Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0602585 · Journal of Physics Condensed Matter

Readout methods and devices for Josephson-junction-based solid-state qubits

G Johansson, L Tornberg, V S Shumeiko, Goran P. Wendin

Published May 12, 2006• 35 citations
arXivHTMLPDF

Abstract

We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular, we focus attention on dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular, we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time.

DOI
10.1088/0953-8984/18/21/s14

Related papers

Readout methods and devices for Josephson-junction-based solid-state qubits

Göran Johansson, Tornberg, Lars, Shumeiko, Vitaly +1 more

We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular, we focus attention on dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular, we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time.

•Jan 1, 2006•18 citations

Josephson-Junction Qubits

Yuriy Makhlin, Gerd Schön, Alexander Shnirman

Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.

Fortschritte der Physik•Sep 1, 2000•9 citations

Read-out of superconducting qubits - a quantum measurement process

Lars Tornberg

In this work we consider measurements on quantum systems emphasizing\non read-out of superconducting qubits. The qubit is always coupled to an\nenvironment, containing a macroscopic number of degrees of freedom. This\nperturbs the qubit and destroys the phase coherence of the quantum state.\nOne tries to minimize this destructive effect by encoding the quantum information in quantum states which do not couple strongly to the dominant\nnoise sources. It is therefore necessary to design read-out methods that can\ndistinguish these states.\n\nWe focus primarily on the single Cooper-pair box (SCB) charge qubit, whose\nproperties are based on the Josephson effect and Coulumb blockade in superconducting electrical circuits. By encoding the information in the qubit\nenergy eigenstates, it is possible to protect it from the most dangerous decoherence source - charge fluctuations in the environment. We investigate\nthe measurement setup, where the SCB is coupled to a lumped element LCoscillator whose resonance frequency is orders of magnitude smaller than the qubit energy splitting. In this regime the SCB will act as an effective positive or negative capacitance, depending on the quantum state. This quantum capacitance then shifts the oscillator resonance frequency, which can be detected in a homodyne phase measurement.\n\nWe have found that reading out a charge qubit by measuring its quantum\ncapacitance in this manner is quantum limited, independently of the oscillator\nquality factor Q. Moreover, we have found that the low-Q oscillator\nis advantageous for the measurement in two ways: first, such an oscillator\nbetter protects the qubit from thermal dephasing, and, second, it allows to\nincrease the speed of the read-out, making it possible to distinguish the qubit states in a single shot measurement.

•Jan 1, 2007•0 citations

Josephson-Junction Qubits and the Readout Process by Single-Electron Transistors

Yuriy Makhlin, Gerd Schön, Alexander Shnirman

Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions, exploiting the coherence of tunneling in the superconducting state combined with the possibility to control individual charges by Coulomb blockade effects (cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits, with logical states differing by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits the resulting quantum state has to be read out. This can be accomplished by coupling a single-electron transistor capacitively to the qubit (cond-mat/9801125). To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. Only when a transport voltage is turned on, the transistor destroys the phase coherence of the qubit; in this case within a short time. The measurement is accomplished after a longer time scale, when the signal resolves the different quantum states. At still longer times the measurement process itself destroys the information about the initial state. We present a suitable set of system parameters, which can be realized by present-day technology.

arXiv:cond-mat/9811029•Nov 3, 1998•10 citations

Dispersive readout scheme for a Josephson phase qubit

Wirth, Tobias

We present experimental results on a dispersive scheme for reading out a Josephson phase qubit. A capacitively shunted dc-SQUID is used as a nonlinear resonator which is inductively coupled to the qubit. We detect the flux state of the qubit by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, we reduce the qubit state measurement time down to 25 microseconds, which is much faster than using the conventional readout performed by switching the SQUID to its non-zero dc voltage state. The demonstrated readout scheme allows for reading out multiple qubits using a single microwave line by employing frequency-division multiplexing.

