Analytic Controllability of Time-Dependent Quantum Control Systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page

A universal gap for non-spin quantum control systems

We prove the existence of a universal gap for minimum time controllability of finite dimensional quantum systems, except for some basic representations of spin groups. This is equivalent to the existence of a gap in the diameter of orbit spaces of the corresponding compact connected Lie group unitary actions on the Hermitian spheres

Effects of uncertainties and errors on Lyapunov control

Lyapunov control (open-loop) is often confronted with uncertainties and errors in practical applications. In this paper, we analyze the robustness of Lyapunov control against the uncertainties and errors in quantum control systems. The analysis is carried out through examinations of uncertainties and errors, calculations of the control fidelity under influences of the certainties and errors, as well as discussions on the caused effects. Two examples, a closed control system and an open control system, are presented to illustrate the general formulism.Comment: 4 pages, 5 figure

Higher order traps for some strongly degenerate quantum control systems

Quantum control is necessary for a variety of modern quantum technologies as it allows to optimally manipulate quantum systems. An important problem in quantum control is to establish whether the control objective functional has trapping behaviour or no, namely if it has or no traps -- controls from which it is difficult to escape by local search optimization methods. Higher order traps were previously introduced in [A. N. Pechen, D. J. Tannor, "Are there traps in quantum control landscapes?", Phys. Rev. Lett., 106 (2011), 120402], where 3-rd order traps were found. In this note we show that traps of arbitrarily high order exist for controllable quantum systems with special symmetry in the Hamiltonian.Comment: 4 pages, final versio

A system design approach toward integrated cryogenic quantum control systems

In this paper, we provide a system level perspective on the design of control electronics for large scale quantum systems. Quantum computing systems with high-fidelity control and readout, coherent coupling, calibrated gates, and reconfigurable circuits with low error rates are expected to have superior quantum volumes. Cryogenic CMOS plays a crucial role in the realization of scalable quantum computers, by minimizing the feature size, lowering the cost, power consumption, and implementing low latency error correction. Our approach toward achieving scalable feed-back based control systems includes the design of memory based arbitrary waveform generators (AWG's), wide band radio frequency analog to digital converters, integrated amplifier chain, and state discriminators that can be synchronized with gate sequences. Digitally assisted designs, when implemented in an advanced CMOS node such as 7 nm can reap the benefits of low power due to scaling. A qubit readout chain demands several amplification stages before the digitizer. We propose the co-integration of our in-house developed InP HEMT LNAs with CMOS LNA stages to achieve the required gain at the digitizer input with minimal area. Our approach using high impedance matching between the HEMT LNA and the cryogenic CMOS receiver can relax the design constraints of an inverter-based CMOS LNA, paving the way toward a fully integrated qubit readout chain. The qubit state discriminator consists of a digital signal processor that computes the qubit state from the digitizer output and a pre-determined threshold. The proposed system realizes feedback-based optimal control for error mitigation and reduction of the required data rate through the serial interface to room temperature electronics