Most of the publications on Quantum Computing and its main building block; the Qubit, rely on the Quantum Theory and use its terminologies. It is therefore not an easy task for the Electrical Engineers to fully understand the concept of the qubits, and how they are designed, controlled, readout, and used for computation. The primary aim of this paper is to show that the physical quantities describing the superconducting Transmons-the microwave realizations of the qubits-are just noisy signals similar to those encountered in e.g. Mobile and Satellite Communications. The nature of the noise in the qubit case, which will be simply called Quantum Noise, is essentially different from that of e.g. the thermal one. Contrary to the well-studied Thermal Noise, the Quantum one enjoys precise probability distributions and can interfere coherently. In particular, the so-called Stationary States resemble individually pure noise. However, a superposition of at least two of them results in a noisy signal, whose signal-to-noise ratio improves (goes higher) as more stationary states enter the superposition. Furthermore, the excitation (control) and readout of the qubits will be treated from the perspectives of the Electrical Engineering.
Most of the publications on Quantum Computing and its main building block; the Qubit, rely on the Quantum Theory and use its terminologies. It is therefore not an easy task for the Electrical Engineers to fully understand the concept of the qubits, and how they are designed, controlled, readout, and used for computation. The primary aim of this paper is to show that the physical quantities describing the superconducting Transmons-the microwave realizations of the qubits-are just noisy signals similar to those encountered in e.g. Mobile and Satellite Communications. The nature of the noise in the qubit case, which will be simply called Quantum Noise, is essentially different from that of e.g. the thermal one. Contrary to the well-studied Thermal Noise, the Quantum one enjoys precise probability distributions and can interfere coherently. In particular, the so-called Stationary States resemble individually pure noise. However, a superposition of at least two of them results in a noisy signal, whose signal-to-noise ratio improves (goes higher) as more stationary states enter the superposition. Furthermore, the excitation (control) and readout of the qubits will be treated from the perspectives of the Electrical Engineering.
In a quantum computer, the information carriers, which are bits in ordinary computers, are implemented as devices that exhibit coherent superpositions of physical states and entanglement. Such components, known as quantum bits or qubits, can be realized with various different types of two-state quantum systems. Quantum computers will be built for computational speed, with hoped for applications especially in cryptography and in other tasks where classical computers remain inefficient. Circuit quantum electrodynamics (cQED) is a quantum-computer architecture which employs superconducting electronic components and microwave photon fields as building blocks. Compared to cavity quantum electrodynamics (CQED), where atoms are trapped in physical cavities, cQED is more attractive in that its qubits are tunable and conveniently integrable with the electronics already in use. This architecture has shown some of the most promising qubit designs, despite their coherence times reaching tens of microseconds, are still below the state of the art with spin qubits, which reach milliseconds. Coherence times are historically the most relevant parameters describing the fitness of a qubit, although these days not necessarily the limiting factor. This thesis presents a comprehensive set of theoretical and experimental methods for measuring the characteristic parameters of superconducting qubits. We especially study transmission-line-shunted plasma oscillation qubits, or transmons, and presents experimental results for a single sample. Transmon capacitively couples a superconducting quantum interference device (SQUID) with a coplanar waveguide (CPW) resonator, often with added frequency tunability utilizing an external magnet. The number of superconducting charge carriers tunnelled through a junction in the SQUID are used as qubit degrees of freedom. Readout of the qubit state is carried out by measuring transmission through the CPW. A cryogenic setup is employed with measurement and driving pulses delivered from microwave sources. Steady-state spectroscopy is employed to determine the resonance frequencies of the qubit and the resonator, qubit-resonator coupling constants, and the energy parameters of the qubit. Pulse-modulated measurements are employed to determine the coherence times of the qubit. The related analysis- and simulation programs and scripts are collected togithub.com/patomaki.