Verhandlungen der Deutschen Physikalischen Gesellschaft•Jan 1, 2011•0 citations

Simultaneous readout of two charge qubits

Jian Li, Göran Johansson

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.

arXiv:cond-mat/0611143•Physical Review B•Feb 9, 2007•8 citations
We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular, we focus attention on dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular, we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time.
We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular, we focus attention on dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular, we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time.
Among the potential physical implementations of quantum bits (qubits) solid state devices appear most promising for large scale applications and integration in electronic circuits. Devices based on low-capacitance Josephson junctions exploit the coherence of the superconducting state, combined with the possibility to control individual charges by Coulomb blockade effects. The logical states in these systems differ by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. If, in addition, the strength of the Josephson coupling is controlled (e.g. by currents in SQUID loops) the system is ideal for quantum computation. Recent experiments by Nakamura et al. show the feasibility of this approach. In addition to the manipulations of qubits the resulting quantum state has to be read out. This quantum measurement process can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. We investigate the process by analyzing the time-evolution of the density matrix of the coupled system. The measurement process is characterized by three time scales: the dephasing time, which is fast when a dissipative current flows in the SET, a longer ‘measurement time’ needed to read out the signal, and a third, even longer ‘mixing time’, characterizing measurement induced transitions which destroy the information about the initial quantum state. The noise spectrum of the current in the SET displays these time scales and allows their direct observation.
In this work we consider measurements on quantum systems emphasizing\non read-out of superconducting qubits. The qubit is always coupled to an\nenvironment, containing a macroscopic number of degrees of freedom. This\nperturbs the qubit and destroys the phase coherence of the quantum state.\nOne tries to minimize this destructive effect by encoding the quantum information in quantum states which do not couple strongly to the dominant\nnoise sources. It is therefore necessary to design read-out methods that can\ndistinguish these states.\n\nWe focus primarily on the single Cooper-pair box (SCB) charge qubit, whose\nproperties are based on the Josephson effect and Coulumb blockade in superconducting electrical circuits. By encoding the information in the qubit\nenergy eigenstates, it is possible to protect it from the most dangerous decoherence source - charge fluctuations in the environment. We investigate\nthe measurement setup, where the SCB is coupled to a lumped element LCoscillator whose resonance frequency is orders of magnitude smaller than the qubit energy splitting. In this regime the SCB will act as an effective positive or negative capacitance, depending on the quantum state. This quantum capacitance then shifts the oscillator resonance frequency, which can be detected in a homodyne phase measurement.\n\nWe have found that reading out a charge qubit by measuring its quantum\ncapacitance in this manner is quantum limited, independently of the oscillator\nquality factor Q. Moreover, we have found that the low-Q oscillator\nis advantageous for the measurement in two ways: first, such an oscillator\nbetter protects the qubit from thermal dephasing, and, second, it allows to\nincrease the speed of the read-out, making it possible to distinguish the qubit states in a single shot measurement.
Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions, exploiting the coherence of tunneling in the superconducting state combined with the possibility to control individual charges by Coulomb blockade effects (cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits, with logical states differing by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits the resulting quantum state has to be read out. This can be accomplished by coupling a single-electron transistor capacitively to the qubit (cond-mat/9801125). To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. Only when a transport voltage is turned on, the transistor destroys the phase coherence of the qubit; in this case within a short time. The measurement is accomplished after a longer time scale, when the signal resolves the different quantum states. At still longer times the measurement process itself destroys the information about the initial state. We present a suitable set of system parameters, which can be realized by present-day technology.
We present experimental results on a dispersive scheme for reading out a Josephson phase qubit. A capacitively shunted dc-SQUID is used as a nonlinear resonator which is inductively coupled to the qubit. We detect the flux state of the qubit by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, we reduce the qubit state measurement time down to 25 microseconds, which is much faster than using the conventional readout performed by switching the SQUID to its non-zero dc voltage state. The demonstrated readout scheme allows for reading out multiple qubits using a single microwave line by employing frequency-division multiplexing.
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.