Minimizing the Discrimination Time for Quantum States of an Artificial Atom
I. Takmakov, P. Winkel, F. Foroughi, Luca Planat, D. Gusenkova, M. Spiecker, D. Rieger, Lukas Grünhaupt, Alexey Vladimirovich Ustinov, Wolfgang Wernsdorfer, Ioan M. Pop, Nicolas Roch
Fast discrimination between quantum states of superconducting artificial atoms is an important ingredient for quantum information processing. In circuit quantum electrodynamics, increasing the signal-field amplitude in the readout resonator, dispersively coupled to the artificial atom, improves the signal-to-noise ratio and increases the measurement strength. Here, we employ this effect over 2 orders of magnitude in readout power, made possible by the unique combination of a dimer-Josephson-junction-array amplifier with a large dynamic range and the fact that the readout of our granular aluminum fluxonium artificial atom remains quantum nondemolition (QND) at relatively large photon numbers in the readout resonator, up to $\overline{n}=110$. Using Bayesian inference, this allows us to detect quantum jumps faster than the readout-resonator response time $2/\ensuremath{\kappa}$, where $\ensuremath{\kappa}$ is the bandwidth of the readout resonator.
Fast discrimination between quantum states of superconducting artificial atoms is an important ingredient for quantum information processing. In circuit quantum electrodynamics, increasing the signal-field amplitude in the readout resonator, dispersively coupled to the artificial atom, improves the signal-to-noise ratio and increases the measurement strength. Here, we employ this effect over 2 orders of magnitude in readout power, made possible by the unique combination of a dimer-Josephson-junction-array amplifier with a large dynamic range and the fact that the readout of our granular aluminum fluxonium artificial atom remains quantum nondemolition (QND) at relatively large photon numbers in the readout resonator, up to n=110. Using Bayesian inference, this allows us to detect quantum jumps faster than the readout-resonator response time 2/\ensuremathκ, where \ensuremathκ is the bandwidth of the readout resonator.
Fast discrimination between quantum states of superconducting artificial atoms is an important ingredient for quantum information processing. In circuit quantum electrodynamics, increasing the signal-field amplitude in the readout resonator, dispersively coupled to the artificial atom, improves the signal-to-noise ratio and increases the measurement strength. Here, we employ this effect over 2 orders of magnitude in readout power, made possible by the unique combination of a dimer-Josephson-junction-array amplifier with a large dynamic range and the fact that the readout of our granular aluminum fluxonium artificial atom remains quantum nondemolition (QND) at relatively large photon numbers in the readout resonator, up to n=110. Using Bayesian inference, this allows us to detect quantum jumps faster than the readout-resonator response time $2/\ensuremath{\kappa}$, where $\ensuremath{\kappa}$ is the bandwidth of the readout resonator.
Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulating photon number n in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing n is generally observed to also monotonously increase these transition rates. Here we present a fluxonium artificial atom in which, despite the fact that the measured transition rates show nonmonotonous fluctuations within a factor of 6, for photon numbers up to $\overline{n}\ensuremath{\approx}200$, the signal-to-noise ratio continuously improves with increasing n. Even without the use of a parametric amplifier, at n=74, we achieve fidelities of 99% and 93% for feedback-assisted ground and excited state preparations, respectively. At higher n, leakage outside the qubit computational space can no longer be neglected and it limits the fidelity of quantum state preparation.
We propose a quantum nondemolition (QND) readout scheme for a superconducting artificial atom coupled to a resonator in a circuit QED architecture, for which we estimate a very high measurement fidelity without Purcell effect limitations. The device consists of two transmons coupled by a large inductance, giving rise to a diamond-shaped artificial atom with a logical qubit and an ancilla qubit interacting through a cross-Kerr-like term. The ancilla is strongly coupled to a transmission line resonator. Depending on the qubit state, the ancilla is resonantly or dispersively coupled to the resonator, leading to a large contrast in the transmitted microwave signal amplitude. This original method can be implemented with a state-of-the-art Josephson parametric amplifier, leading to QND measurements in a few tens of nanoseconds with fidelity as large as 99.9.
Though superconducting qubits offer the potential for a scalable quantum computing architecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting amplifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout resonator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp).We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to-noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.
Though superconducting qubits offer the potential for a scalable quantum computing architecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting amplifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout resonator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp).We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to-noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.
In this thesis, experimentally relevant aspects and open questions of quantum information processing and measurement in circuit quantum electrodynamics have been investigated theoretically. Circuit quantum electrodynamics is a relatively young field combining superconducting transmission line resonators on-chip with superconducting quantum bits which serve as artificial atoms. Remarkable experiments have underlined the prospects of circuit QED as a possible architecture for quantum information processing as well as a framework within which quantum optics experiments can be performed. In contrast to their optical counterparts, these experiments reach the ultra-strong coupling limit and allow e.g. the generation of Fock states, the study of decoherence and the observation of quantum jumps. We present the physics of superconducting circuits based on the Josephson junction as a non-linear circuit element. We discuss the various types of quantum bits (qubits) before turning to an introduction on cavity QED and conclude the introduction with a brief presentation of the most relevant experiments and a short introduction to the principles and prospects of quantum information processing. Building on the pioneering theoretical and experimental work in which up to three qubits have been integrated on a chip and successfully coupled via a cavity mode, we propose a scheme to overcome the natural limits concerning scalability in these systems. Usually, scalability is severely limited by the resonance width of the qubit transitions and the attainable frequency range for both qubit transition and cavity resonance frequencies. This limits the present setups to at most ten qubits. As a possible solution, we propose and investigate a cross-bar grid layout of cavities with qubits at the intersections. It turns out that this setup, allowing for up to about 1000 qubits, offers significant advantages over e.g. nearest-neighbor coupling schemes. In addition, it can serve as a building block for a truly scalable scheme for fault-tolerant quantum information processing with superconducting circuits by combining 7x7 arrays in a staircase manner. Furthermore, we discuss and simulate different possibilities to improve upon the suggested scheme by e.g. using resonant gates and optimal control theory. Another focus of the present thesis is measurement physics. In order to investigate e.g. the possibilities of using a circuit QED system to dispersively detect single microwave photons or to generate multi-qubit entangled states, we introduce in a pedagogical manner the basics of stochastic master equations which generate quantum trajectories before turning to concrete applications. Quantum trajectories have proven to be a state-of-the-art tool to analyze measurement situations in a very realistic manner by giving access to both the measurement record as well as the internal quantum dynamics conditioned on this record. Using the method of quantum trajectories as generated by stochastic master equations, we discuss a scheme to efficiently generate multi-qubit entangled states in a very flexible way. The method is based on a collective, dispersive qubit readout. By this measurement, a suitable product state of N qubits can be reliably converted into e.g. an N-qubit Greenberger-Horne-Zeilinger or W state. We propose and discuss the scheme and investigate the effects of decoherence and parameter spread as they would be encountered in experiment. Last but not least, we propose and fully analyze a scheme to dispersively detect single itinerant microwave photons. While experiments to generate single microwave photons have already been successfully performed, their single-shot quantum non-demolition detection has not been possible so far. The scheme presented in this thesis closes this gap in the circuit QED toolbox and reaches detection efficiencies of 30% only limited by fundamental quantum mechanics in this case the Quantum Zeno effect. This detection scheme could be used in quantum communication or quantum cryptography applications.