INVITED Cryo-CMOS Electronic Control
for Scalable Quantum Computing
, Harald Homulle
, Bishnu Patra
, Rosario Incandela
, Jeroen van Dijk
, Masoud Babaie
, Andrei Vladimirescu
, Edoardo Charbon
Delft University of Technology, Delft, The Netherlands,
Tsinghua Univ., Beijing, P.R. China,
U.C. Berkeley, Berkeley,
Intel Corp., Hillsboro, OR, U.S.A.,
EPFL, Neuchâtel, Switzerland
could revolutionize computing in a profound
way due to the massive speedup they promise. A quantum
computer comprises a cryogenic quantum processor and a
classical electronic controller. When scaling up the cryogenic
quantum processor to at least a few thousands, and possibly
millions, of qubits required for any practical quantum algorithm,
cryogenic CMOS (cryo-CMOS) electronics is required to allow
feasible and compact interconnections between the controller and
the quantum processor. Cryo-CMOS leverages the CMOS
fabrication infrastructure while exploiting the continuous
improvement of performance and miniaturization guaranteed by
Moore’s law, in order to enable the fabrication of a cost-effective
practical quantum computer. However, designing cryo-CMOS
integrated circuits requires a new set of CMOS device models,
their embedding in design and verification tools, and the
possibility to co-simulate the cryo-CMOS/quantum-processor
architecture for full-system optimization. In this paper, we address
these challenges by focusing on their impact on the design of
complex cryo-CMOS systems.
Hardware → Quantum computation; Electronic design
automation; Analog and mixed-signal circuits; Application
specific integrated circuits.
Cryo-CMOS, cryogenics, quantum computation, qubit, error-
correcting loop, device models.
Quantum computers hold the promise to successfully address
computational problems that are intractable by standard
computing paradigms. These problems include efficient search in
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extremely large datasets, factorization of large integers in their
prime factors and simulations of quantum systems for the
optimization of drug synthesis, materials and industrial chemical
processes . In a quantum computer, standard logic bits are
replaced by quantum bits (qubits), which can be represented as a
point on the surface of a three-dimensional sphere, the so-called
Bloch sphere, shown in Figure 1. In this construct, standard logic
‘1’ and ‘0’ are replaced by quantum states
|0 and |1, and are
manipulated, so as to exploit the fundamental phenomena of
quantum mechanics for computation, i.e. superposition and
entanglement . Qubits can exist in a superposition of both state
|0 and |1 simultaneously, which results in a computing power
that doubles with every additional qubit, thus resulting in a
massive speedup with respect to traditional computers. For
example, it has been estimated that the state of a 50-qubit system
cannot be stored in the memory of the world’s most powerful
computers today .
In addition to a quantum processor comprising several qubits,
a quantum computer also requires a classical controller to
manipulate and read out qubit states (Figure 2). Classical
controller and quantum processor must be placed in close
proximity, because of the need for physical interconnections
between them. This requirement will be especially stringent when
the number of qubits, and hence the wires connecting them, will
grow to very large numbers. Since most quantum processors
nowadays require operation at deep-cryogenic temperature well
below 1 K, such as in the examples shown in Figure 2, the
Figure 1. Bloch sphere representation of a qubit.
classical controller must also operate at cryogenic temperature. To
address this issue, a cryogenic CMOS (cryo-CMOS) electronic
controller has been proposed -. The controller must satisfy
stringent requirements on noise, accuracy, and bandwidth, in
order not to reduce qubit performance, and to comply with power
dissipation limits imposed by the cooling technology. Meeting
those demands requires effort and innovations both in the
development of new system and circuit architectures and in the
creation of novel design and verification strategies and tools. In
regard to design tools, few topics require specific attention: the
co-simulation of the electronic interface with the quantum
processor for a full system optimization; the need for models of
CMOS devices operating at cryogenic temperature and their
embedding in commercial EDA tools to enable the design of
complex circuits and systems.
In this paper, we focus on those challenges and their impact on
the design of complex cryo-CMOS circuits. The paper is
organized as follows. The motivations and the requirements for
the cryo-CMOS controller are presented in section 2. Section 3
and 4 discuss the challenges for the development of the quantum-
processor/controller co-simulations and cryo-CMOS device
models, respectively, while remarks on cryo-CMOS design
automation occupy section 5. Conclusions are drawn in section 6.
