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Current Science

Quantum Measurements with Superconducting Circuits

Tanay Roy, A. M. Vadiraj, Madhavi Chand, Arpit Ranadive, Suman Kundu, Meghan P. Patankar, Rajamani Vijay

Published Dec 1, 2015• 2 citations
Publisher

Abstract

We measure the state of a superconducting quantum bit (qubit) coupled to a microwave cavity by scattering a microwave signal from the cavity. The scattered signal is amplified using a low-noise Josephson parametric amplifier. We carried out measurements to infer the coherence properties of the qubit. In the strong measurement regime, we observe quantum jumps between the qubit states in real time, while we observe stochastic quantum trajectories in the weak measurement regime. The coherence times and measurement fidelity obtained are sufficient for implementing quantum error correction.

DOI
10.18520/cs/v109/i11/2069-2076

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We measure the state of a superconducting quantum bit (qubit) coupled to a microwave cavity by scattering a microwave signal from the cavity. The scattered signal is amplified using a low-noise Josephson parametric amplifier. We carried out measurements to infer the coherence properties of the qubit. In the strong measurement regime, we observe quantum jumps between the qubit states in real time, while we observe stochastic quantum trajectories in the weak measurement regime. The coherence times and measurement fidelity obtained are sufficient for implementing quantum error correction.
Real-time monitoring of a quantum state provides powerful tools for studying the backaction of quantum measurement and performing quantum feedback. Historically, this monitoring capability has been the exclusive province of atomic and optical physics. This thesis describes the implementation of the first such high-fidelity readout scheme in a solid state circuit, a superconducting quantum bit (qubit) coupled to a microwave cavity in the circuit quantum electrodynamics (circuit QED) architecture. The qubit-state-dependent resonance frequency of the cavity is probed with a microwave drive tone, and the resulting signal amplified using a fast, ultralow-noise superconducting parametric amplifier. This arrangement enables the observation of quantum jumps between the qubit states in real time. The ability to monitor the qubit continuously with high fidelity and resolve quantum jumps can be used to investigate the backaction of the measurement process on the qubit. This thesis examines the quantum Zeno effect--where strong measurement inhibits the evolution of a quantum system-- as well as the transition to non-ideal measurement with increasing measurement strength in the circuit QED architecture, a phenomenon shown to be due to the upconversion of low-frequency dephasing noise. These data allow probes of ``universal'' flux noise in previously inaccessible frequency ranges. The work presented here opens the door for quantum feedback and error correction in solid-state quantum systems using continuous weak measurement.
The act of observing a quantum object fundamentally perturbs its state, resulting in a random walk toward an eigenstate of the measurement operator. Ideally, the measurement is responsible for all dephasing of the quantum state. In practice, imperfections in the measurement apparatus limit or corrupt the flow of information required for quantum feedback protocols, an effect quantified by the measurement efficiency. Here, we demonstrate the efficient measurement of a superconducting qubit using a nonreciprocal parametric amplifier to directly monitor the microwave field of a readout cavity. By mitigating the losses between the cavity and the amplifier, we achieve a measurement efficiency of (72±4)%. The directionality of the amplifier protects the readout cavity and qubit from excess backaction caused by amplified vacuum fluctuations. In addition to providing tools for further improving the fidelity of strong projective measurement, this work creates a test bed for the experimental study of ideal weak measurements, and it opens the way toward quantum feedback protocols based on weak measurement such as state stabilization or error correction.
In the early 1980’s, it was suggested that a computer obeying the laws of quantum mechanics would be able to solve problems beyond the capabilities of a classical computer. The novel ways in which such a quantum computer works relies on the quantum properties of the quantum bits (qubits) used to store the information. Any candidate for a quantum computer must thus be able to sustain these properties and offer means to manipulate and read-out the information. One such candidate are quantum mechanical, superconducting circuits, where the logical bit is encoded in the energy eigenstates of the system. In circuit quantum electrodynamics, such a qubit is coupled to a microwave cavity allowing the qubit to be coherently controlled and read-out by probing the cavity. In this thesis, we theoretically investigate the destructive effects of noise which couple to the system as one tries to measure and control the qubits. We study the so called quantum capacitance read-out scheme, where the state of the qubit is mapped onto an equivalent capacitance of the circuit. It is shown that this is quantum limited, in the sense that the state of the qubit can be determined while simultaneously adding a minimum amount of noise to the system. Apart from the added noise, a measurement on a qubit will perturb it, causing the state to collapse to one of the measurement eigenstates. Such a state collapse can be utilized to generate entanglement between qubits by measuring on the cavity. We show that high-fidelity entangled states can be produced in this way and discuss the potential of the measurement to violate a bound given by local hidden variable theories. The possibility to prolong the life-time of the quantum state by active error correction is also investigated and we discuss limits on gate operation times to benefit from such a code, given realistic values for the error probabilities. This work was supported by the European Commission through IST-015708 EuroSQIP integrated pro ject, and by the Swedish Research Council.
Nowadays, it is possible to control and measure the quantum state of systems with a few degrees of freedom, whether they are microscopic objects like cold atoms and single photons, or macroscopic objects like superconducting circuits. Such delicate experiments require an interface which bridges the gap of orders of magnitudes in energy between the quantum object and the data acquisition system. This problem is solved by an active device: the amplifier. Although the amplifier is necessary to overcome the noise at the stage of data acquisition, it eventually alters the signal. We have developed an amplifier for microwave signals which adds only the minimum of noise allowed by quantum laws: the equivalent of half a photon of noise referred to the input. Our amplifier is based on a superconducting circuit of Josephson junctions in superconducting resonators. We found a way to make it practical to use by tuning its center frequency over 500 MHz. We are now trying to increase its bandwidth for a given gain using more compact resonators. In this talk, I will show how the amplifier works and also its applications to quantum information processing. This circuit can be used to generate and combine twin microwave photons within an integrated circuit. Finally, I will show that such an amplifier allows real time measurement of the state of a qubit and quantum feedback protocols.
Coherent circuits based on superconducting elements hold tremendous promise for the practical implementation of quantum information technology: advanced computation, cryptography, and hardware simulation of complex materials systems are envisioned applications. Such circuits are essentially engineered atoms with level transitions in the 4-8 GHz regime; as such “read” and “write” operations are performed with the aid of fast microwave pulses and low-noise amplifiers, respectively. Recent advances in cavity-based superconducting parametric amplifiers have enabled real-time measurement and feedback in one and two qubits. We demonstrate a novel Josephson junction transmission-line based traveling-wave amplifier which employs sub-wavelength phase matching resonators to achieve high gain, several GHz of bandwidth, and near quantum-noise limited performance. Such devices will enable multiplexed qubit readout in integrated architectures comprised of a variety of microwave frequency analog and digital superconducting technologies: signal sources, multiplexers, ADCs, DACs, mixers, and amplifiers.