signal delivery system of claim 16
wherein the O/E converter reconstitutes the one or more
microwave pulses into the other electrical signal.

18. The cryogenic signal delivery system of claim 11
wherein the target comprises a superconducting qubit within
a readout cavity and wherein a shift in resonance of the
readout cavity causes a shift in amplitude and phase of the
other electrical signal.

19. The cryogenic signal delivery system of claim 18
further comprising a drive link that carries a drive signal into
the cryogenic environment, wherein the drive signal stimu-
lates a state transition of the superconducting qubit within
the readout cavity to cause the shift in resonance of the
readout cavity.

20. The cryogenic signal delivery system of claim 19
further comprising readout circuitry that carries a readout
signal out of the cryogenic environment, wherein the read-
out signal has an amplitude and phase indicative of the shift
in the amplitude and the phase of the other electrical signal.

+e Ree



US 2023/0059433 Al

throughout the several views, While several embodiments
are described in connection with these drawings, the disclo-
sure is not limited to the embodiments disclosed herein. On
the contrary, the intent is to cover all alternatives, modifi-
cations, and equivalents.

[0011] FIG. 1 illustrates an operational environment in an
implementation.

[0012] FIG. 2 illustrates a method in an implementation.
[0013] FIG. 3 illustrates another operational environment
in an implementation.

[0014] FIG. 4 illustrates another operational environment
in an implementation.

[0015] FIG. 5 illustrates another operational environment
in an implementation.

[0016] FIG. 6 illustrates another operational environment
in an implementation.

[0017] FIG. 7 illustrates another operational environment
in an implementation.

DETAILED DESCRIPTION

[0018] A number of leading quantum information archi-
tectures, such as superconducting circuits and quantum dots,
rely on carefully shaped microwave pulses delivered to a
cryogenic environment to control and readout the quantum.
state of each qubit. Presently, these pulses are generated at
room temperature and then routed through heavily filtered
and attenuated coaxial transmission lines to the qubits held
at temperatures below 100 mK. As these systems continue to
scale, the heat load, cost, and complexity ofa large number
of coaxial microwave signal lines become a significant
limitation on the achievable size and complexity. Photonic
links offer a potential scaling solution, due to their large
intrinsic bandwidth, low noise, and the low thermal conduc-
tivity of optical fiber. However, it must first be established
that qubit interaction via a photonic link can be realized
without corrupting the qubit’s fragile quantum state. Here
we demonstrate readout of a superconducting qubit using
microwave signals transmitted over optical fiber and pho-
todetected in the 20 mK environment of a superconducting
qubit. When compared to operation with microwave pulses
delivered via standard coaxial cabling, no degradation of the
qubit coherence time is observed, and a single-shot readout
fidelity of 98% is maintained. By reducing the heat load in
quantum computing systems through the use of photonic
links, large-scale quantum information systems with super-
conducting qubits become viable.

[0019] For a superconducting qubit in the dispersive
regime, there are two ways classical microwave signals
directly interact with the qubit for quantum information
processing. First is the qubit drive, where gate operations are
performed with a microwave signal that is resonant with the
qubit transition frequency. Second is the qubit state readout,
where a microwave signal measures the resonance shift of a
high-Q cavity that is coupled to the qubit. In both cases, the
required microwave powers are small, typically well below
a nanowatt (nW). For readout, coupling between the cavity
and qubit results in a shift in the cavity resonance depending
on the state (ground or excited) of the qubit. As such, phase
and amplitude shifts of a weak probe field with frequency
near the cavity resonance “read out” the qubit state. The
qubit is extremely sensitive to excess noise carried along the
drive and readout lines, where a single stray microwave
photon can decohere the qubit state. Since the strongest

Feb. 23, 2023

noise coupling is at the cavity resonance frequen
fidelity cavity readout is the focus of some embodiments
disclosed herein.

[0020] Delivering on the revolutionary promise of a uni-
versal quantum computer will require processors with mil-
lions of quantum bits. In superconducting quantum proces-
sors, each qubit is individually addressed with microwave
signal lines that connect room-temperature electronics to the
cryogenic environment of the quantum circuit. The com-
plexity and heat load associated with the multiple coaxial
lines per qubit limits the maximum possible size of a
processor to a few thousand qubits. In some embodiments,
a photonic link is disclosed that uses an optical fiber to guide
modulated laser light from room temperature to a cryogenic
photodetector, capable of delivering  shot-noise-limited
microwave signals directly at millikelvin temperatures. The
photonic link may enable high fidelity control and readout of
a superconducting qubit and can meet the stringent require-

ments of superconducting quantum information processing.
Leveraging the low thermal conductivity and large intrinsic
bandwidth of optical fiber enables the efficient and mas-
sively multiplexed delivery of coherent microwave control
pulses, providing a path towards a million-qubit universal
quantum computer.

[0021] Superconducting circuits have emerged as a lead-
ing technology for quantum computing, thanks to steady
progress in gate and measurement fidelity combined with the
capability of lithographically producing large and complex
qubit networks. However, the demonstration of a complete
architecture that can truly scale to millions of qubits remains
an elusive milestone. Indeed, such quantum processors must
operate in a cryogenic environment to be superconducting
and, more importantly, initialized close to their quantum
ground state. As these processors operate at microwave
frequencies on the order of 10 Gigahertz (GHz), they require
a temperature well below 100 millikelvin (mK) to eliminate
thermally activated transitions. This is achieved in commer-
cial dilution refrigerators, whose base temperatures rou-
tinely reach below 20 mK. In current architectures, the
superconducting qubits are controlled and measured with
microwave pulses generated at room temperature and deliv-
ered via heavily attenuated coaxial lines. Besides simple
space limitations, this approach results in considerable heat
loads as the number of qubits scales, both passive, due to the
thermal conductivity of the coaxial lines, and also active,
due to the signal power dissipated in the attenuators. This
heat load competes against the limited cooling power of the
cryostat, typically ~20 microwatts Therefore, with current
technologies one could imagine systems with a few thou-
sand qubits at best, far from the predicted numbers required
for compelling applications of quantum computers.

