Continuous measurements for control of superconducting quantum circuits

Abstract

Developments over the last two decades have opened the path towards quantum technologies in many quantum systems, such as cold atoms, trapped ions, cavity-quantum electrodynamics (QED), and circuit-QED. However, the fragility of quantum states to the effects of measurement and decoherence still poses one of the greatest challenges in quantum technology. An imperative capability in this path is quantum feedback, as it enhances the control possibilities and allows for prolonging coherence times through quantum error correction. While changing parameters from shot to shot of an experiment or procedure can be considered feedback, quantum mechanics also allows for the intriguing possibility of performing feedback operations during the measurement process itself. This broader approach to measurements leads to the concepts of weak measurement, quantum trajectories, and numerous types of feedback with no classical analogs. These types of processes are the primary focus of this review. We introduce the concept of quantum feedback in the context of circuit-QED, an experimental platform with significant potential in quantum feedback and technology. We then discuss several experiments and see how they elucidate the concepts of continuous measurements and feedback. We conclude with an overview of coherent feedback, with application to fault-tolerant error correction.

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups

“…Advancing the normalized density operator by one increment, one finds and this yields the conventional stochastic master equation [ 24 , 25 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 ], which is written in terms of the innovations. It is instructive to write the first term as This term, nonlinear in because of the expectation value , describes how the outcomes affect the evolving quantum state: each innovation , drawn from the Born-rule measure, is conjugate to the deviation of the corresponding observable from its expected value.…”

Monitoring fast superconducting qubit dynamics using a neural network

“…Quantum trajectory theory describes how an observer's estimate of a quantum state evolves as it is updated with a weak measurement record [8,61]. The measurement record is translated to quantum state evolution by first applying the unitary evolution and then updating the state with the measurement record at each time step, as the backaction of the measurement on the state can be derived [25]. Thus, with knowledge of the initial state and the Hamiltonian driving unitary evolution, the density matrix ρ ij (t i ) can be repeatedly updated.…”

“…Weak measurements allow the observer to reconstruct the dynamics of a quantum system, and to track the evolution of a wavefunction before its collapse to an eigenstate. For superconducting quantum circuits in particular, reconstructing individual quantum trajectories [1][2][3][4][5][6][7][8][9][10] has served as a tool to monitor quantum jumps [11][12][13][14], track diffusion statistics [15][16][17][18], generate entanglement via measurement [19,20], coherently control quantum evolution using feedback [21][22][23][24][25], and implement continuous quantum error correction [26][27][28][29]. In weak measurements with superconducting qubits coupled to a readout resonator, the dynamics of the latter are typically much faster than the former.…”

Demonstration of universal control between non-interacting qubits using the Quantum Zeno effect

“…In contrast, incoherent control is based on non-deterministic measurement outcomes to prepare the system for the desired state. The two schemes may complement each other to enrich quantum control [1][2][3][4][5][6][7][8] . On the boundary between the two schemes lies the quantum Zeno effect, in which frequent measurements effectively freeze the system dynamics, holding the system at an eigenstate of the measurement observable.…”