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arXiv:quant-ph/0310083 · Physical review. B, Condensed matter

Projective measurement scheme for solid-state qubits

Lin Tian, Seth Lloyd, Terry P. Orlando

Published Jun 26, 2003• 4 citations
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Abstract

We present an effective measurement scheme for the solid-state qubits, which does not introduce extra decoherence to the qubits until the measurement is switched on by a resonant pulse. The resonant pulse then maximally entangles the qubit with the detector. The scheme has the feature of being projective, noiseless, and switchable. This method is illustrated on the superconducting persistent-current qubit, but can be applied to the measurement of a wide variety of solid-state qubits, the direct detection of the electromagnetic signals of which gives poor resolution of the qubit states.

DOI
10.1103/physrevb.67.220505

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We present an effective measurement scheme for the solid-state qubits, which does not introduce extra decoherence to the qubits until the measurement is switched on by a resonant pulse. The resonant pulse then maximally entangles the qubit with the detector. The scheme has the feature of being projective, noiseless, and switchable. This method is illustrated on the superconducting persistent-current qubit, but can be applied to the measurement of a wide variety of solid-state qubits, the direct detection of the electromagnetic signals of which gives poor resolution of the qubit states.
We present the implementation of a scheme to detect the quantum state of a persistent-current qubit. It relies on the dependency of the measuring superconducting quantum interference device plasma frequency on the qubit state, which we detect by resonant activation. With a measurement pulse of only 5ns5\phantom{\rule{0.3em}{0ex}}\mathrm{ns}5ns, we observed Rabi oscillations with high visibility (65%).
We present experiments that address the issue of measurement of superconducting qubits. A quantum non‐demolition (QND) type of readout is used to implement a projective measurement, which is an important component of many protocols in quantum information. The state of a persistent current qubit is measured using a driven non‐linear resonator, based on DC‐SQUID whose Josephson inductance is qubit‐state dependent. When properly optimized, the readout is efficient and projective. We discuss the relation between the concept of QND detection and the observed projective character of the measurement.
A full-scale quantum computer requires physical qubits that can be controlled with high precision and accuracy. Unfortunately, few state-of-the-art qubits can perform all their elementary operations (preparation, measurement, single-qubit gates and two-qubit gates) with sufficient fidelity. In this thesis, we investigate alternative schemes for such operations in solid-state qubits. Specifically, two-qubit gates and measurements, which are often the noisiest of the four. \n \nWe first provide a preliminary introduction to quantum computing, and describe how quantum information can be encoded and manipulated in quantum systems. We include background information for the three different solid-state qubit architectures that feature in this thesis: spin qubits, superconducting qubits and Majorana qubits. \n \nFollowing this, we investigate a scheme for mediating a two-qubit interaction between spin qubits via a multielectron quantum dot. We study a multielectron dot in detail, and characterise its exchange interaction with a single spin. With the aid of a theoretical model, we show that the multielectron dot possesses an irregular triplet-preferring ground state, analogous to Hund's rule from atomic physics. Using these findings, we then demonstrate that the multielectron dot can be used to mediate a fast, long-range exchange interaction between two spin qubits. \n \nSubsequently, we examine two resonator-based measurement schemes for Majorana qubits. We first propose a readout technique based on a longitudinal qubit-resonator interaction. This leads to a measurement that is fast, high-fidelity and quantum non-demolition (QND). We then investigate a more conventional dispersive readout scheme. Not only does this yield a high quality measurement, but it can also offers a more protected readout mechanism in comparison to the dispersive readout of conventional superconducting qubits.
We show that two identical solid-state qubits can be made fully entangled (starting from a completely mixed state) with probability 1/4 just by measuring them with a detector, equally coupled to the qubits. This happens in the case of repeated strong (projective) measurements as well as in a more realistic case of weak continuous measurement. In the latter case, the entangled state can be identified by a flat spectrum of the detector shot noise, while the nonentangled state (probability 3/4) leads to a spectral peak at the Rabi frequency with the maximum peak-to-pedestal ratio of 32/3.
The quantum evolution of an individual solid-state qubit during the process of its continuous measurement can be described by the recently developed Bayesian formalism. In contrast to the conventional ensemble-averaged formalism, it takes into account the measurement record (in a way similar to the standard Bayesian analysis) and therefore is able to consider individual realizations of the measurement process. The formalism provides testable experimental predictions and can be used for the analysis of a quantum feedback control of solid-state qubits. The Bayesian formalism can be also applied to the continuous measurement of entangled qubits; in particular, it shows how to create a fully entangled pair of qubits without their direct interaction, just by measuring them with an equally coupled detector.