[0022] These crucial challenges outlined in the preceding
paragraphs have motivated new approaches that seek to
increase the possible size of superconducting quantum pro-
cessors. The development of quantum coherent intercon-
nects, which are capable of sharing fragile quantum states
between processors in separate cryostats remains a long-
standing challenge. Concurrently, innovations in classical
interconnects aim to reduce the heat load associated with
interfacing with the quantum processor, taking the form of
high-density wiring or cryogenic electronics. Indeed, even
with successful quantum coherent interconnects, a scalable
technology capable of delivering classical signals suitable


Patent Application Publication Feb. 23,2023 Sheet 6 of 7 US 2023/0059433 Al

EADOUT CAVITY
603

saad
Readout

ZHPE

CO»
4

i:

FIGURE6

+e

CAVITY DRIVE 601
t_)
Ns
QUBIT DRIVE 602
t
ee



US 2023/0059433 Al

Feb. 23, 2023 Sheet 5 of 7

Patent Application Publication

20S
LUNOHIO WALNWND

Ly pOSSHOLWINGON
fe | fy IN Old OOH
sd Mes
£06 SHOLWHENSO ae
SIAVMOHOIN ee ZOGHESWIMO
DA) ®) &) © é ‘
ae D OARIG es Nas


US 2023/0059433 Al

DELIVERING SIGNALS TO CRYOGENIC
ENVIRONMENTS VIA PHOTONIC LINKS

CROSS-REFERENCE TO RELATED,
APPLICATIONS

[0001] This U.S. patent application claims priority to U.S.
Provisional Patent Application No. 63/187,227 entitled,
“DELIVERING SIGNALS TO CRYOGENIC ENVIRON-
MENTS VIA PHOTONIC LINKS” which was filed on May
11, 2021, and which is incorporated by reference into this
US. patent application in its entirety.

STATEMENT REGARDING FEDERALLY
FUNDED RESEARCH
[0002] This invention was made with government support
under grant number 7ONANB18H006 awarded by NIST.
The government has certain rights in the invention.

BACKGROUND

[0003] Quantum computing is a computing technology
that utilizes the properties of quantum physics to process
information. In quantum computing architectures, the
elementary building block is referred to as a quantum bit (or
qubit), in analogy with a “bit” of information in classical
computers (0 or 1). Superconducting circuits are a leading
technology for enabling quantum computing. Superconduct-
ing circuits use microwaves to interact with and read infor-
mation from the qubits. Since the microwave frequencies
used are on the order of 10 Gigahertz, (GHz), the supercon-
ducting circuits must be operated at cryogenic temperatures
below 100 millikelvin (mK). Dilution refrigerators can oper-
ate below 20 mK and are used to create the cryogenic
temperatures. In traditional quantum computing systems, the
qubits are controlled and measured with microwave pulses
that are generated at room temperature and then delivered
into the cryogenic environment via coaxial lines. The use of
coaxial lines creates space limitations and results in consid-
erable heat loads as the number of qubits scales. This heat
load caused by the coaxial lines competes against the limited
cooling power of the dilution refrigerators. This limits the
maximum number of qubits in the quantum computer and
therefore limits its computer power.

OVERVIEW,

[0004] Technology is disclosed herein that improves the
ability for signals to be delivered into cryogenic environ-
ments in such a manner as to improve the scalability and
performance of such systems. In some examples, a method
for delivering electric signals into a cryogenic environment
comprising an optical link is disclosed. The method begins
by generating an optical signal external to the cryogenic
environment. The optical signal may be encoded with one or
more microwave pulses. The method continues by routing
the optical signal into the cryogenic environment. The
method continues by converting, in the cryogenic environ-
ment, the optical signal to an electrical signal. When the
optical signal is encoded with microwave pulses, the micro-
wave pulses may be reconstituted into the electrical signal
during conversion. The method continues by routing the
electric signal to a target

[0005] In some examples, the method may further com-
prise sending the electric signal to drive control or readout
circuitry of a superconducting qubit. This may be accom-

Feb. 23, 2023

plished by routing the electric signal converted in the
cryogenic environment to a target in a readout cavity in the
cryogenic environment and producing a readout signal. The
readout signal may then be routed out of the cryogenic
environment.

[0006] In some examples, a signal delivery system com-
prising a photonic link is disclosed. The signal delivery
system comprises a signal source, an Electric-to-Optical
(E/O) signal converter, an optical link, and an Optical-to-
Electrical (O/E) signal converter. The signal source gener-
ates an electrical signal outside of the cryogenic environ-
ment. The F/O signal converter is positioned external to the
cryogenic environment and converts the electrical signal to
an optical signal. The optical link carries the optical signal
generated by the F/O signal converter into the cryogenic
environment. The O/E signal converter is positioned within
the cryogenic environment and converts the optical signal
delivered by the optical link back into an electric signal. The
O/E signal converter may then deliver the electrical signal
that it generated to a signal target within the cryogenic
environment.

[0007] The signal target may comprise a readout cavity in
which a superconducting qubit resides. The signal target
may comprise one or more superconducting quantum bits
and their associated control and readout circuitry. The elec-
trical signal delivered to the signal target may control the
state of the quantum bits as well as drive the readout
circuitry to measure the state of the quantum bits. The O/E
signal converter may comprise a photodetector, photodiode
or another type of electro-optical device. The photodiode
may utilize the photoelectric effect. Alternatively, or in
addition to, the O/E signal converter may comprise an
electro-optical device relying on the piezoelectric effect, the
Pockel effect, or some other type of nonlinear optical
property.

[0008] The signal delivery system may further comprise a
drive link that carries a drive signal into the cryogenic
environment to stimulate the signal target. For example, the
drive link may carry a drive signal that causes a state
transition of a superconducting qubit coupled to a readout
resulting in a shift in resonance of the readout cavity.
The signal delivery system may additionally comprise read-
out circuitry that carries a readout signal characterizing the
signal target out of the cryogenic environment. For example,
the interaction between the electric signal converted in the
cryogenic environment and the signal target may cause a
shift in amplitude and phase of the electric signal. The
readout circuitry may transfer a readout signal that indicates
the shift in amplitude and phase of the electric signal.
[0009] The photonic link(s) proposed herein may also be
usefull in other applications requiring the delivery of elec-
trical signal to a cryogenic environment like radio
astronomy (detector arrays and electronics), quantum elec-
tronic devices (spin qubit, parametric amplifiers, Josephson
Arbitrary Microwave Generators and Voltage standards), or
even classical computing applications.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Many aspects of the disclosure may be better
understood with reference to the following drawings. The
components in the drawings are not necessarily to scale,
emphasis instead being placed upon clearly illustrating the
principles of the present disclosure. Moreover, in the draw-
ings, like reference numerals designate corresponding parts


as) United States

a2) Patent Application Publication

Lecocq et al.