Atoms and photons, two things so different but yet so alike. The former, the building block of matter, something we learn about in school and imagine it as some tiny marbles encircled by other tinier marbles. The latter, an electromagnetic wave, a light particle or an excitation of the electromagnetic field. Quantum mechanics tells us about the properties of these two entities. And even if it sounds, looks and writes counter-intuitive, it has proven right for over a century now. In this work, I elaborate on how we tested the laws of quantum mechanics and how we used them learn more about the tiny building blocks of nature and the fields they use to talk to each other. The atoms we use, are artificial. Superconducting qubits, small electrical circuits with quantized energy levels behave like electrons that transition between different orbitals in an atom. One of the qubits' advantages, is also a big disadvantage. We design the circuits' energy levels and fabricate them in a cleanroom. This allows for arbitrary spaced energy levels but in contrast to real atoms, prevents two superconducting qubits from being alike. Still, this qubit platform is one of the frontrunners for future quantum computing technology and testing fundamental physics due to their scalability. We interface superconducting qubits, which operate in the GHz regime, with microwave photons. We use 3D aluminum cavities as mediators between qubits and photons. The cavities allow for non-destructive readout of the qubit state, they shield the qubits from noise at the qubit frequency and they give us an easy way to frequency-tune these joint systems. We need to operate superconducting qubits and their cavities at millikelvin temperatures in dilution refrigerators. At higher temperatures, superconductivity suffers and even worse, the environment is filled with thermal noise photons. This poses a fundamental limitation on the scalability of superconducting qubit devices. Also connecting multiple devices in different fridges does not work over room temperature links because the microwave photons used for this purpose will be covered in noise and the quantum information they carry, will be unusable. Infrared photons do not suffer from this noise problem since there are close to zero thermal noise photons at their frequencies at room temperature. We cannot simply interface superconducting devices with optical photons due their frequency mismatch and the destructive effect of optical photons on superconductors. Therefore, we use microwave-to-optics transducers that allow to convert microwave photons into optical ones and vice-versa. The transducers that we use are macroscopic electro-optic transducers using the Pockels effect in a disk-shaped Lithium Niobate whispering gallery mode resonator. By using a strong optical pump, photons from the two frequency domains experience a beam-splitter interaction and get converted from one to the other. We measure the generated optical photons using elaborate optical setups, optical heterodyning and single photon detectors to gain knowledge about the qubit state or the converted microwave photons. Bridging the microwave and the optical world allows us to take advantage of both of their strengths but it also requires deep knowledge about both of their working principles. In this work, we describe two experiments that our group conducted to showcase the opportunities that arise from interfacing superconducting qubits with optical photons but also the pitfalls, one may encounter on the way. In the first experiment, we managed to all-optically read out a superconducting qubit. We show that the assignment fidelity, the probability that a measurement of the qubit state matches the prepared state, is close to equal for all-optical, microwave-to-optics and conventional microwave readout. We show T1 and T2 measurements for all three readout types and give an analysis of the noise caused by the optics. Finally, we show that the infrared light does not affect the qubit performance in a negative way but that the heating it causes does. This is an important insight that we used in the next experiment. The second experiment is the upconversion of itinerant single microwave photons to the optical domain. We show that we can generate single microwave photons from a qubit-cavity system. We upconvert these single photons, measure them with a single photon detector and reconstruct their shape. By conducting a single photon Rabi measurement, we show correlations between the microwave and the optical domain. And by thorough signal-to-noise measurements and noise analysis, we find that we can generate single infrared photons with high signal-to-noise ratio 5.1 and low transducer added noise (<0.012 quanta). We show that this measurement creates a path towards entanglement of a superconducting qubit and an optical photon and what parameters need to be improved to achieve it. Additionally, this experiment is a proof of principle for an on-demand infrared single photon source. More generally, it allows to link microwave quantum technology in general to the optical domain.
