In particular, I appreciate being open to trying new things in the lab and supporting all my research wholeheartedly. Also, I would like to express special gratitude to my colleague Xueyue (Sherry) Zhang, with whom I spent more time in the laboratory and in the office.
INTRODUCTION
Quantum light-matter interface
Here, the first factor is the ratio between the scattering cross section 𝜎0 of the atom and the effective state area 𝐴. In this case, the efficiency of the coupling is enhanced by the number of passes a photon makes through the atom before leaking out of the cavity.
Quantum computation
A widely accepted viable approach for quantum error correction is the surface code [ 65 , 66 ], which is based on topological error correcting codes called toric code invented by Sergey Bravyi and Alexei Kitaev [ 67 ]. In parallel with the frontier of pushing the frontier of quantum error correction, new types of building blocks for quantum computing are constantly being developed.
Quantum many-body physics
Light-matter interface Quantum Computation
Many-body PhysicsWorkOur
Outline of the thesis
Next, I will describe the experimental techniques used throughout the work in the thesis in Chapter 3. In Chapter 4 I discuss the interaction between superconducting qubits mediated by a common waveguide channel in the strong coupling regime, published in Ref.
WAVEGUIDE QUANTUM ELECTRODYNAMICS
- From cavity QED to waveguide QED
- Quantum emitters coupled to a waveguide with linear dispersion
- Waveguide QED in a dispersive photonic channel
- Experimental realizations of waveguide QED
This can be attributed to the destructive interference of the incident photonic wave packet with the emitter's radiation in the forward direction. First, the magnitude of 𝑐𝑥 decays exponentially on a length scale 𝜉 with respect to the location 𝑥 = 𝑥0 of the emitter.
DEVICE FABRICATION AND EXPERIMENTAL TECHNIQUES
- Fabrication of superconducting quantum circuits
- Microwave packaging of quantum devices
- Cryogenic setup
- Room-temperature electronics and signal processing
In the case of new packaging, the fabricated chip is attached to substrates using GE Varnish (VGE-7031) to provide strong mechanical support against wire bonding and the cryogenic cooler [155]. Throughout the figure, signals corresponding to the real (imaginary) part of the corresponding complex phasor representation are colored red (blue).
WAVEGUIDE-MEDIATED COOPERATIVE INTERACTIONS OF SUPERCONDUCTING QUBITS
- Introduction
- Strong-coupling regime of waveguide QED: cavity QED with atom-like mirrorsmirrors
- Spectroscopic characterizations
- Time-domain characterizations
- Compound atomic mirrors
- Methods QubitsQubits
𝐷iis coupled to the excited state of the probe qubit|𝑒ip with a cooperatively enhanced rate of 2𝐽 = p. After excitation of the probe qubit, we use a fast (5 ns) flux bias pulse to tune the probe qubit. 4.4 we show a timing diagram and plot three measured curves of the probe qubit's population dynamics versus 𝜏.
The tunable interaction time in our measurement sequence also allows state transfer between the probe qubit and the dark state of mirror qubits using an iSWAP gate. Finally, we measured the state of the probe qubit and performed an exponential fit to the resulting decay curve.
DEVELOPMENT OF SUPERCONDUCTING METAMATERIALS FOR WAVEGUIDE QED
- Introduction
- Band-structure analysis and spectroscopy
- Physical realization using lumped-element resonators
- Disorder and Anderson localization
- Anomalous Lamb shift near the band-edge
- Enhancement and suppression of spontaneous emission
- Discussion
An alternative approach to fitting dispersion in the microwave domain is to take advantage of the metamaterial concept. The vertical axis marks the distance from the qubit (𝑥/𝑑) in units of the lattice period𝑑. Fabrication of the waveguide is performed using electron beam deposited Al film (See Methods).
Another signature of the qubit-waveguide interaction is the change in the spontaneous emission rate of the qubit. Due to the weaker scattering at the upper end of the bandpass, the photon-bound state stretching has a noticeable impact on the qubit lifetime in the finite-length waveguide 𝑁 =9.
QUANTUM ELECTRODYNAMICS IN A TOPOLOGICAL WAVEGUIDE
- Introduction
- Description of the topological waveguide
- Properties of quantum emitters coupled to the topological waveguide The non-trivial properties of the topological waveguide can be accessed by couplingThe non-trivial properties of the topological waveguide can be accessed by coupling
- Quantum state transfer via topological edge states
- Discussion and outlook
For qubits located within the center bandgap, the topology of the waveguide manifests itself in the spatial profile of the resulting qubit-photon bound states. In general, bound states with a symmetric photonic envelope arise due to the inversion symmetry of the photonic bath with respect to the qubit location [215]. The opposite directionality is expected in the case of the topological phase of the waveguide.