(10) Pub. No.: US 2023/0059433 Al
(43) Pub. Date: Feb. 23, 2023

U!

S 20230059433A1

G4)

ay

(72)

@)
(22)

(60)

DELIVERING
ENVIRONMI

NALS TO CRYOGENIC
VIA PHOT IC LINKS

Applicant: The Regents of the University of
Colorado, a body corporate, Denver,
CO (US)
Inventors: Florent Lecoeq, Boulder, CO (US);
Josue Davila-Rodriguez, Boulder, CO
(US); Franklyn John Quinlan,
Longmont, CO (US); John Teufel, Erie,
CO (US); Scott A. Diddams,
Louisville, CO (US); Jose Aumentado,
Boulder, CO (US)

Appl. No.: 17/742,252

Filed: May 11, 2022

Related U.S. Application Data

Provisional application No. 63/187,227, filed on May
11, 2021.

ON

ELECTRIC

Publication Classification
(51) Int. CL.

HO4B 10/70 (2006.01)

HOAB 10/2575 (2006.01)
(52) US. Cl.

CPC HO4B 10/70 (2013.01); HO4B 10/25759

(2013.01)

(57) ABSTRACT

An operational environment is disclosed herein that includes
a cryogenic environment and a signal source. The cryogenic
environment includes a signal target, an optical link, signal
converter devices, and an electrical link. Outside of the
cryogenic environment, the signal source generates an elec-
tric signal. An electric-to-optical converter converts the
electrical signal into an optical signal. The optical link
delivers the optical signal into the cryogenic environment
Inside the cryogenic environment, an optical-to-electrical
converter converts the optical signal back into an electrical
signal. The optical-to-electrical converter transfers the elec
tric signal to the signal target

LINK 103 EO

104

CONVERTER

SOURCE

102

LINK 105

ELECTRIC
LINK 107

O/E

106

CONVERTER

SIGNAL
TARGET 108

CRYOGENIC ENVIRONMENT 101,



US 2023/0059433 Al

[0031] In operation, Continuous Wave (CW) laser 402
outputs a laser. The output is intensity modulated by ampli-
fication and modulation device 403. For example, device
403 may modulate the laser with a pulsed microwave whose
carrier frequency matched that of the readout cavity near 11
GHz. The depth of modulation of the optical power may be
near 100%. The output of the modulator 403 is attenuated by
attenuator 404, then transmitted to photodetector 406 over
optical fiber 405. Photodetector 406 comprises a high-speed
photodetector that reconstitutes the microwave pulses
encoded onto the output of laser 402. Photodetector 406
transfers the reconstituted microwave pulses to transmon
qubit 412 coupled to readout cavity 411. Upon reflection
from cavity 412, the microwave pulses are amplified by
amplifier 416 and routed to room temperature via readout
link 415. /Q detector 417 receives the readouts and resolves
shifts in the readout cavity resonance frequency. Readout
pulses may be directed either to the photonic link or a
standard coaxial line that was used to establish the baseline
readout performance. Qubit drive pulse generator 413 trans-
fers pulses over drive link 415 to drive the qubit transition
of transmon qubit 413. The coaxial drive and readout lines
are routed through a series of cold attenuators to bring the
room temperature microwave signals to the coherent state of
the microwave field. The photonic link implemented by
environment 400 has a comparative simplicity advantage
since signal attenuation was performed in a single step at
room temperature.

[0032] Ramsey interferometry may be performed to mea-
sure the qubit decoherence through the T2 relaxation time.
A pair of p/2 pulses each ~40 ns in duration is delivered
through the coaxial drive line with a microwave carrier
slightly detuned from the qubit transition frequency. The
time delay between p/2 pulses may be varied, with a ~500
ns duration readout pulse occurring just after the second p/2
pulse. Repeated measurements of the qubit state (ground or
excited) may be taken for each delay, such that the prob-
ability of finding the qubit in the excited state could be
determined. Coherence of the qubit over the duration
between p/2 pulses results in an oscillation in the excited
state probability as a function of delay. However, as the qubit
decoheres, ground and excited state become equally likely,
and the fringe contrast disappears. Ramsey oscillations may
be measured with readout pulses delivered via the photonic
link. In some examples, the Ramsey oscillations between
those generated via the photonic link and standard coaxial
line are virtually indistinguishable. Thus, despite the poten-
tial of the photonic link to add detrimental excess noise, the
coherence of the qubit is preserved.

[0033] In this example, the qubit is prepared in either the
excited state or the ground state, and the state is then
measured with a single readout pulse. Fidelity of the readout
is reduced when the readout state does not correspond to the
prepared state. A fidelity of 98% may be achieved with both
the photonic link. Again, these results indicate any excess
noise in the photonic link is below the level that would
corrupt readout fidelity. A cryogenic photonic link can
deliver readout pulses to a superconducting qubit without
reducing the qubit coherence or readout fidelity, thus meet-
ing the stringent requirements of quantum information pro-
cessing systems based on superconducting qubits. Measure-
ments on qubit drive demonstrate both control and readout
pulse delivery with photonic links.

Feb. 23, 2023

[0034] FIG. 5 illustrates environment 500. Environment
500 comprises cryogenic environment 501, CW laser 502,
microwave generators 503, and electro-optic modulators
504. Cryogenic environment 501 comprises optical fiber
505, photodetectors 506, and quantum circuit 507. Cryo-
genic environment 501 comprises a 4° K temperature
region, an 800° mK temperature region, and a 100° mK
temperature region. Photodetectors 506 and quantum cir-
cuitry 507 are positioned in the 100° mK temperature region
of cryogenic environment 501. Optical fiber 505 links the
region outside of cryogenic environment 501 to the 10 mK
region.

[0035] Environment 500 utilizes ubiquitous telecommu-
nication technologies and standard radio frequency-photon-
ics components, designed for room-temperature operation
(300 k), to demonstrate an ultra-cryogenic photonic link. In
this temperature regime, the photonic link exhibits noise
levels approaching microwave vacuum fluctuations,
enabling the control and measurement of highly coherent
quantum states. The microwave control signals are upcon-
verted to the optical frequency domain using Electro-Optic
Modulators (EOMs) 504, guided along optical fibers 505 to
cryogenic environment 501 of the processor and down-
converted back to microwave frequencies using high-speed
photodetection 506. The vanishing thermal conductivity of
optical fibers at low temperature and their large intrinsic
bandwidth enables the delivery of millions of control signals
directly to the millikelvin stage with no substantial passive
heat load. To evaluate this photonic link, a high-speed
photodiode at 20 mK controls and measures a supercon-
ducting transmon qubit residing in quantum circuit 507.
Environment 500 enables the ability to perform high-fidelity
single-shot qubit readout and fast qubit gates while main-
taining quantum coherence. Environment 500 exploits the
extreme noise sensitivity of the qubit to measure the pho-
todiode noise at sub-microampere photocurrents, revealing
shot-noise-limited performance.