Atoms and photons, two things so different but yet so alike. The former, the building block of matter, something we learn about in school and imagine it as some tiny marbles encircled by other tinier marbles. The latter, an electromagnetic wave, a light particle or an excitation of the electromagnetic field. Quantum mechanics tells us about the properties of these two entities. And even if it sounds, looks and writes counter-intuitive, it has proven right for over a century now. In this work, I elaborate on how we tested the laws of quantum mechanics and how we used them learn more about the tiny building blocks of nature and the fields they use to talk to each other. The atoms we use, are artificial. Superconducting qubits, small electrical circuits with quantized energy levels behave like electrons that transition between different orbitals in an atom. One of the qubits' advantages, is also a big disadvantage. We design the circuits' energy levels and fabricate them in a cleanroom. This allows for arbitrary spaced energy levels but in contrast to real atoms, prevents two superconducting qubits from being alike. Still, this qubit platform is one of the frontrunners for future quantum computing technology and testing fundamental physics due to their scalability. We interface superconducting qubits, which operate in the GHz regime, with microwave photons. We use 3D aluminum cavities as mediators between qubits and photons. The cavities allow for non-destructive readout of the qubit state, they shield the qubits from noise at the qubit frequency and they give us an easy way to frequency-tune these joint systems. We need to operate superconducting qubits and their cavities at millikelvin temperatures in dilution refrigerators. At higher temperatures, superconductivity suffers and even worse, the environment is filled with thermal noise photons. This poses a fundamental limitation on the scalability of superconducting qubit devices. Also connecting multiple devices in different fridges does not work over room temperature links because the microwave photons used for this purpose will be covered in noise and the quantum information they carry, will be unusable. Infrared photons do not suffer from this noise problem since there are close to zero thermal noise photons at their frequencies at room temperature. We cannot simply interface superconducting devices with optical photons due their frequency mismatch and the destructive effect of optical photons on superconductors. Therefore, we use microwave-to-optics transducers that allow to convert microwave photons into optical ones and vice-versa. The transducers that we use are macroscopic electro-optic transducers using the Pockels effect in a disk-shaped Lithium Niobate whispering gallery mode resonator. By using a strong optical pump, photons from the two frequency domains experience a beam-splitter interaction and get converted from one to the other. We measure the generated optical photons using elaborate optical setups, optical heterodyning and single photon detectors to gain knowledge about the qubit state or the converted microwave photons. Bridging the microwave and the optical world allows us to take advantage of both of their strengths but it also requires deep knowledge about both of their working principles. In this work, we describe two experiments that our group conducted to showcase the opportunities that arise from interfacing superconducting qubits with optical photons but also the pitfalls, one may encounter on the way. In the first experiment, we managed to all-optically read out a superconducting qubit. We show that the assignment fidelity, the probability that a measurement of the qubit state matches the prepared state, is close to equal for all-optical, microwave-to-optics and conventional microwave readout. We show T1 and T2 measurements for all three readout types and give an analysis of the noise caused by the optics. Finally, we show that the infrared light does not affect the qubit performance in a negative way but that the heating it causes does. This is an important insight that we used in the next experiment. The second experiment is the upconversion of itinerant single microwave photons to the optical domain. We show that we can generate single microwave photons from a qubit-cavity system. We upconvert these single photons, measure them with a single photon detector and reconstruct their shape. By conducting a single photon Rabi measurement, we show correlations between the microwave and the optical domain. And by thorough signal-to-noise measurements and noise analysis, we find that we can generate single infrared photons with high signal-to-noise ratio 5.1 and low transducer added noise (<0.012 quanta). We show that this measurement creates a path towards entanglement of a superconducting qubit and an optical photon and what parameters need to be improved to achieve it. Additionally, this experiment is a proof of principle for an on-demand infrared single photon source. More generally, it allows to link microwave quantum technology in general to the optical domain.
Electrical engineers and physicists are naturally very interested in noise in circuits, amplifiers and detectors. With the advent of quantum computation and other high frequency electronics operating at low temperatures, we have entered a regime where quantum noise and quantum-limited detectors are important. Here we describe the general concept of a two-level system as a quantum spectrum analyzer and apply it to a simple superconducting qubit, the Cooper-pair box. We then discuss the coupling of a Cooper-pair box to its electromagnetic environment, whose noise leads to a finite polarization and excited-state lifetime of the qubit. Finally, we describe a theoretical technique for treating a qubit coupled to a measurement system, which allows one to calculate the full quantum noise of the measurement device. We present results for such a calculation for the case of a normal SET.
