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Physical Review B

Optimal local control of coherent dynamics in custom-made nanostructures

Thomas Blasi, Mario F. Borunda, E. Räsänen, Eric J. Heller

Published Jun 13, 2013• 17 citations
Publisher

Abstract

We apply quantum optimal control theory to establish a local voltage-control scheme that operates in conjunction with the numerically exact solution of the time-dependent Schr\"odinger equation. The scheme is demonstrated for high-fidelity coherent control of electronic charge in semiconductor double quantum dots. We find tailored gate voltages in the viable gigahertz regime that drive the system to a desired charge configuration with $>99%$ yield. The results could be immediately verified in experiments and would play an important role in applications towards solid-state quantum computing.

DOI
10.1103/physrevb.87.241303

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We apply quantum optimal control theory to establish a local voltage-control scheme that operates in conjunction with the numerically exact solution of the time-dependent Schr"odinger equation. The scheme is demonstrated for high-fidelity coherent control of electronic charge in semiconductor double quantum dots. We find tailored gate voltages in the viable gigahertz regime that drive the system to a desired charge configuration with >99>99%>99 yield. The results could be immediately verified in experiments and would play an important role in applications towards solid-state quantum computing.
Abstract Semiconductor quantum dots are ideal candidates for quantum information applications in solid-state technology. However, advanced theoretical and experimental tools are required to coherently control, for example, the electronic charge in these systems. Here we demonstrate how quantum optimal control theory provides a powerful way to manipulate the electronic structure of coupled quantum dots with an extremely high fidelity. As alternative control fields we apply both laser pulses as well as electric gates, respectively. We focus on double and triple quantum dots containing a single electron or two electrons interacting via Coulomb repulsion. In the two-electron situation we also briefly demonstrate the challenges of timedependent density-functional theory within the adiabatic local-density approximation to produce comparable results with the numerically exact approach.
We present theory and calculations for coherent high-fidelity quantum control of many-particle states in semiconductor quantum wells. We show that coupling a two-electron double quantum dot to a terahertz optical source enables targeted excitations that are one to two orders of magnitude faster and significantly more accurate than those obtained with electric gates. The optical fields subject to physical constraints are obtained through quantum optimal control theory that we apply in conjunction with the numerically exact solution of the time-dependent Schr\"odinger equation. Our ability to coherently control arbitrary two-electron states, and to maximize the entanglement, opens up further perspectives in solid-state quantum information.
We use optimal control theory to construct external electric fields that coherently transfer the electronic charge in a double quantum-dot system. Without truncation of the eigenstates we operate on desired superpositions of the states in order to prepare the system to a localized state and to coherently transfer the charge from one well to another. Within a fixed time interval, the optimal processes are shown to occur through several excited states. The obtained yields are generally between 99% and 99.99% depending on the field constraints, and they are not dramatically affected by strict frequency filters which make the fields (e.g., laser pulses) closer to experimental realism. Finally we demonstrate that our scheme provides simple access to hundreds of sequential processes in charge localization while preserving the high fidelity.
We propose an efficient control protocol for charge transfer in a double quantum dot. We consider numerically a two-dimensional model system, where the quantum dots are subjected to time-dependent electric fields corresponding to experimental gate voltages. Our protocol enables navigation in the charge stability diagram from a state to another through controllable variation of the fields. We show that the well-known adiabatic Landau-Zener transition-when supplemented with a time-dependent field tailored with optimal control theory-can remarkably improve the transition speed. The results also lead to a simple control scheme obtained from the experimental charge stability diagram that requires only a single parameter. Eventually, we can achieve the ultrafast performance of the composite pulse protocol that allows the system to be driven at the quantum speed limit.
The double-quantum-dot device benefits from the advantages of both the spin and charge qubits, while offering ways to mitigate their drawbacks. Careful gate voltage modulation can grant greater spinlike or chargelike dynamics to the device, yielding long coherence times with the former and high electrical susceptibility with the latter for electrically driven spin rotations or coherent interactions with microwave photons. As this architecture is a serious contender for the realization of a versatile physical qubit, improving its control is a critical step toward building a large-scale spin-based universal quantum computer. We show that optimal control pulses generated using the gradient ascent pulse engineering algorithm can yield higher fidelity operating regime transfers than can be achieved using linear methods.
We theoretically investigate electron spin operations driven by applied electric fields in a semiconductor double quantum dot (DQD) formed in a nanowire with longitudinal potential modulated by local gating. We develop a model that describes the process of loading and unloading the DQD taking into account the overlap between the electron wave function and the leads. Such a model considers the spatial occupation and the spin Pauli blockade in a time-dependent fashion due to the highly mixed states driven by the external electric field. Moreover, we present a road map based on the quantum optimal control theory (QOCT) to find a specific electric field that performs two-qubit quantum gates on a faster timescale and with higher possible fidelity. By employing the QOCT, we demonstrate the possibility of performing within high efficiency a universal set of quantum gates ${$cnot, H, and $\mathrm{T}}$, where cnot is the controlled-not gate, H is the Hadamard gate, and T is the $\ensuremath{\pi}/8$ gate, even in the presence of the loading/unloading process and charge noise effects. Furthermore, by varying the intensity of the applied magnetic field BBB, the optimized fidelity of the gates oscillates with a period inversely proportional to the gate operation time tf{t}_{f}tf​. This behavior can be useful to attain higher fidelity for fast gate operations (>1>1>1 GHz) by appropriately choosing BBB and tf{t}_{f}tf​ to produce a maximum of the oscillation.