[0036] The optical generation of microwave control sig-
nals relies on the photoelectric effect in a photodiode. An
incident optical photon generates an electron-hole pair in a
semiconductor, with a quantum efficiency 1. The carriers are
then swept away to the electrodes of the diode owing to a
built-in or applied voltage, creating a current pulse. Sum-
ming over many incident photons yields the photocurrent,
I=RP,, where R=ne/ft, is the responsivity, e is the electron
charge, Py is the incident optical power, ( is the frequency
of the optical photons, and fi is the reduced Planck constant.
Full-depth modulation of the optical power at a microwave
(Ww) frequency @, that is well within the bandwidth of the
photodiode results in an oscillating photocurrent at that same
frequency, with an output microwave power

where T=(I) is the average photocurrent and Z.is the imped-
ance of the load.

[0037] The transmon qubit used in quantum circuitry 507
comprises a single Josephson junction shunted by a capaci-
tor, forming an oscillator that is nonlinear at the single-
photon level. Full control over its quantum state |’) =alg

)+Ble) , where Ig) and le) are, respectively, the ground and


US 2023/0059433 Al

for high-fidelity qubit operation could be instrumental in
building a large-scale quantum computer. Now referring to
the Figures

[0023] FIG. 1 illustrates operational environment 100 in
an implementation. Operational environment 100 comprises
cryogenic environment 101, signal source 102, electric link
103, electric-to-optical (E/O) converter 104, optical link
108, optical-to-electrical (O/E) converter 106, electric link
107, and signal target 108.

[0024] Signal source 102 represents one or more devices
capable of producing an electric signal. Electric links 103
and 107 represent any link suitable for carrying one or more
electric signals, examples of which include coaxial cables
and metallic wiring. Electric link 103 carries the resulting
electric signal generated by signal source 102 to converter
104. Converters 104 and 106 represent any device capable
of converting an optical signal to an electrical signal and
vis-versa. For example, O/E converter 106 may comprise a
photodetector. Converter 103 transforms the electric signal
generated by signal source 102 into and optical signal which
is carried into cryogenic environment 101 via optical link
105. Optical link 105 represents any link suitable for car-
rying one or more optical signals, example of which include,
optical fibers, or free space optical links. Converter 106
receives the optical signal from converter 104 via optical
link 105 and converts the optical signal back into an electric
signal within cryogenic environment 101. Converter 106
transfers the resulting electrical signal to signal target 108
over electric link 107. Signal target 103 is representative of
any device or sub-system such as a Three-Dimensional (3D)
readout cavity, qubit drive line or an image sensor, photocell
(8), or the like. The interaction between the electric signal
and signal target 108 generates a readout signal. In some
examples, environment 100 implements process 200 illus-
trated in FIG. 2.

[0025] FIG. 2 illustrates process 200 in an implementa-
tion. Process 200 begins with a signal generating device
generating optical signals outside of the cryogenic environ-
ment (step 201). Each optical signal may have one or more
microwave signals modulated onto it. The signal generating
device routes the optical signals into the cryogenic environ-
ment to one or more optical-to-electrical signal converters
(step 202). The converters convert the optical signals to an
electrical signal (step 203). The converters deliver the result-
ing electrical signals to the target(s) over electrical links
(step 204)

[0026] Referring back to FIG. 1, environment 100
includes a brief example of process 200 as employed by the
various components that comprise environment 100. In
operation, signal source 102 generates an electric signal and
transfers the electric signal to E/O converter 104 over
electric link 103. E/O converter 104 converts the electric
signal into an optical signal with one or more microwave
signals modulated into it (step 201). E/O converter 104
routes the optical signal to O/E converter 106 in cryogenic
environment 101 over optical link 105 (step 202). For
‘example, converter 104 may transfer the optical signal over
a free space optical link to converter 106. O/E converter 106
transforms the optical signal received from E/O converter
104 into an electrical signal for delivery to signal target 108
(step 203). O/E converter 106 transfers the electric signal to
signal target 108 over electric link 107 (step 204). For
example, signal target 108 may comprise a readout cavity

Feb. 23, 2023

with a qubit. Converter 106 may transfer the electric signal
to control the qubit and generate a readout signal.

[0027] FIG. 3 illustrates operational environment 300 in
another implementation. Operational environment 300 com-
prises cryogenic environment 301, Continuous Wave (CW)
laser 302, amplifier and modulator (AMP/MOD) 303,
attenuator 304, drive pulse generator 308, UQ detector 317,
and qubit readout pulse generator 313. Cryogenic environ-
ment 301 is representative of a cryogenically cooled region
(~20° mK). For example, cryogenic environment 401 may
comprise a dilution refrigerator that can cool to 20° mK.
Cryogenic environment 301 comprises optical fiber 305,
photodetector 306, drive pulse link 307, coaxial line 309,
coupler 310, 3D resonant cavity 311, readout link 314,
readout link 315, and amplifier 316. 3D resonant cavity
comprises transmon qubit 413.

[0028] In operation, Continuous Wave (CW) laser 302
outputs a laser. The output is intensity modulated by ampli-
fication and modulation device 303. Device 303 may modu-
late the laser with a pulsed microwave generated by drive
pulse generator 306 to control the state of transmon qubit
312. The depth of modulation of the optical power may be
near 100%, For example, drive pulse generator 408 may
transfer a pulsed microwave with a carrier frequency near 5
GHz to amplification/modulation device 403 to drive trans-
mon qubit 312 to transition from a ground state to an excited
state. The output of the modulator 303 is attenuated by
attenuator 304, then transmitted to photodetector 306 over
optical fiber 305. Photodetector 306 comprises a high-speed
photodetector that reconstitutes the microwave pulses gen-
erated by laser 302. Photodetector 306 transfers the recon-
stituted drive microwave pulses to transmon qubit 312
coupled to readout cavity 311. The drive microwave pulses
drive the state transition of transmon qubit 313.