After decades of pure science phase, the research on quantum technologies is finally reaching the engineering phase, getting out of the labs into business reality. Quantum technologies relies on quantum bits, aka qubits, which are the equivalent of classical bits used in classical information processing. Similarly to bits, the information stored in qubits can be corrupted by classical noise. Differently from bits, qubits are also vulnerable to quantum noise, a type of noise with no counterpart in the classical world. Hence, it becomes crucial to understand, from an engineering perspective, how the quantum noise corrupts the information stored within a qubit. To this aim, in this invited paper, we overview the effects of the quantum noise on an arbitrary qubit from a signal-processing perspective.
"Can we do this with a new type of computer - a quantum computer?". This famous quotation of the brilliant Richard Feynman within a conference talk on "Simulating physics with computers.” is often reverently praised as the origin of the field of quantum computing. The idea was to use quantum mechanical systems itself to simulate "Nature", which is inherently quantum mechanical. Now, 43 years later, the theoretical framework of how such a computer can operate has been developed. Two main important concepts for a potential quantum supremacy, superposition and entanglement, have been exploited to design quantum algorithms to significantly speed up certain tasks. Yet, the specific hardware implementation is still far from being certain, in fact the race between the most promising platforms such as superconducting qubits, bosonic codes, cold atoms, trapped ions, optical computing as well as spin qubits has recently intensified. If one also includes the most mature applications of quantum communication technologies, secure quantum key distribution and quantum random number generators, as part of a quantum information technology ecosystem, we are confronted with a plethora of different materials, concepts, and also operation frequencies. While superconducting qubits, bosonic codes and spin qubits work in the regime of approximately 5 GHz and are controlled by electrical fields, trapped ions, cold atoms, and optical quantum computing operate with light in the infrared or visible range. Consequently, a quantum frequency converter or microwave-optic transducer is required to interface the different frequency domains or establish a long-range network connection with suitable telecom fibers. In fact, the combination of different frequency regimes is also an essential part in our classical modern communication network, where computations are performed in electrical circuits and the information exchange over longer distances happens via optical fibers. However, the specific challenges specific to building a quantum computer, also apply to the development of such a quantum frequency transducer: 1) As we deal with single excitations as the carrier of information, i.e. the smallest possible quantity, the signal can easily be corrupted by other noise sources which needs to be avoided by all means. This is also the reason why microwave quantum computers operate at temperature environments close to zero temperature (< 0.1 Kelvin) to avoid corruption by thermal noise. 2) The frequency interface generally needs to preserve the phase of the signal as an essential part of the quantum state. And 3) Quantum signals cannot be copied which would be a typical strategy to account for errors in classical computers. And finally, there is a challenge specific to microwave-optic transducers: While quantum computers are operating in one specific frequency domain, microwave-optic transducers combine microwave and optical fields in one device. This results in the particular challenge that high-energy optical radiation, which is usually well-shielded from superconducting microwave quantum processors, are now an essential part of the device. The concomitant optical radiation in the operating transducer will inevitably have a detrimental effect on the superconducting microwave components. Together with the requirement of minimal background noise for quantum-limited operation as described above, v heating from the absorption of optical photons within the same device where single microwave excitations are processed forms a formidable challenge. This thesis aims to address this challenge by developing microwave-optic transducers where the impact of optical absorption on superconducting circuits in general and superconducting qubits specifically can be mitigated. In our first approach, we developed a compact device with optimized interaction strengths between the different frequency domains. This minimizes the optical powers used for transducer operation and thus the optical absorption heating. This work was - to the best of our knowledge - the first comprehensive noise study, in an integrated microwave-optic transducer. Unfortunately, we saw that the optical absorption heating added noise way above a single excitation. Consequently, a potential quantum signal would have been buried in the noise, added by the transduction. Building on this insight, we utilized a three-dimensional microwave-optic transducer instead of an integrated device. The larger heat capacity of the macroscopic device with a size of a few millimeters can absorb a larger fraction of the optical heating before it increases the temperature of the device. This allowed us to interface the transducer directly with a superconducting qubit to readout the qubit state in a novel all-optical manner. We showed that the microwave-optic transducer can be operated in a regime in which optical fields don’t harm the sensitive qubit. This is an important prerequisite for the operation of microwave-optic transducers in conjunction with microwave quantum processors and brings the integration and seamless orchestration of different frequency components in a quantum network a step closer.