2 THE NEED FOR CRYO-CMOS CONTROL
Several physical implementations have been proposed for
qubits, however solid-state alternatives are currently the most
promising in terms of scalability to a large number of qubits,
although no more than a dozen qubits have been demonstrated in
such platforms so far . Solid-state qubits come in several
variants, such as electron spins in quantum dots, superconducting
circuits, and nitrogen-vacancies in diamond lattices -. A
common feature of most of those technologies is the required
operation at deep-cryogenic temperatures, typically below
100 mK. This is required both to expose their quantum behavior
and to increase the coherence time of their quantum state. The
coherence time is usually far below a second, that is a time frame
much shorter than what is required for the execution of any
practical quantum algorithms. Consequently, to counteract the
loss of the quantum state, quantum error-correction techniques
have been developed to exploit information redundancy by
encoding the quantum information on a large number of qubits,
thus trading off simplicity for fidelity in execution of the quantum
algorithm . Thus, although a quantum computer with 50
logical qubits can already exceed the memory capabilities of
today’s supercomputers and non-trivial quantum chemistry
problems can be solved with the availability of just 100 logical
qubits , thousands, or even millions, of physical qubits, i.e. the
real physical devices, are required to enable practical quantum
The classical controller in Figure 2 must serve this large
number of qubits by taking care of the execution of the quantum
algorithm and, in parallel, by implementing an error-correction
loop intended to maintain the fidelity of the computation beyond
coherence times. Interfacing solid-state qubits usually involves the
generation and acquisition of purely electrical signals, such as
microwave bursts with frequencies ranging from a few GHz to
tens of GHz and voltage and current pulses with a bandwidth of
tens of MHz.
Since existing state-of-the-art quantum processors comprise
only a few qubits, most of the electronics making up the classical
controller operate at room temperature and it is wired to the qubits
in the cryogenic chamber. Only a few functionalities, such as low-
noise amplification of read-out signals and attenuation of control
signals, are implemented at cryogenic temperature in close
proximity to the quantum processors. However, when scaling up
the number of qubits to the large number required for any
practical computation, this approach may incur a number of
limitations, including the thermal load of the large number of
cables, or the latency of the error-correction loop . Although
there is not yet a general consensus about whether those
limitations are critical or may be circumvented in the near future,
it is clear that wiring thousands of low-frequency and high-
frequency wires from room temperature to the cryogenic quantum
processor would lead to an extremely expensive, bulky, unreliable
and, hence, unpractical quantum computer.
As an alternative, a cryogenic controller may be employed, in
order to relieve the requirements on interconnections, system size
and reliability. Several technologies have demonstrated
functionality at cryogenic temperature, such as junction field-
effect transistors (JFET), high-electron-mobility transistors
(HEMT), superconducting devices based on Josephson junctions,
compound semiconductors (e.g. GaAs) and CMOS transistors
. However, by relying on the progress of the
semiconductor industry, only CMOS technology can ensure low
power consumption and functionality down to 30 mK ,
while offering the integration of billions of transistors on a single
chip, as it will be required to handle the complexity of future
quantum processors. Moreover, CMOS is preferred also because
the design automation infrastructure is very mature for the
standard industrial and military temperature ranges, i.e. down
to -55 °C.
Figure 3 shows a generic platform for control and read-out of a
quantum processor. It comprises a frontend for (de)multiplexing,
amplification, analog-to-digital conversion (ADC) and digital-to-
analog conversion (DAC) for the analog signals coming from and
Figure 2. Quantum-classical interface.
feeding to all qubits. Ideally, quantum processors and electronics
should operate at the same temperature, if not even on the same
chip, to eliminate the need for any off-chip interconnect.
However, currently available refrigeration technologies limit the
available cooling power to less than ~1 mW at temperature below
100 mK , and it is unlikely that the full electronic controller
can operate with such power budget in the near future. On the
contrary, a cooling power exceeding 1 W is usually available at
the 4-K stage, thus allowing the majority of the electronics to
operate there. A limited amount of low-power electronics,
including (de)multiplexers to reduce the number of connections to
the 4-K stage, is envisioned to operate at the same temperature as
the quantum processor, as shown in Figure 3.
