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Physical Review A

Measurement of a charge qubit using a single-electron transistor based on a triple quantum dot

Alexander V. Tsukanov

Published Dec 4, 2019• 12 citations
Publisher

Abstract

A scheme for determining an arbitrary pure state of a charge qubit by measuring a steady-state current through a single-electron transistor is proposed. In order to increase the sensitivity of the transistor its operating part consists of three quantum dots, the energy levels of which form a symmetrical configuration. Such a choice makes it possible to realize high-precision measurements in a nonresonant steady-state regime when a maximum distance of the qubit from this structure is several hundreds of nanometers. Time-dependent populations of the structure states are obtained; a current and a measurement contrast are calculated as functions of system geometric parameters and the optimal values of these parameters are found.

DOI
10.1103/physreva.100.062305

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A scheme for determining an arbitrary pure state of a charge qubit by measuring a steady-state current through a single-electron transistor is proposed. In order to increase the sensitivity of the transistor its operating part consists of three quantum dots, the energy levels of which form a symmetrical configuration. Such a choice makes it possible to realize high-precision measurements in a nonresonant steady-state regime when a maximum distance of the qubit from this structure is several hundreds of nanometers. Time-dependent populations of the structure states are obtained; a current and a measurement contrast are calculated as functions of system geometric parameters and the optimal values of these parameters are found.
Abstract A circuit of a measuring chip for determining an arbitrary pure state of a charge qubit is proposed. The strength of the current flowing through a single-electron transistor in the steady-state mode depends on the state of the qubit. To enhance the sensitivity of the transistor, its working part is built from three quantum dots (QDs) with the energy levels forming a symmetric configuration. The parameters of the system are calculated using a microscopic model of two-dimensional QDs. The time dependences of the population of the structure’s states are obtained and the current strength, sensitivity, and measuring contrast as functions of the geometric parameters of the system are determined. The effect of dissipative processes related to the acoustic phonons on the measurements is investigated and the rates of electron relaxation and dephasing in a two-level system are calculated.
Abstract A scheme for measuring the state of a charge qubit on a semiconductor single-electron double quantum dot (DQD) coupled to a photonic molecule (PM) consisting of three optical microresonators is proposed. The DQD that is the qubit plays the role of a nonlinear element whose electron state affects a PM response to an external laser field. Analysis of the spectroscopic response of the structure in the steady-state regime allows one to determine the state of the qubit. As an example, the spectrum of the PM formed by three GaAs microdisk resonators are calculated. The effect of various system parameters on the measuring contrast and the signal-to-noise ratio is studied. It is shown that this ratio can reach values of 15 000–20 000 for certain sets of parameters.
Single-electron transistors have been proposed to be used as a read-out device for Cooper pair charge qubits. Here we show that a coupled superconducting transistor at a threshold voltage is much more effective in measuring the state of a qubit than a normal-metal transistor at the same voltage range. The effect of the superconducting gap is to almost completely block the current through the transistor when the qubit is in the logical state 1, compared to the mere diminishment of the current in the normal-metal case. The time evolution of the system is solved when the measuring device is driven out of equilibrium, the effect of higher-order contributions is examined and the setting is analyzed numerically for parameters accessible by lithographic aluminum structures.
We consider a system of two solid state charge qubits, coupled to a single readout device, consisting of a single-electron transistor (SET). The conductance of each tunnel junction is influenced by its neighboring qubit, and thus the current through the transistor is determined by the qubits' state. The full counting statistics of the electrons passing the transistor is calculated, and we discuss qubit dephasing, as well as the quantum efficiency of the readout. The current measurement is then compared to readout using real-time detection of the SET island's charge state. For the latter method we show that the quantum efficiency is always unity. Comparing the two methods a simple geometrical interpretation of the quantum efficiency of the current measurement appears. Finally, we note that full quantum efficiency in some cases can be achieved measuring the average charge of the SET island, in addition to the average current.
We report on an optimal single-electron charge qubit for a solid-state double quantum dot (DQD) system and analyse its dynamics under a time-dependent linear detuning, using GPU accelerated numerical solutions to the time-dependent Schrödinger equation. The optimal qubit is found to have basis states defined as the symmetric and antisymmetric linear combinations of the lowest energy bonding and anti-bonding states of the DQD at zero bias. In contrast to charge qubits defined by the two localised ground states of the uncoupled DQD, this choice of the basis causes the resulting dynamics to have a maximal overlap with an idealised two-state model. Our optimal qubit basis states are not localised to a single quantum dot and, as such, initialising the qubit requires a particular sequence of gate pulses to take the system from an initial fiducial state of the DQD to the logical 000 or 111. We determine this sequence using pulses that incorporate the expected experimental finite rise times. We also show how to perform arbitrary single qubit operations on the Bloch sphere using spin-echo type pulsing, allowing us to obtain any qubit state with at most two single pulses. Measurement of the optimal qubits is achieved by determining the probability of finding the electron in one of the dots.
In quantum computing based on semiconductor quantum dots, adding dots (or just electrons) allows a wider search for an optimal qubit-encoding scheme that is both controllable and coherent. This work reports experiments to realize a hybrid charge-spin qubit in a linear triple quantum dot with asymmetric tunnel couplings, in a multielectron charge configuration. This qubit's energy splitting can be tuned conveniently over a wide range, and the authors attain qualitative understanding of the observations in terms of a three-electron system. This should stimulate further exploration of quantum coherent dynamics in the few-electron regime for semiconductor quantum processors.