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Physica C Superconductivity

Reading-out the state of a qubit: an analysis of the quantum measurement process

Gerd Schön, Yuriy Makhlin, Alexander Shnirman

Published Apr 1, 2001• 2 citations
Publisher
DOI
10.1016/s0921-4534(00)01704-4

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For quantum computers to become reality, not only do the qubits have to be carefully engineered to be well isolated during operation time, but this also puts great strain on the measurement setup. We have looked at the backaction from a single-electron transistor (SET), operated both in the normal and in the superconducting state, on a single Cooper-pair box qubit. We have also designed a new read-out setup for a flux qubit using a Cooper-pair transistor that would allow read-out at the flux degeneracy point. In the first case we calculate the mixing time and the influence on the qubit steady-state distribution. We find that the mixing time is larger than typical experimental measurement times, indicating the possibility of single shot read-out. For the steady-state distribution of the qubit, we calculate the Coulomb staircase, finding additional structure due to the noise in the SET. For the flux qubit we design a read-out scheme involving a quantum flip-flop process, where the measurement outcome results in the presence or absence of an incoherent tunneling process. We estimate read-out and mixing times and find that single shot read-out should be achievable.
Measurement of coupled quantum systems plays a central role in quantum information processing. We have realized independent single-shot read-out of two electron spins in a double quantum dot. The read-out method is allelectrical, cross-talk between the two measurements is negligible and read-out fidelities are about 86% on average. This allows us to directly probe the anticorrelations between two spins prepared in a singlet state, and to demonstrate the operation of the two-qubit exchange gate on a complete set of basis states. The results provide a possible route to the realization and efficient
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.