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International Conference on Solid State Devices and Materials (SSDM)

Measurement of Two-Qubit States using a Two-Island Single Electron Transistor

Tetsufumi Tanamoto, Shinobu Fujita, Xuedong Hu

Published Sep 18, 2004• 0 citations
Publisher

Abstract

Department of Physics, University at Buffalo, SUNY, Buffalo, NY 14260-1500(Dated: May 20, 2011)We solve the master equations of two charged qubits measured by a single-electron transistor(SET) consisted of two islands. We show that in the sequential tunneling regime the SET currentcan be used for reading out results of quantum calculations and providing evidences of two-qubitentanglement, especially when the interaction between the two qubits is weak.

DOI
10.7567/ssdm.2004.h-1-3

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Department of Physics, University at Buffalo, SUNY, Buffalo, NY 14260-1500(Dated: May 20, 2011)We solve the master equations of two charged qubits measured by a single-electron transistor(SET) consisted of two islands. We show that in the sequential tunneling regime the SET currentcan be used for reading out results of quantum calculations and providing evidences of two-qubitentanglement, especially when the interaction between the two qubits is weak.
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 an experimental observation of the backaction of a single-electron transistor (SET) measuring the Coulomb staircase of a single-electron box. As current flows through the SET, the charge state of the SET island fluctuates. These fluctuations capacitively couple to the box and cause changes in the position, width, and asymmetry of the Coulomb staircase. A sequential tunneling model accurately recreates these effects, confirming this mechanism of the backaction of a SET. This is a first step toward understanding the effects of quantum measurement on solid-state qubits.
We report an experimental observation of the backaction of a Single Electron Transistor (SET) measuring the Coulomb staircase of a single electron box. As current flows through the SET, the charge state of the SET island fluctuates. These fluctuations capacitively couple to the box and cause changes in the position, width, and asymmetry of the Coulomb staircase. A sequential tunnelling model accurately recreates these effects, confirming this mechanism of the backaction of an SET. This is a first step towards understanding the effects of quantum measurement on solid state qubits.
Quantum information processing systems can be used in a variety of applications. Among proposed realizations of quantum bits nano-electronic circuits appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. In one limit, two logic states of the quantum bit differ by a Cooper pair charge, 2e, on a superconducting island. In the other limit different magnetic fluxes penetrate a superconducting loop in two states. Single-qubit and two-qubit logic operations can be performed by means of voltage or current pulses. Weak coupling to the environment allows a series of these elementary steps before the phase coherence is lost. To read out the result of the computation a quantum measurement is needed. For charge qubits this can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. Monitoring the current in the transistor one can extract the information about the state of the qubit. We discuss recent experiments and present a suitable set of circuit parameters available with the present-day technology.
We consider charge qubit monitoring (continuous-in-time weak measurement) by a single-electron transistor (SET) operating in the sequential-tunneling regime. We show that commonly used master equations for this regime are not of the Lindblad form that is necessary and sufficient for guaranteeing valid physical states. In this paper we derive a Lindblad-form master equation and a corresponding quantum trajectory model for continuous measurement of the charge qubit by a SET. Our approach requires that the SET-qubit coupling be strong compared to the SET tunneling rates. We present an analysis of the quality of the qubit measurement in this model (sensitivity versus back action). Typically, the strong coupling when the SET island is occupied causes back action on the qubit beyond the quantum back action necessary for its sensitivity, and hence the conditioned qubit state is mixed. However, in one strongly coupled, asymmetric regime, the SET can approach the limit of an ideal detector with an almost pure conditioned state. We also quantify the quality of the SET using more traditional concepts such as the measurement time and decoherence time, which we have generalized so as to treat the strongly responding regime.