The specifications for the cryo-CMOS electronic controller are
extremely challenging. To ensure the target performance in the
quantum processor, electronic signals driving the qubits must be
highly accurate (in terms of amplitude, timing, frequency and
phase) and contribute a negligible amount of noise. As a
comparison, the control of state-of-the-art quantum processors is
achieved by using the most accurate (and expensive) bench-top
electronic instrumentation available on the market -. The
read-out must be very sensitive to detect the weak signals from
the quantum processor , and to ensure a low kickback, so as to
avoid altering qubit states. These specifications must be granted
while keeping the latency of the error-correction loop much lower
than the qubit coherence time. Moreover, while ensuring the
above-mentioned functionalities and specifications, the controller
must dissipate very low power. Although more than 1-W cooling
power is available at 4 K, a processor with only 1000 qubits
would limit the power budget to 1 mW/qubit, which is already
very challenging, as shown in . Thus, while targeting for a
power budget of 1 mW/qubit is ambitious, but probably
achievable in the short and medium term, it becomes clear that the
development of advanced cryo-CMOS systems must go hand in
hand with the development of more advanced and powerful
In addition to the above-mentioned challenges, proper design
tools and design flows are required to support the development of
a complex system as the one in Figure 3. Cryo-CMOS can already
exploit the design automation infrastructure already in place for
standard CMOS. However, specific issues related both to the
operation at cryogenic temperature and the interfacing with a
quantum system must be addressed, as elaborated in the following
3 CO-SIMULATING THE ELECTRONIC
CONTROLLER AND THE QUANTUM
The tight power budget coupled with very demanding
specifications calls for a careful system optimization. While
electronic controllers operating at room temperature can be
overdesigned to make the performance of the full quantum
computer limited by the qubits by a wide margin, this cannot be
allowed in a cryogenic implementation. It is then necessary to
understand clearly the effect of any non-ideality of the electronic
controller on the system performance.
For example, in the case of spin qubits and transmons ,
single-qubit operations, i.e. rotations of the qubit state
| in the
Bloch sphere in Figure 1, can be executed by exciting the qubit
with a microwave pulse with a specific carrier frequency and
phase and specific pulse shape, amplitude and duration, which all
together determine the axis of rotation and the angle of rotation in
the coordinate system in Figure 1. The possible error sources for
this example are listed in Table 1. Any error or any additional
noise on the pulse parameters would cause an error in the
operation that can be quantified by the fidelity of the quantum
operation . The fidelity, which should be as close as possible
to 100%, is a measure of the reliability of the quantum operation,
similar to the Bit Error Rate (BER) for classical communication
systems. Knowing how much each single source of error
contributes to the final fidelity enables a better optimization of the
design, since, for example, providing accuracy/noise in the pulse
amplitude may be more expensive in terms of power consumption
than ensuring accuracy/noise in the pulse duration. Error
budgeting for a minimum power consumption would then become
Table 1. Error sources for a microwave pulse for single-
qubit operation (assuming a square pulse).
Microwave frequency Accuracy
Microwave amplitude Accuracy
Microwave duration Accuracy
Microwave phase Accuracy
Figure 3. Generic electronic
latform for the control and
read-out of quantum processors.
Bias / References
For this purpose, we have developed a MATLAB simulation
tool that receives as input a description of the required electrical
signals and simulates the quantum system with those excitations
by numerically solving the Schrödinger equation (Figure 4). As a
result, the fidelity of the operation is computed. Since the
simulation is computationally intensive, we are currently only
able to simulate two spin qubits. However, since this allows the
simulation of single- and two-qubit operations and qubit read-out
(which are sufficient building blocks for most quantum computer
implementations), it is sufficient, together with a theoretical
model, to derive an accurate error budget for the general
electronic platform of Figure 3. Moreover, the MATLAB model
of the quantum processor can be used for verification of the
developed cryo-CMOS circuit during the design phase (or during
experimental validation before connection to the quantum
processor): the simulated (or measured) output waveforms could
be fed to the qubit simulator while the electrical signals generated
for the read-out can be passed to the circuit simulator.