[0029] Qubit readout pulse generator 313 transfers pulses
over readout pulse link 314 to readout the state of transmon
qubit 313. The coaxial drive and readout lines are routed
through a series of cold attenuators to bring the room
temperature microwave signals to the coherent state of the
microwave field. Upon reflection from cavity 311, the
microwave pulses are amplified by amplifier 316 and routed
to room temperature via readout link 315. UQ detector 317
receives the readouts and resolves shifts in the readout
cavity resonance frequency. For example, the required
microwave power generated by photodetector 306 may
comprise approximately -110 dBm with a corresponding
average photocurrent of 20 nA. Readout pulses may be
directed either to the photonic link or a standard coaxial line
that was used to establish the baseline readout performance.
The photonic link implemented by environment 300 has a
comparative simplicity advantage since signal attenuation
was performed in a single step at room temperature.
[0030] FIG. 4 illustrates operational environment 400 in
an implementation. Environment 400 comprises cryoget
environment 401, Continuous Wave (CW) laser 402, ampli
fier and modulator (AMP/MOD) 403, attenuator 404, read-
out pulse generator 408, UQ detector 417, and qubit driver
pulse generator 413. Cryogenic environment 401 is repre-
sentative of a cryogenically cooled region (~20° mK) and
comprises optical fiber 405, photodetector 406, readout
pulse link 407, coaxial line 409, coupler 410, 3D resonant
cavity 411, drive pulse link 414, readout link 415, and
amplifier 416. 3D resonant cavity comprises transmon qubit
412.



Patent Application Publication Feb. 23,2023 Sheet 7 of 7 US 2023/0059433 Al

eadout
READOUT CAVITY
703

O:
2)
5

CAVITY DRIVE 701
QUBIT DRIVE 702
foo
FGURE7

700 \


US 2023/0059433 Al

Feb. 23, 2023 Sheet 3 of 7

Patent Application Publication

eaunow
216 ano TOE LNSWNOHIANS SINSDOAHO
NOWSNVEL
LEAUAVO
rt+—_@® |, INVNOSSY CE
rn
i 308
{__} =a yOLO3L3q
vig y \ 108 -OLOHd
owen ols NTS
usmdnoo Nu
soc uaa
oie |\tWwoldo
usunany Steyn
trocar
606 SNM OE
zie IN swxvoo HOLVNNALLY
HOLOSLAG
ol %
EIEHOLVHSNSO DOE
3S LNOAW3H LIEN —— >| aowany
806 HOLVEEINSD _
asin aAud —9 206 H3SW7 MO



US 2023/0059433 Al

2
22tan"! 2)

that enables qubit state discrimination. One can show that
the measurement rate is I,,=Klal,—0,,I and is maximized by
the distance in phase space between the two coherent states.
‘The qubit measurement fidelity is defined as F=1-P(elq)-P
(gle) where P(xly) is the probability of measuring the qubit
state x when prepared in the state y. In absence of prepara-
tion errors and qubit transitions during the measurement,
and in the steady state, the measurement fidelity after an
integration time t can be written as F=erf (7,2), where
1) is the microwave measurement efficiency.

[0051] Photon number fluctuations and qubit dephasing
fluctuations of the number of photons in the cavity induce
fluctuations of the qubit frequency and therefore dephasing.
‘The Stark-shift and dephasing rate for an average thermal
occupancy of the cavity 0 are shown respectively by Equa-
tion (4).

4 @)
Mon = Aa, and Pf = pn

[0052] In Equation (4), B=K/(K7#42). Note that these
expressions are only valid for 0<<1. The Stark-shift can be
extracted from the frequency of Ramsey oscillations. The
qubit dephasing is extracted from the exponential decay of
the Ramsey oscillations,

and is dominated by photon number fluctuations, P,=T',.
[0053] Under resonant drive, the qubit undergoes Rabi
oscillations between the ground and excited states at the
Rabi rate 0,=2,/iT'.,, where itis the number of photons per
second at antenna. When the Rabi rate approaches the
transmon anharmonicity, Q,~c, the transmon dynamics
involve higher excited states, leaving the computational
subspace. A hallmark of this regime is the deviation from the
linear relation between Rabi rate and drive amplitude. In
practice, typical superconducting quantum processors oper-
ate in the linear regime, Q,<c/2.

[0054] The photodiode can be seen as a high impedance
current source, with an output current I proportional to the
incident optical power Pg such that I=R Po, where R=ne/
hg is the responsivity, e is the electron charge, @ is the
frequency of the optical photons and 1 is the quantum
efliciency (defined as the probability of generating an elec-
tron-hole pair per incident photon). A perfectly efficient
photodiode (n=1) operating at a wavelength of 1490 nm
(@9/2n=201 THz) has a maximum responsivity R=1.2
ce, the quantum efficiency depends on
ch as alignment and Fresnel reflections,
and on the intrinsic efficiency of the detector. Many photo-
diodes comprise a responsivity of 0.7 AW"! at room tem-
perature. At 20 mK the responsivity drops to 0.5 AW"!,
caused by a change of the optical alignment due to thermal
contractions.

Feb. 23, 2023

[0055] Microwaves are generated by modulating the opti-
cal power such that Py(t)=P,(1+m cos(at+)) where P, is the
average optical power, m is the modulation depth (mS1), @
is the modulation frequency, and @ is the modulation phase.
This induces an oscillating photocurrent I(t}=h(t)* R Po(t)
where h(t) is the impulse response of the photodiode. The
corresponding microwave power P,, in a load impedance Z
is

where I=R Pj is the average photocurrent and H(@) is the
transfer function of the photodiode. For the photodiodes
described herein, the response function is limited by the RC
time constant, with a 3 dB cutoff frequency set by the
capacitance of the diode and the impedance of the load.
[0056] The probabilistic nature of creating electron-hole
pairs results in photocurrent shot noise with power spectral
density S,(@)=2eTIH(@)I7, While the photocurrent noise
measurements are consistent with shot noise-limited photo-
detection for photocurrents up to 20 HA, the possible con-
tributions of two other known sources of excess photocur-
rent noise are estimated: voltage noise at the microwave
input of the electro-optic intensity modulator and excess
laser intensity noise.

