Quantum feedback is a technique for measuring a qubit and applying appropriate feedback depending on the measurement results. Here, we propose a new on-chip quantum feedback method where the measurement-result information is not taken from the chip to the outside of a dilution refrigerator. This can be done by using a selective qubit-energy shift induced by measurement apparatus. We demonstrate on-chip quantum feedback and succeed in the rapid initialization of a qubit by flipping the qubit state only when we detect the ground state of the qubit. The feedback loop of our quantum feedback method closed on a chip, and so the operating time needed to control a qubit is of the order of 10 ns. This operating time is shorter than with the convectional off-chip feedback method. Our on-chip quantum feedback technique opens many possibilities such as an application to quantum information processing and providing an understanding of the foundation of thermodynamics for quantum systems.
Quantum feedback is a technique for measuring a qubit and applying appropriate feedback depending on the measurement results. Here, we propose a new on-chip quantum feedback method where the measurement-result information is not taken from the chip to the outside of a dilution refrigerator. This can be done by using a selective qubit-energy shift induced by measurement apparatus. We demonstrate on-chip quantum feedback and succeed in the rapid initialization of a qubit by flipping the qubit state only when we detect the ground state of the qubit. The feedback loop of our quantum feedback method closed on a chip, and so the operating time needed to control a qubit is of the order of 10 ns. This operating time is shorter than with the convectional off-chip feedback method. Our on-chip quantum feedback technique opens many possibilities such as an application to quantum information processing and providing an understanding of the foundation of thermodynamics for quantum systems.
Superconducting circuits have recently risen to the forefront of the solid-state prototypes for quantum computing. Reaching the stage of robust quantum computing requires closing the loop between measurement and control of quantum bits (qubits). This thesis presents the realization of feedback control of superconducting qubits based on projective measurement, with initial applications. The first application is a reset operation which initializes a qubit in the ground state fast and on demand. In a second experiment, we transform a cavity into a two-qubit parity meter, which is capable of generating entanglement starting from an unentangled superposition state. We then employ feedback to turn the generation of entanglement from probabilistic to deterministic, thus combining two key ingredients - parity measurement and feedback - of quantum error correction. As a third application, we transform a superconducting qubit into a charge-parity detector to investigate the limits of quasiparticle tunneling to qubit coherence. We find room for at least a tenfold increase in qubit coherence times before quasiparticles become the bottleneck. Finally, we present our latest results towards implementing the bit-flip error correction code in a five-qubit processor and discuss the role of feedback control in the future development of superconducting quantum circuits.
This chapter covers the development of feedback control of superconducting qubits using projective measurement and a discrete set of conditional actions, here referred to as digital feedback. We begin with an overview of the applications of digital feedback in quantum computing. We then introduce an implementation of high-fidelity projective measurement of superconducting qubits. This development lays the ground for closed-loop control based on the binary measurement result. A first application of digital feedback control is fast and deterministic qubit reset, allowing the repeated initialization of a qubit more than an order of magnitude faster than its relaxation rate. A second application employs feedback in a multi-qubit setting to convert the generation of entanglement by parity measurement from probabilistic to deterministic, targeting an entangled state with the desired parity every time.
We discuss the operation of the one-qubit quantum feedback loop, which may be used for initialization of a qubit in a solid-state quantum computer. The continuous monitoring of a quantum state, which makes the feedback possible, is done by means of a weak continuous measurement and processing of the obtained information via quantum Bayesian equations. The properly designed quantum feedback loop can keep the desired phase of a single-qubit quantum coherent oscillations for infinitely long time, even in presence of a dephasing environment. Various nonidealities reduce the fidelity of the feedback synchronization. We report our study of the effects of finite available bandwidth and time delay on the one-qubit quantum feedback performance, and also discuss the effect of environment-induced dephasing.
A theory of feedback-controlled heat transport in quantum systems is presented. It is based on modelling heat engines as driven multipartite systems subject to projective quantum measurements and measurement-conditioned unitary evolutions. The theory unifies various results presented previously in the literature. Feedback control breaks time reversal invariance. This in turn results in the fluctuation relation not being obeyed. Its restoration occurs through appropriate accounting of the gain and use of information via measurements and feedback. We further illustrate an experimental proposal for the realisation of a Maxwell demon using superconducting circuits and single-photon on-chip calorimetry. A two-level qubit acts as a trap-door, which, conditioned on its state, is coupled to either a hot resistor or a cold one. The feedback mechanism alters the temperatures felt by the qubit and can result in an effective inversion of temperature gradient, where heat flows from cold to hot thanks to the gain and use of information.
The advance of experimental techniques in circuit quantum electrodynamics over last decadehas made it possible to monitor the evolution of qubits under continuous measurements in\nreal time . This kind of measurements, as compared to the discrete ones, provides a stream\nof information for feedback to alter the system's quantum dynamics continuously in a desired\nmanner, thus allowing broader possibilities. We obtain the information at a cost, the backaction on the states. However, the back-action turns out not to be just something disturbing \nand harmful to the control but instead can be harnessed, together with the control, to steer the system to our targets. \nThis thesis discusses one such application, namely to use measurements to create entanglement from remote qubits under locally optimal control. It is illustrated that by carefully designing symmetric measurement and feedback operators, we can construct efficient Markovian or non-Markovian protocols which generate N-qubit W,\ngeneral Dicke and Greenberger-Horne-Zeilinger states with high fidelity above 94% up to\nN = 100. In some cases, the fidelity even approaches unity. Following that, we describe how\nto take advantages of the continuous stream of information to protect the unitary dynamics of\na quantum system subject to noises. We develop a practical protocol for continuous operation\nof a quantum error correcting code for protection of coherent evolution due to an encoded\nHamiltonian against environmental errors, using the three qubit bit-flip code and bit-flip\nerrors as a canonical example. We demonstrate, for both quantum memory and adiabatic\nHamiltonians, that the protocol, once optimized, can significantly reduce logical errors with\na performance which is close to the theoretical limit of the bit-flip code's capability. In the\nadiabatic Hamiltonian case, we also propose some novel correction operators instead of the\nconventional ones to further reduce the logical errors.
This thesis presents a series of experiments highlighting measurement back action and decoherence in a basic open quantum system, the superconducting qubit. These observations are enabled by recent advances in amplification close to the quantum limit using Josephson circuits. The information extracted from the system can then be used as input in quantum feedback. A stroboscopic projective readout is performed and a feedback loop is used to correct for detected errors, thus stabilizing an arbitrary predetermined state of the qubit. When monitoring continuously the environment of the qubit by heterodyne detection of its fluorescence, we reconstruct individual quantum trajectories during relaxation. Conditioning this detection to the outcome of a following projective measurement, we access the weak values of the fluorescence signal. Included in a continuous feedback loop, this detection is also used to stabilize an arbitrary state of the qubit. Finally, a last experiment witnesses quantum Zeno dynamics of a resonant microwave mode, entailed by its coupling to the qubit.