This represents the first step towards a fully integrated
environment for the design and verification of the
controller/quantum-processor system, although several challenges
are already in sight. First, it is well known that quantum systems
cannot be efficiently simulated with traditional computers, and it
is unclear how the simulations can be extended to a larger number
of qubits that can better represent a real scenario. Furthermore, it
would be convenient to embed the qubit simulation in commercial
EDA design/verification flows and tools. Finally, it will be
necessary to fully or partially integrate the physical simulation of
qubit into the full design/validation stack of the quantum system
, which includes the infrastructure for the quantum microcode
execution and for the quantum compiler on top of the above-
discussed physical layer.
4 CRYO-CMOS DEVICE MODELING
Accurate device models are required to reliably design and
simulate complex cryo-CMOS circuits. At deep-cryogenic
temperature, many physical parameters that determine transistor
behavior, such as carrier mobility, show a strong deviation from
room temperature. This results, for example, in a larger drain
current and higher threshold voltage at 4 K. In addition, several
non-idealities that are specific to the cryogenic operation appear,
such as the a so-called ‘kink’, i.e. a sudden increase in drain
current at high drain-source voltage, and hysteresis in the drain
current when sweeping the drain-source voltage upwards or
Although the physics of cryo-CMOS is generally understood
 and a few nanometer technologies have been cryogenically
characterized (65 nm at 78 K , 32 nm at 6 K , 14 nm at 77
K ), there is not yet a general consensus on a standard
cryogenic model for modern technologies, since prior models
were limited to mature technologies (feature size ≥ 160 nm) and
moderate cryogenic temperatures (>20 K) -.
Characterization and modelling of nanometer CMOS technologies
is specifically relevant for implementing low-power circuits for
the platform in Figure 3, where handling of large-bandwidth high-
frequency signals is required.
As a step in that direction, we have characterized a large
number of active and passive components in standard 160-nm and
40-nm CMOS technologies . As an illustration, Figure 5
and Figure 6 shows the output characteristics of NMOS transistors
in both technologies. Despite a non-negligible shift of the
transistor parameters, such as threshold voltage and current gain,
Figure 4: Process for the co-simulation of the electronic
controller and the quantum processor.
Figure 5: I-V characteristics of a 2320 nm/160 nm NMOS
fabricated in 160-nm CMOS: measurements at 300 K (dotted
lines) and 4 K (solid lines); SPICE-compatible model (dashed
Figure 6. I-V characteristics of a 1200 nm/40 nm NMOS in 40-
nm CMOS: measurements at 300 K (dotted lines) and 4
(solid lines); SPICE-compatible model (dashed lines).
[ V ]
Id[ A ]
Vds [ V ]
0 0.2 0.4 0.6 0.8 1 1.1
Id[ A ]
those characteristics are not dissimilar to the ones of a standard
NMOS transistor, thus leading us to believe that standard SPICE
models may be applicable also at cryogenic temperature.
However, although it seems that a SPICE-compatible model for
the DC behavior of cryo-CMOS devices may be feasible, much
work must still be devoted to develop a full cryo-CMOS device
model with the same reliability and accuracy of the models
available for commercial technologies at room temperature, thus
allowing the design of the complex RF, analog, mixed-signal and
digital circuits of Figure 3.
The challenges to be addressed include the modelling and
characterization of dynamic and RF behavior, of noise at low and
high frequency, both for active devices and passives. Moreover,
some preliminary investigations have suggested that transistor
mismatch at 4 K is largely uncorrelated to that at 300 K and that
standard design techniques to mitigate the effect of mismatch may
need to be modified . The large impact of mismatch on the
performance and, hence, the design of analog and mixed-signal
circuits asks for further investigations, and both additional
experimental data and theoretical analysis will be required before
the correct cryogenic mismatch model can be included in design
tools. Finally, self-heating may give a non-negligible effect, since
even a temperature raise of only a few degrees represents a
relatively large increase in absolute temperature that can result in
a large variation of the electrical properties of the devices.
Because of this high sensitivity, it may be necessary to model the
self-heating for each individual device. This would require strong
efforts in properly updating the EDA tools, since self-heating of
single devices or circuit sub-blocks can be highly dependent both
on their physical placement on the die and their surroundings
(including metal interconnections), not to mention the effect of
thermal transients. At the moment, those issues are left largely
unexplored for cryo-CMOS to the best of the author’s knowledge.