[0057] For voltage noise at the EOM input, a lossless
EOM with an infinite extinction ratio can be considered. The
output optical power is Pg(t}=P,(1+sin(xV(t/V,.) where Py
is the average optical power, V,, is the voltage required to go
from maximum transmission to minimum transmission and
V(D=V,,(0+V 4. is the input voltage. For a modulator biased
at quadrature (V,,,=0) and in the limit of small input voltage
(V,(O<<V,) the — output power becomes Pa (t)=
P,(1+RV,,(t/V,,). The noise variance of the optical power is
then (8P,?) =P,?n?(8V,7) V7. The photocurrent noise
variance is then ( 81y*) =R ( 6P.*) =Px*( 8V_") /V,> where
T=R P, is the average photocurrent. In terms of the current
noise power spectral density, this becomes $,°%(@)=S (@)
Priv? where $(@)=4kgTyZpo,, i8 the input voltage
noise power spectral density set by the noise temperature Ty,
of the input impedance of the EOM Zor.

[0058] Laser intensity noise is usually given as a fractional
variation, termed Relative Intensity Noise (RIN), defined as
RIN(@)=S(@)/Po” where Sp() is the power spectral den-
sity of the optical power fluctuations, in units of W? Hz7!.
The linear relationship between optical power and photo-
current leads to a photocurrent noise due to RIN given by
S/"(@)=PRIN(@).

(0059] | The total current noise emitted by the photodiode is
then S{@)=2el+S,%(@)}+S;"""(@). For a photocurrent of,
120 pA, the photocurrent shot noise is 2el=8x107* A?
Hz“. In the embodiments presented herein, $,5=3x10~>
A? Hz", more than an order of magnitude smaller than the
photocurrent shot-noise. The RIN of readily available com-
mercial semiconductor distributed feedback (DFB) lasers is
below 107" Hz", and can approach 10-'® Hz", leading to
a current noise $,*’%, 5x10~* A? Hz7'. Since deviations
from photocurrent shot-noise are not resolved, it can be
concluded that the laser RIN is below 107! Hz".

[0060] It should be appreciated that the measurement is
sensitive only to noise above microwave vacuum fluctua-



US 2023/0059433 Al

10-°, far below what has been achieved in traditional
technologies. Note that as qubit coherence improves, the
coupling rate to the control line will decrease, which reduces
the minimum error probability.
[0071] It should be appreciated that that the spectrum of
microwave noise induced by the photocurrent shot noise on
the photodiode is white up to the bandwidth of the photo-
diode. When considering an architecture where multiple
qubits are addressed using a single photodiode, one would
have to consider that all these qubits are driven by the
microwave noise of the photodiode.
[0072] Here calculations and assumptions used to estimate
and compare the heat load of the regular coaxial approach
and the photonic link approach are detailed. For simplicity,
the focus is on the heat load associated with the qubit
microwave control lines, and all other heat loads are
neglected, such as those associated with qubit readout and
de-flux biasing. For both approaches, the heat can be divided
into a passive and active heat load. The passive heat load is
set by the heat flow through the coaxial cables or optical
fibers. The active heat load comes from the Joule heating in
the attenuators in the coaxial approach and from the dissi-
pated optical power in the photonic link approach.
[0073] The heat load from a 0.085 diameter stainless steel
coaxial cable has been measured to be 14 nW, slightly larger
than the estimated value of 4 nW. Following the same
reasoning, the heat load of an optical fiber is estimated to be
3 pW. The optical fiber comprises a silica core and cladding
of 125 um diameter with a coating increasing the diameter
to 250 um. The microwave power required at the qubit
control line, P(t)=fim,i(t), depends on the Rabi rate and
coupling rate so that P(t)=fi,,(t7/4T,,, where Q,(t)
=©,S(t) and S(t) is the time domain pulse shape. The
average power of a pulse of duration t is defined as Pf,"
PO =hw,Q,7874F,,, with S={* S(O/t. In the coaxial
approach, attenuation at the mixing chamber is necessary to
reduce the black body radiation from higher temperature
stages. This leads to an active heat load per control pulse
Pring'=Px(1/A-1) where A<1 is the attenuation. In the
photonic link approach, the optical power is fully dissipated
as heat, leading to an active heat load per control pulse

Prin“-V 2P/Z R?, neglecting loss between the photodiode
and the control line. The total heat load strongly depends on
the duty eyele per qubit pass pa D. Pasexsint
DxPooantint The total number of qubits that can be
addressed’ in both approaches i Noga jim-PeootP coun ink
where P.,,, is the cooling power at the mixing chamber.
[0074] While some examples provided herein are
described in the context of quantum computing systems
utilizing a photodiode, it should be understood that the
condition systems and methods described herein are not
limited to such embodiments and may apply to a variety of
other extension implementation environments and their
associated systems. As will be appreciated by one skilled in
the art, aspects of the present invention may be embodied as
a system, method, computer program product, and other
configurable systems. Accordingly, aspects of the present
invention may take the form of an entirely hardware
embodiment, an entirely software embodiment, or an
embodiment combining software and hardware aspects that
may all generally be referred to herein as a “circuit,”
“module” or “system.”

[0075] Unless the context clearly requires otherwise,
throughout the description and the claims, the words “com-

Feb. 23, 2023

prise,” “comprising,” and the like are to be construed in an
inclusive sense, as opposed to an exclusive or exhaustive
sense; that is to say, in the sense of “including, but not
limited to.” As used herein, the terms “connected,”
“coupled,” or any variant thereof means any connection or
coupling, either direct or indirect, between two or more
elements; the coupling or connection between the elements
can be physical, logical, or a combination thereof. Addition-
ally, the words “herein,” “above,” “below,” and words of
similar import, when used in this application, refer to this
application as a whole and not to any particular portions of
this application. Where the context permits, words in the
above Detailed Description using the singular or plural
number may also include the plural or singular number,
respectively. The word “or” in reference to a list of two or
more items, covers all of the following interpretations of the
word: any of the items in the list, all of the items in the list,
and any combination of the items in the list.

[0076] The phrases “in some embodiments,” “according to
some embodiments,” “in the embodiments shown,” “in other
embodiments,” and the like generally mean the particular
feature, structure, or characteristic following the phrase is
included in at least one implementation of the present
technology and may be included in more than one imple-
mentation. In addition, such phrases do not necessarily refer
to the same embodiments or different embodiments.
[0077] The above Detailed Description of examples of the
technology is not intended to be exhaustive or to limit the
technology to the precise form disclosed above. While
specific examples for the technology are described above for
illustrative purposes, various equivalent modifications are
possible within the scope of the technology, as those skilled
in the relevant art will recognize. For example, while
processes or blocks are presented in a given order, alterna-
tive implementations may perform routines having steps, or
employ systems having blocks, in a different order, and
some processes or blocks may be deleted, moved, added,
subdivided, combined, and/or modified to provide alterna-
tive or subcombinations. Each of these processes or blocks
may be implemented in a variety of different ways. Also,
while processes or blocks are at times shown as being
performed in series, these processes or blocks may instead
be performed or implemented in parallel or may be per-
formed at different times. Further any specific numbers
noted herein are only examples: alternative implementations
may employ differing values or ranges.