The topology of the SSH model can be visualized by plotting the complex-valued momentum-space coupling 𝑓(𝑘) for values𝑘 in the first Brillouin zone (Fig. 6.3a). After a variable frequency modulation pulse duration, the state of the qubit is read.
AN INTERMEDIATE-SCALE QUANTUM PROCESSOR BASED ON DISPERSIVE WAVEGUIDE QED
- Introduction
- Metamaterial quantum processor
- Single-qubit characterization
- Interaction between qubit-photon bound states
- High-fidelity single-shot readout
- Quantum many-body dynamics
- Discussion and outlook
Here, ˆ𝑎𝑛 ( ˆ𝑎† . 𝑛) is the cavity annihilation (creation) operator at the 𝑛th site of the metamaterial. Underneath this description lies the transmission band at [−2𝐽 ,2𝐽] declarations with respect to the resonant frequency𝜔𝑐of the cavity. We also perform measurements of the anharmonicity 𝛼=𝜔𝑒 𝑓 −𝜔𝑔 𝑒 of bound qubit-photon states in the bandgap regime by performing spectroscopy conditioned by the qubit initialized in the first excited state |𝑒i (Figure 7.3b).
A remarkable property of the metamaterial waveguide is the interaction between qubit-photon bound states arising from the spatial overlap of photonic tails, enabling qubit-qubit connectivity beyond the nearest neighbors. In the simplest description of the metamaterial waveguide in terms of coupled cavity array discussed in Eq. 7.1), it is known that the coupling𝐽𝑖 𝑗 between a pair of qubit photon-bound states associated with qubits at locations (𝑖, 𝑗) of the metamaterial is given by [205].
OUTLOOK AND FUTURE DIRECTIONS
Opportunities for studying many-body physics
We envisage an experimental investigation of the canonical model in a new regime with an unprecedented degree of control and with new methods for the dissipative stabilization of many-body quantum states [101, 277]. We are currently working on the development of hybrid quantum-classical protocols to decode encoded quantum information from chaotic many-body quantum evolution by measurement and feed-forward. Recently, theoretical studies have been performed on the competition between entanglement growth in a quantum many-body system and local projective measurements [292–295] .
It was shown that if the rate of randomly interspersed local projective measurement exceeds a certain threshold, the entanglement growth of the quantum many-body system is constrained to follow the area law. Experimental investigation of the measurement-induced phase transition has been a formidable task as it requires the ability to perform random center-circuit readout of arbitrary subsets of qubits without fully collapsing the many-body wavefunction.
New directions for scaling up quantum processors
A pioneering experiment performed in a trapped ion quantum simulator overcame this challenge by exploiting entangled gates between the system and ancilla qubits to push the measurement to the end of the circuit [296]. However, this method limits the total number of measurements to the number of anvils and is therefore only applicable for short time evolution and small system size. Using the superconducting metamaterial waveguide as an efficient Purcell filter for the readout, we expect to probe the full regimes of the measurement-induced phase transition, including its criticality.
BIBLIOGRAPHY
FABRICATION DETAILS
- Cleaning the chip tray and glass beakers
- Chip cleaning
- Pre-spin/bake or pre-evaporation cleaning
- Spin & bake
- Electron-beam lithography
- Development
- Evaporation
- Liftoff
We perform HF wet cleaning before resist spinning and annealing or before e-beam evaporation as long as there is no aluminum deposited on the chip. The chip is also baked on a hot plate either before or after turning the resistor. Finally, the chip is spun again with 950 PMMA A9 resist and annealed with identical settings as before.
We develop the chip in ZED-N50 developer for 2 minutes and 30 seconds, followed by rinsing in methyl isobutyl ketone (MIBK) for 30 seconds and gently blow-drying with a nitrogen gun. The chip is then rinsed in IPA for 10 seconds, followed by blow-drying with nitrogen.
DESIGNING JOSEPHSON JUNCTIONS FOR TRANSMON QUBITS
- Basics
- Design
- Fabrication of test junctions
- Imaging
- Determination of critical dimensions
B.1a, in which we can observe a clear boundary of a Josephson junction precisely within about a few nanometers. Note that images taken with the Hitachi S4300 SEM in the Painter lab cleanroom did not have enough resolution to accurately determine the critical dimensions of Josephson junctions. The dimensional calibration in the Hitachi S4300 SEM also appears to be unreliable in terms of accuracy within about 40 nm, which can often be greater than 10% of the dimensions of Josephson junctions.