5 DESIGN AUTOMATION FOR CRYOGENIC
Although the characteristic of CMOS transistors show a very
wide alteration at cryogenic temperature, it has been shown that
even complex commercial components not designed or specified
outside the commercial temperature range, such as FPGAs, can
reliably operate at cryogenic temperature -. Extensive
characterization showed not only that all major components of a
standard Xilinx Artix 7 FPGA, including look-up tables (LUT),
phase-locked loops (PLL) and IOs, operate correctly down to 4 K
but also that their logic speed is very stable over temperature .
An ADC based on a time-to-digital converter (TDC) has also been
implemented in the same FPGA platform and its continuous
operation from 300 K down to 15 K has been demonstrated,
although specific care had to be taken in designing the firmware
to minimize the temperature sensitivity, and calibration was
extensively used to compensate for temperature effects .
Apart from showing the functionality of standard CMOS
components at cryogenic temperature, FPGAs can also have a
practical application for the implementation of the system in
Figure 3, which at least in the first instance will not be necessarily
limited to application-specific integrated circuits (ASIC). FPGAs
could be beneficial thanks to their reconfigurability, which could
prevent expensive and time-consuming cool-down-warm-up
cycles. In addition, FPGA design tools leverage a mature
synthesis and place-and-route technology, with advanced
verification tools that could be used to emulate the operation of
the circuit at cryogenic temperatures.
For the design and verification of the cryogenic FPGA,
standard tools for firmware design were employed. The
characterization of a standard FPGA library was an important step
in creating the firmware, thus enabling correct operation at deep-
cryogenic temperature. Similar efforts are needed in ASIC digital
libraries, where transistor models are part of this characterization
and could enable fast library certification. Ultimately, logic gate
farms will be required to verify simulations and to validate the
proposed models. In this context, the process of digital library
characterization is not unlike a conventional one, with the
difference that it requires care in measuring the circuits at various
temperatures with a well-controlled measurement setup and
particular attention to self-heating. The library characterization
will also yield non-functional library elements, depending on
temperature, thus requiring that synthesis and place-and-route
tools be temperature-driven and/or temperature-aware.
A less trivial task would be the design of digital circuits that
exploit the specific features of cryo-CMOS. The main challenge
of operating large CMOS circuits and systems at cryogenic
temperatures is power dissipation. In order to minimize power
dissipation, the supply voltage could be reduced even down to a
few tens of millivolt by exploiting the relaxed requirement on
noise margins due to the low thermal-noise level at cryogenic
temperature. Operation in sub-threshold regime can also be
heavily exploited thanks to the improved subthreshold slope at
low temperature and to the resulting large on/off-current ratio
) ratio. Furthermore, the expected extremely low leakage
current in cryo-CMOS may lead to power-efficient use of existing
dynamic logic, or even bring in the possibility of new dynamic
logic families. This can pose problems in the synthesis and
verification of logic circuits, prompting the EDA industry to
rethink models and perhaps even simulators, so as to achieve the
necessary accuracy in the simulation of these regimes.
Finally, the operating temperature can be exploited as a new
design parameter. Since the cooling power in a cryogenic
refrigerator is larger at higher temperature, higher computational
power could be placed at a higher temperature. However,
particular care should then be devoted to the interconnections that,
apart from becoming unpractical, could also occupy a relevant
fraction of the cooling power budget due to their thermal
conduction. The full digital back-end of a quantum computer
would then spread over several temperature stages, eventually
with a lower inter-stage data communication rate for circuits at
lower temperatures. Although conceptually interesting, such
approach would require an ad-hoc EDA infrastructure covering
several multidisciplinary domains, including device modelling
and library characterization over a very wide temperature range,
thermal modelling, interconnect optimization and novel synthesis
The design of cryo-CMOS controllers for quantum computers
presents several challenges for the design automation industry.
First steps have already been taken, especially for device
modelling and simulation/optimization of the quantum/classical
interface. However, we are still far from the EDA infrastructure
that will enable the design of the classical controller satisfying
both the demanding electrical specifications and its very tight
power budget. With the growing academic and industrial interest
in the field of quantum computation, we foresee that several of the
presented challenges will be soon picked up by the research
community. This would result in an accelerating virtuous cycle
including the design of cryo-CMOS circuits and systems with
ever increasing complexity on one hand and more performant
EDA tools on the other hand, thus facilitating the fabrication of
practical quantum computers.
The authors are grateful to Intel Corp. for funding the project.
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