[0078] The teachings of the technology provided herein
can be applied to other systems, not necessarily the system
described above. The elements and acts of the various
examples described above can be combined to provide
further implementations of the technology. Some alternative
implementations of the technology may include not only
additional elements to those implementations noted above,
but also may include fewer elements.

[0079] These and other changes can be made to the
technology in light of the above Detailed Description. While
the above description describes certain examples of the
technology, and describes the best mode contemplated, no
matter how detailed the above appears in text, the technol-
ogy can be practiced in many ways. Details of the system
may vary considerably in its specific implementation, while
still being encompassed by the technology disclosed herein.
As noted above, particular terminology used when describ-
ing certain features or aspects of the technology should not



US 2023/0059433 Al

Feb. 23, 2023 Sheet 2 of 7

Patent Application Publication

@3YNoY

woe

“LS9eVLSHLOL
SIVWNOIS WOlwLOS TS YANTSG

i

coe

"SIWNOIS WORLOF OL
STWNOIS WOLLAO SHLLESANOO.

i

z0e|

“LNSIWNOUIANS DINSDOAHO SHL OLN!
STVNOIS WOUdO SHE SLNOY

t

“LNSIWNOXIANS SINSDOAHO SHLSGISLNO
STVNOIS WOLdO SIWHSNS9,



US 2023/0059433 Al

Feb. 23, 2023 Sheet 1 of 7

Patent Application Publication

Layndy

TOF LNSWNOUIANA OINSDOAHO

—_ 90T
BOF LSOHVL ualuSANoo
JWNOIS ) WO
201 MN
OLOF
SOL INT
WOO

£01 MNT
OWLOTS

ro
BOWNOS
TWNOIS

yor
YSLYSANO9
OA


US 2023/0059433 Al

first excited states, is achieved through coherent drives at the
transition frequency «,. The qubit is dispersively coupled to
a linear microwave cavity of linewidth K such that the cavity
resonance frequency depends on the qubit state, @, =04%
with @, the mean cavity resonance frequency and x the
dispersive shift. A drive at the mean cavity frequency is
therefore reflected with a qubit-state-dependent phase shift
+2 tan”!2y/k, which is detected by a microwave homodyne
set-up.

[0038] FIGS. 6 and 7 comprise environments 600 and 700
and demonstrate two embodiments of the present technol-
ogy. Environment 600 illustrates the use of a photonic link
to generate microwave pulses that readout a transmon qubit
embedded in a three-dimensional microwave cavity. Envi-
ronment 700 illustrates the use of a photonic link to generate
microwave pulses that control a transmon qubit embedded in
a three-dimensional microwave cavity. In both environment
600 and 700, a single antenna is used to address both the
qubit and the cavity. Drives at

« @
20 55.1 Gite and 2 5 109 Giz

are physically separated by a microwave diplexer. The
average qubit relaxation time is T,=43 ps and the cavity
linewidth is

3 23 Mik.

The photonic link comprises a diode laser operating at a
wavelength of 1,490 nm and a commercial EOM at room
temperature, connected via an optical fiber to an Indium-
Gallium-Arsenic (InGaAs) photodiode at 20° mK. For com-
parison, microwave signals can be routed to the quantum
circuit with full vector control either through the photonic
link or through a regular coaxial line.

[0039] Referring to FIG. 6, environment 600 comprises
cavity drive 601, qubit drive 602, and readout cavity 603.
Signals generated by photodiode cavity drive 601 drive
microwave readout cavity 603. The laser power is sup-
pressed during the qubit state manipulation, and then turned
on and modulated at the cavity frequency @, to perform the
readout. The cavity is driven into a coherent state of approxi-
mately 15 photons, using an average photocurrent I=20 nA
during the measurement pulse. The resulting homodyne
signal can be measured with the qubit initialized in the
ground or excited state to generate a Gaussian distribution
resulting in two well separated Gaussian distributions cor
responding to the ground and excited state of the qubit. A
single-shot measurement fidelity of 98% may be obtained
and is identical to the fidelity obtained using a traditional
coaxial line. To determine the effect that readout with a
photonic link may have on qubit coherence, the qubit
coherence may be compared when measured using the
photodiode or the coaxial line. The ensemble average of two
representative sets of measurements may be modeled as a
function of the delay between two 1/2 pulses, yielding
Ramsey oscillations. Additionally, there is no indication that
the qubit relaxation rate is degraded by stray optical light.
[0040] Referring to FIG. 7, environment 700 comprises
cavity drive 701, qubit drive 702, and readout cavity 703.

Feb. 23, 2023

Signals generated by photodiode qubit drive 702 drive the
qubit resident in readout cavity 703. The laser power is
modulated at the qubit frequency «, to control the qubit
state, followed by a readout pulse at the cavity frequency
using a coaxial line. When driven on resonance, the qubit
undergoes Rabi oscillations between its ground and excited
states at a frequency Q,. The oscillations may be modeled
asa function of the amplitude of the drive at the cavity, using
either the photodiode or a regular coaxial line. For Rabi
frequencies much less than the transmon’s anharmonicity,
the transmon is well approximated by a two-level system,
and the Rabi frequency increases linearly with the drive
amplitude. At higher drive power, the Rabi frequency devi-
ates from the linear scaling, as expected from multilevel
dynamics. The precise matching of the Rabi rates of the
photonic link to the coaxial line drive may be achieved
without any signal predistortion to compensate for nonlin-
earities of the photonic link. High qubit gate fidelity is
expected as the Rabi rate exceeds the decay rate of the
oscillations by more than three orders of magnitude.