The critical dimensions of Josephson junctions can be obtained by using built-in scanning electron microscope software to draw lines on the image and extract the corresponding dimensions. For a fast and reliable determination of critical dimensions of Josephson junctions, I have developed an image processing routine to detect the boundary of Josephson junctions from an image and calculate the area.
SUPPLEMENTARY INFORMATION FOR CHAPTER 4
Spectroscopic measurement of individual qubits
Now, let us consider the case where a qubit is coupled to the waveguide with the decay rate of Γ1D. In the following, we define the rate of parasitic decoherence of the qubit as Γ0=2Γ2−Γ1D = Γloss+2Γ𝜑, where Γloss denotes the rate of decay of the qubit induced by channels other than the waveguide. Using this relation, we can estimate the upper limit of the ambient temperature based on our extinction measurement.
The minimum transmittance was measured at |𝑡 before (after) installation of the attenuator, which corresponds to the upper limit of the number of thermal photons ¯𝑛th. With an attenuator this corresponds to a temperature of 43 mK, close to the temperature values given in ref.
Detailed modeling of the atomic cavity
To reach the dark state of the atomic cavity, we first apply a local gate |𝑔ip|𝐺i. The decay rate of the dark state scales as Γ1D,D ≈ Γ1D(Δ𝜙)2/2 which just adds. a small contribution to the dark state decay rate. The dephasing rate of the probe qubit is derived from time domain population decay and Ramsey order measurements Γ𝜑 = Γ2−Γ1/2.
In the case of mirror qubits, the table shows effective single qubit parameters derived from measurements of the dark state lifetime. Similarly, the waveguide decay rate of mirror qubits is found from the spectroscopy of the bright collective state as Γ1D,m = Γ1D,B/2.
Shelving
The decay rate in this model can be found by modeling the bright state as a cavity in the Purcell regime, and calculating the decay rate of the dark state using the Purcell factor ash4 ˜Δ𝑑(𝑡)2/ΓBi. 2Ω1, where Ω1 is the Rabi frequency of one of the mirror qubits from the probe signal along the waveguide. 1 From the master equation, the time evolution of a portion of the density matrix elements is written approximately as.
In the measurement, we use the state transfer protocol to transfer part of the ground state population to the dark state. The lower value of the dark state population can be understood considering the finite dark state lifetime (757 ns), which leads to a partial population decay during the measurement time (the single-shot measurement time is set by the duration of the input pulse).
SUPPLEMENTARY INFORMATION FOR CHAPTER 5
- Band structure analysis
- Characterization and modeling of the metamaterial waveguide
- Characterization of lumped-element microwave resonators
- Disorder and Anderson localization
- Qubit frequency shift and lifetime Circuit theory modeling
- Group delay and the qubit lifetime profile
- Scaling the waveguide length
It is clear that reducing the group velocity increases the radiative decay rate of the qubit. Several competing effects in the design of the metamaterial waveguide affect its utility within a waveguide QED environment. The parameters 𝜔q and𝜔0,𝑚 indicate the fundamental transition frequency of the qubit and the resonance frequency of the waveguide mode, respectively.
The normalized slope of the lifetime profile near the band edge can be written as Scaling the length of the waveguide to the extreme limits requires dealing with a number of technical challenges.
SUPPLEMENTARY INFORMATION FOR CHAPTER 6
Modeling of the topological waveguide
By calculating the inverse of this relation, the Lagrangian (E.1) of the system can be rewritten in 𝑘-space as. The Hamiltonian can be written as a sum ˆ𝐻 = 𝐻ˆ0+𝑉ˆ, where. uncoupled” part ˆ𝐻0 and coupling term ˆ𝑉 is written as ˆ. E.5) with the effective self-capacitance𝐶eff. We first consider the band structure of the system within the rotating wave approximation (RWA), discarding the counter-rotating terms ˆ𝑎𝑏ˆ and ˆ𝑎†𝑏ˆ† i.
This assumption is known to be valid when the strength of the couplings |𝑔𝐿(𝑘) |, |𝑔𝐶(𝑘) | is small compared to the decoupled oscillator frequency 𝜔0(𝑘). E.2, the kernel of the Hamiltonian in Eq. E.10) has an inversion symmetry in the sublattice unit cell known to result in bands with quantized Zak phase [260].
