Solid-state qubits incorporating quantum dots can be read out dispersively. Here, we theoretically describe physical mechanisms that render such reflectometry-based readout schemes imperfect. We discuss charge qubits, singlet-triplet spin qubits, and Majorana qubits. In our model, we account for readout errors due to slow charge noise, and due to overdriving, when the large amplitude of the probe field generates errors. A key result is that for charge and spin qubits, the readout fidelity saturates at large probe strengths, whereas for Majorana qubits, there is an optimal probe strength which provides a maximized readout fidelity. We also point out the existence of severe readout errors appearing in a resonancelike fashion as the pulse strength is increased, and show that these errors are related to probe-induced multiphoton transitions. Besides providing practical guidelines toward optimized readout, our study might also inspire ways to use gate reflectometry for device characterization.
Solid-state qubits incorporating quantum dots can be read out dispersively. Here, we theoretically describe physical mechanisms that render such reflectometry-based readout schemes imperfect. We discuss charge qubits, singlet-triplet spin qubits, and Majorana qubits. In our model, we account for readout errors due to slow charge noise, and due to overdriving, when the large amplitude of the probe field generates errors. A key result is that for charge and spin qubits, the readout fidelity saturates at large probe strengths, whereas for Majorana qubits, there is an optimal probe strength which provides a maximized readout fidelity. We also point out the existence of severe readout errors appearing in a resonancelike fashion as the pulse strength is increased, and show that these errors are related to probe-induced multiphoton transitions. Besides providing practical guidelines toward optimized readout, our study might also inspire ways to use gate reflectometry for device characterization.
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.
Spin qubits in gate-defined semiconductor quantum dots are a promising platform for realising a scalable quantum computer. This platform encodes quantum information into the intrinsic angular momentum (spin) of individual electrons or holes. In particular, hole spins in quantum dots enable the possibility of all-electrical spin control due to their intrinsic spin-orbit coupling. One important criterion of a quantum computer is the ability to reliably read out the state of the qubit. This is done by mapping spin information to the charge degree of freedom, combined with a method for charge detection. Charge detection can be facilitated by coupling a resonator directly to the quantum dot gate or to a charge sensor and measuring the resonator's phase or amplitude response. In this thesis, we describe a set of experiments relating to the implementation of hole spin qubit readout with superconducting resonators. First, we study gate-based charge sensing in a Si fin field-effect transistor (finFET) device using a superconducting NbN nanowire resonator. We find that the resonator amplifies capacitive crosstalk when electrical control pulses are applied to gate electrodes in this device. This occurs whenever a spectral component of qubit control pulses overlaps with the resonance frequency, which we show may occur for both baseband and radio-frequency (RF) drive signals. We quantify this crosstalk in a transport-based method, and attribute its source to the capacitance between the bondpads of neighbouring gate electrodes. In a second experiment, we use an RF charge sensor with the same nanowire technology to read out hole spin qubits formed in the quantum well of a Ge/SiGe heterostructure. A screening layer approach is used to facilitate RF matching due to large RF dissipation found in the heterostructure. We implement a double-latched readout scheme in this system to reduce errors arising from both spin and charge decay during readout. The spin-to-charge conversion process and its dependence on magnetic field orientation is studied. Spin and charge decay processes arising after spin-to-charge conversion are mitigated by choosing an optimal working point for the field orientation, field amplitude and readout pulse times. By doing so, we achieve an average single-shot state-preparation-and-measurement fidelity of 97%, primarily bounded by imperfect state preparation and limited signal-to-noise ratio. Finally, we study coplanar waveguide resonators fabricated from NbN. We investigate the feasibility of integrating this type of resonator onto the same chip as the Si finFET quantum dots. We then develop a novel resonator readout technique by the interference of two microwave sidebands. We demonstrate the insensitivity of this technique to common-mode phase and amplitude noise both theoretically and experimentally. This technique is then used to study resonator noise arising from two-level system defects. These results highlight both the practical constraints and the potential for achieving high readout fidelities using resonator-based hole spin qubit readout. This work establishes a blueprint for mitigating resonator-induced crosstalk and enabling high-fidelity readout in lossy materials by incorporating a screening layer.
We theoretically study a scheme to distinguish the two ground states of a one-dimensional topological superconductor, which could serve as a basis for the readout of Majorana qubits. The scheme is based on parity-to-charge conversion, i.e., the ground-state parity of the superconductor is converted to the charge occupation on a tunnel-coupled auxiliary quantum dot. We describe how certain error mechanisms degrade the quality of the parity-to-charge conversion process. We consider (i) leakage due to a strong readout tunnel pulse, (ii) incomplete charge Rabi oscillations due to slow charge noise, and (iii) charge relaxation due to phonon emission and absorption. To describe these effects, we use simple model Hamiltonians based on the ideal Kitaev chain, and draw conclusions to generic one-dimensional topological superconductors wherever possible. In general, the effects of the error mechanisms can be minimized by choosing a smooth shape and an optimal strength for the readout tunnel pulse. In a case study based on InAs heterostructure device parameters, we estimate that the parity-to-charge conversion error is mainly due to slow charge noise for weak tunnel pulses and leakage for strong tunnel pulses.
Qubit readout schemes often deviate from ideal projective measurements, introducing critical issues that limit quantum computing performance. In this Letter, we model charge-sensing-based readout for semiconductor spin qubits in double quantum dots, and identify key error mechanisms caused by the backaction of the charge sensor. We quantify how the charge noise of the sensor, residual tunneling, and g-tensor modulation degrade readout fidelity, induce a mixed postmeasurement state, and cause leakage from the computational subspace. For state-of-the-art systems with strong spin-orbit interaction and electrically tunable g tensors, we identify a readout sweet spot, that is, a special device configuration where readout is closest to projective. Our framework provides a foundation for developing effective readout error mitigation strategies, with broad applications for optimizing readout performance for a variety of charge-sensing techniques, advancing quantum protocols, and improving adaptive circuits for error correction.
Electron spins in semiconductor quantum dots are a promising platform for qubits. An essential step toward quantum error correction with spin qubits requires the ability to read out states and identify errors in the two-spin logical basis in a fast and high-fidelity way. Here we propose a scheme for spin singlet-triplet readout in a double quantum dot, with a superconducting resonator serving as the detector. Making use of a spin driving pulse sequence, this procedure can read out the spin states with a fidelity of 99.9 in a time 100 ns. Interestingly, this method makes use of the spin driving pulse to adjust the resonator signal field, leading to significant improvement of the spin readout. In addition, this method can be directly applied to multiplexed readout of qubits and repeated readout to identify logical errors. These results pave the way for the implementation of quantum error correction and scalable quantum processor with spin qubits.
We present recent progress in the implementation of scalable schemes for spin qubit readout in one dimensional quantum registers based on fully-depleted silicon-on-insulator (FDSOI) technology. We compare two schemes both based on rf gate reflectometry. The first one, denoted as dispersive readout, minimizes the device overhead thereby facilitating scale-up to large qubit registers. The second one, denoted as charge-sensing readout, requires additional readout components but is less sensitive to the strength of the interdot coupling facilitating operation in the few-electron regime. We demonstrate single-shot charge sensing with a fidelity of 97% in 5 μs. Finally, we propose a scalable device architecture for linear qubit registers relying on charge-sensing readout.