[0041] Excess photocurrent noise could potentially limit
qubit gate or readout fidelity. Predicting the effect of pho-
tocurrent noise requires its precise measurement in a tem-
perature and photocurrent regime previously unexplored for
high-speed photodiodes. In some examples, the qubit-cavity
systems illustrated in the preceding figures may act as a
quantum spectrum analyzer to measure the noise perfor-
mance of the photodiode with excellent sensitivity. In the
absence of technical noise, the photocurrent noise is funda-
mentally limited by shot noise, with a power spectral density
given by S=2el. This shot noise spectrum is white until the
frequency cut-off of the photodiode, nominally 20 GHz. In
each case the microwave diplexer ensures that the noise
drives only either the cavity or the qubit into a thermal state.
Photocurrent noise leads to an average cavity occupancy.
Owing to the dispersive coupling, this results in a Stark shift
of the qubit frequency as well as qubit dephasing, which can
be resolved by measuring Ramsey oscillations in the pres-
ence of a constant laser intensity. As expected with shot
noise, the cavity occupancy increases linearly with photo-
current with an experimental background of about 1%.
Photocurrent noise may lead to depopulation of the qubit
ground state. The population of the excited states as a
function of the photocurrent may comprise a linear behavior,
again in good agreement with shot noise, and a background
qubit occupancy of about 10%. The preceding photodiode
systems do not show any major deviation from shot noise
that could indicate, for example, excess optical intensity
noise, excess thermal noise due to local heating within the
photodiode, or excess noise from the voltage noise at the
microwave input of the EOM. At the photocurrents used for
the qubit readout or control. As such the optical shot noise
has negligible impact on measurement and gate fidelity.

[0042] The approaches described in the preceding figures
can scale to a large number of qubits. The number of qubits
in a processor is limited by the heat load of the classical
interconnects on the mixing chamber of the dilution refrig-
erator. It is estimated that the passive heat load of a typical
optical fiber is around 3 pW, allowing a typical dilution
refrigerator with a cooling power of 20 HW at 20 mK to be
wired with millions of optical fibers. In addition, each
optical fiber has the bandwidth to easily support hundreds of
qubits. With negligible passive heat load, the active heat
load due to the dissipation of optical power during qubit


US 2023/0059433 Al

tions and that any residual thermal noise is already included
in the qubit Stark-shift or qubit population at zero photo-
current.

[0061] Here a procedure is disclosed to move the reference
plane from the cavity antenna to the photodiode. As the
hardware and frequencies differ slightly between the qubit
control and readout experiments, they require separate in-
situ calibrations.

[0062] ‘The microwave power at the cavity antenna can be
calibrated by using the coaxial line. The Rabi rate can be
compared to extract the coupling rate between the qubit and
cavity antenna. The loss can be defined between the photo-
diode and the cavity antenna, A, so that the power at the
cavity antenna is

Lp
AP, = AST,

where A includes the effect of explicit loss and the response
funetion of the photodiode. The current noise spectral den-
sity can be extracted for the photocurrent, S,, using the qubit
ground state population P,. From detailed balance it can be
found that (1,41 ..)8=V yy, AT egley, Where n=(1-P,)/P,,

1, is the average photon number in the internal’ bath
extracted from the equilibrium population at zero photocur-
rent, and n,,=AZS,/h@,. This in turn yields Equation (5).

(5)

Sp = FET Cine + Dene) = inti

as

[0063] The photocurrent can be fixed, and the Stark shift
used to calibrate the intra-cavity photon number and there-
fore extract the power at the cavity antenna

Lp
AP, = ASZT

As the measurement cavity is over-coupled, the current
noise spectral density of the photocurrent can be extracted
from the cavity occupancy, S=nhiw,/AZ.
[0064] Microwave noise may be induced by the photocur-
rent shot noise of the photodiode. In the context of qubit
readout, extraneous noise at the cavity frequency (1) de-
phases the qubits coupled to it and (2) reduces the micro-
wave measurement efficiency, which in turn impacts the
qubit measurement fidelity. In the context of qubit control,
extraneous noise at the qubit frequency induces transitions
to the excited states which reduces gate fidelity. To simplify
the discussion, a photodiode with unity quantum efficiency
and operating well within its bandwidth is used, and loss
between the photodiode and the cavity or the qubit control
line is neglected.
[0065] For qubit readout, optimal measurement speed and
separation in phase space between 0., and 0., is obtained for
2y=K and w=, leasing to lot,-=la,,!°S\al=2n/k. The
corresponding average e photocurrent is IeViOlaul. In turn the
microwave noise is n=2e Yk/Ololl, which induces qubit
dephasing according to Equation (4) and limits the efficiency
of the measurement chain to n=1/(1+2n). For a typical
operating conditions, the microwave measurement effi-
ciency limited to 1=94%, much larger than the traditional

Feb. 23, 2023

systems. Additionally, qubit measurement infidelity is typi-
cally dominated by gubit relaxation events during the mea-
surement with only a small contribution due to the limited
measurement efficiency. Therefore, the assignment errors
due to the photocurrent shot noise can be expected to be
neg!

[0066] For qubit control, it can be assumed a qubit gate
error rate dominated by the relaxation rate, IM, and the
excitation rate, 'T, which are linked by detailed balance
IT. The error probability for a gate of length tis given
by Equation (6).

e=1explr Tar ye]=1-exp{ 40] 6

[0067] For a x-pulse at a Rabi rate Q,>>(14i)T'L, the
error probability is given by Equation (7).

alt o
~ Oe

[0068] The qubit relaxation rate can be decomposed into
an external contribution from the coupling to the control
line, I,.,, and an internal contribution from all other degrees
of freedom, I’,,,. The Rabi rate is defined as Q,=2al",,,
where is the photon flux in photon/s at the control line. The
effective qubit population, 0, is linked to the population of
the internal and external bath, n,,, and 1,,,, by detailed
balance so that PUD ,j,/T ex Nexe In the following it can
be assumed the internal bath is cold, 2,,=0.

[0069] For a photodiode operating well within its band-
width driving a control line of impedance Z, the photon flux
is set by the microwave power generated by the photodiode

Lia
hog = 527°

and the external bath occupancy is set by the photon
shot-noise /,0,,,=2eIZ, leading to equation (8).

. ATi of } .

[0070] At low photocurrent,

heal 4
2eZT ex”

the microwave noise generated by the photodiode is negli-
gible, n<<1. In this regime the error probability decreases as
the ratio between Rabi rate and relaxation rate increases. In
contrast, at high photocurrent,

heagh 4

Tara

the error probability plateaus as the errors induced by the
photocurrent shot noise balances the increase in Rabi rate.
For a realistic cases, the error probability saturates at €>4x