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Science

Coherent State Evolution in a Superconducting Qubit from Partial-Collapse Measurement

Nadav Y. Katz, M. Ansmann, Radoslaw C. Bialczak, Erik A. Lucero, R. McDermott, M. Neeley, Matthias Steffen, Eva Maria Weig, Andrew N. Cleland, John M. Martinis, Alexander N. Korotkov

Published Jun 8, 2006• 174 citations
Publisher

Abstract

Measurement is one of the fundamental building blocks of quantum-information processing systems. Partial measurement, where full wavefunction collapse is not the only outcome, provides a detailed test of the measurement process. We introduce quantum-state tomography in a superconducting qubit that exhibits high-fidelity single-shot measurement. For the two probabilistic outcomes of partial measurement, we find either a full collapse or a coherent yet nonunitary evolution of the state. This latter behavior explicitly confirms modern quantum-measurement theory and may prove important for error-correction algorithms in quantum computation.

DOI
10.1126/science.1126475

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Measurement is one of the fundamental building blocks of quantum-information processing systems. Partial measurement, where full wavefunction collapse is not the only outcome, provides a detailed test of the measurement process. We introduce quantum-state tomography in a superconducting qubit that exhibits high-fidelity single-shot measurement. For the two probabilistic outcomes of partial measurement, we find either a full collapse or a coherent yet nonunitary evolution of the state. This latter behavior explicitly confirms modern quantum-measurement theory and may prove important for error-correction algorithms in quantum computation.
We demonstrate in a superconducting qubit the conditional recovery (uncollapsing) of a quantum state after a partial-collapse measurement. A weak measurement extracts information and results in a nonunitary transformation of the qubit state. However, by adding a rotation and a second partial measurement with the same strength, we erase the extracted information, canceling the effect of both measurements. The fidelity of the state recovery is measured using quantum process tomography and found to be above 70% for partial-collapse strength less than 0.6.
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Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction intact. In this dissertation, we employ partial measurements to study two phenomena. First, we investigate an uncertainty relation -- in the style of Heisenberg's 1929 thought experiment -- which includes partial measurements in addition to projective measurements. We find that a weak partial measurement can decrease the uncertainty between two incompatible (non-commuting) observables. In the second study, we investigate the foundation of irreversible dynamics resulting from partial measurements. We do so by comparing the forward and time-reversed probabilities of measurement outcomes resulting from post-selected feedback protocols with both causal and reversed-causal order. We find that the statistics of partial measurements produce entropy in accordance with generalized second laws of thermodynamics. We perform these experiments using superconducting qubits. This dissertation also describes the fabrication process for these devices and details a novel fabrication technique that allows fast, single-step lithography of Josephson-junction superconducting circuits. The technique simplifies processing by utilizing a direct-write photolithography system, in contrast to traditional electron-beam lithography. Despite their large lithographic area, Josephson junctions made with this method have low critical currents and high coherence times.
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