I investigate the dynamics and power spectrum of two coupled qubits (two-level systems) under incoherent continuous pump and dissipation. New regimes of strong coupling are identified, that are due to additional paths of coherence flow in the system. Dressed states are reconstructed even in the regime of strong decoherence. The results are analytical and offer an exact description of strong-coupling in presence of pumping and decay in a nontrivial (nonlinear) system.
We study a pair of capacitively coupled singlet-triplet spin qubits. We characterize the two-qubit decoherence through two complementary measures, the decay time of coupled-qubit oscillations and the fidelity of entangled state preparation. We provide a quantitative map of their dependence on charge noise and field noise, and we highlight the magnetic field gradient across each singlet-triplet qubit as an effective tool to suppress decoherence due to charge noise.
Although single and two-qubit gates are sufficient for universal quantum computation, single-shot three-qubit gates greatly simplify quantum error correction schemes and algorithms. We design fast, high-fidelity three-qubit entangling gates based on microwave pulses for transmon qubits coupled through a superconducting resonator. We show that when interqubit frequency differences are comparable to single-qubit anharmonicities, errors occur primarily through a single unwanted transition. This feature enables the design of fast three-qubit gates based on simple analytical pulse shapes that are e…
We study the decoherence effect of charge noise on a single flip-flop qubit and two dipole-coupled qubits. We find that a single flip-flop qubit is highly resistant to charge noise at its sweet spots. However, due to the proximity of the charge excited states to the flip-flop logical states, the presence of charge noise greatly reduces the fidelity of two-qubit operations. We identify leakage from the qubit Hilbert space as the main culprit for the reduced gate fidelity. We also explore different bias conditions to mitigate this decoherence channel.
The maximum entanglement between two coupled qubits in the steady state under two independent incoherent sources of excitation is reported. Asymmetric configurations where one qubit is excited while the other one dissipates the excitation are optimal for entanglement, reaching values three times larger than with thermal sources. The reason is the purification of the steady state mixture (that includes a Bell state) thanks to the saturation of the pumped qubit. Photon antibunching between the cross emission of the qubits can be used to experimentally evidence the large degrees of entanglement.
Charge noise is the main hurdle preventing high-fidelity operation, in particular that of two-qubit gates, of semiconductor-quantum-dot-based spin qubits. While certain sweet spots where charge noise is substantially suppressed have been demonstrated in several types of spin qubits, the existence of one for coupled singlet-triplet qubits is unclear. We theoretically demonstrate, using full configuration-interaction calculations, that a range of nearly sweet spots appear in the coupled singlet-triplet qubit system when a strong enough magnetic field is applied externally. We further demonstrate…
We present composite pulse sequences that perform fault-tolerant two-qubit gate operations on exchange-only quantum dot spin qubits in various experimentally relevant geometries. We show how to perform dynamically corrected two-qubit gates in exchange-only systems with the leading hyperfine error term cancelled. These pulse sequences are constructed to conform to the realistic experimental constraint of strictly non-negative couplings. We establish that our proposed pulse sequences lead to several orders of magnitude improvement in the gate fidelity compared with their uncorrected counterparts…
Recent work on Ising-coupled double-quantum-dot spin qubits in GaAs with voltage-controlled exchange interaction has shown improved two-qubit gate fidelities from the application of oscillating exchange along with a strong magnetic field gradient between adjacent dots. By examining how noise propagates in the time-evolution operator of the system, we find an optimal set of parameters that provide passive stroboscopic circumvention of errors in two-qubit gates to first order. We predict over 99% two-qubit gate fidelities in the presence of quasistatic and 1/$\textit{f}$ noise, which is an order…
The search of a sweet spot, locus in qubit parameters where quantum control is first-order insensitive to noises, is key to achieve high-fidelity quantum gates. Efforts to search for such a sweet spot in conventional double-quantum-dot singlet-triplet qubits where each dot hosts one electron ("two-electron singlet-triplet qubit"), especially for two-qubit operations, have been unsuccessful. Here we consider singlet-triplet qubits allowing each dot to host more than one electron, with a total of four electrons in the double quantum dots ("four-electron singlet-triplet qubit"). We theoretically …
We present a quantum heat switch based on coupled superconducting qubits, connected to two $LC$ resonators that are terminated by resistors providing two heat baths. To describe the system we use a standard second order master equation with respect to coupling to the baths. We find that this system can act as an efficient heat switch controlled by the applied magnetic flux. The flux influences the energy level separations of the system, and under some conditions, the finite coupling of the qubits enhances the transmitted power between the two baths, by an order of magnitude under realistic con…
We study the manipulation of quantum entanglement by periodic external fields. As an entanglement measure we compute numerically the concurrence of two flux qubits coupled inductively and/or capacitively, both driven by a dc+ac magnetic flux. Also we find an analytical lower bound for the concurrence, where the dominant terms correspond to the concurrence in the Floquet states. We show that it is possible to create or destroy entanglement in a controlled way by tuning the system at or near multiphoton resonances. We find that when the driving term of the Hamiltonian does not commute with the q…
Capacitively coupled semiconductor spin qubits hold promise as the building blocks of a scalable quantum computing architecture with long-range coupling between distant qubits. However, the two-qubit gate fidelities achieved in experiments to date have been severely limited by decoherence originating from charge noise and hyperfine interactions with nuclear spins, and are currently unacceptably low for any conceivable multi-qubit gate operations. Here, we present control protocols that implement two-qubit entangling gates while substantially suppressing errors due to both types of noise. These…
We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio-frequency pulses. Moreover, the multi-level structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.
We report the observation and quantitative characterization of driven and spontaneous oscillations of quantum entanglement, as measured by concurrence, in a bipartite system consisting of a macroscopic Josephson phase qubit coupled to a microscopic two-level system. The data clearly show the behavior of entanglement dynamics such as sudden death and revival, and the effect of decoherence and ac driving on entanglement.
A spin qubit in semiconductor quantum dots holds promise for quantum information processing for scalability and long coherence time. An important semiconductor qubit system is a double quantum dot trapping two electrons or holes, whose spin states encode either a singlet-triplet qubit or two single-spin qubits coupled by exchange interaction. In this article, we report progress on spin dephasing of two exchange-coupled spins in a double quantum dot. We first discuss the schemes of two-qubit gates and qubit encodings in gate-defined quantum dots or donor atoms based on the exchange interaction.…
Inspired by creation of a fast exchange-only qubit (Medford et al., Phys. Rev. Lett., 111, 050501 (2013)), we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same or different than the first. We demonstrate that coupling between qubits can be detected by reading the re…
We propose a scheme for generating the Schrödinger cat state based on geometric operations by a nanomechanical resonator coupled to a superconducting charge qubit. The charge qubit, driven by two strong classical fields, interacts with a high-frequency phonon mode of the nanomechanical resonator. During the operation, the charge qubit undergoes no real transitions, while the phonon mode of the nanomechanical resonator is displaced along different paths in the phase space, dependent on the states of the charge qubit, which yields the Schrödinger cat state. The robustness of the scheme is justif…
The implementation of high fidelity two-qubit gates is a bottleneck in the progress towards universal quantum computation in semiconductor quantum dot qubits. We study capacitive coupling between two triple quantum dot spin qubits encoded in the $S = 1/2$, $S_z = -1/2$ decoherence-free subspace -- the exchange-only (EO) spin qubits. We report exact gate sequences for CPHASE and CNOT gates, and demonstrate theoretically, the existence of multiple two-qubit sweet spots (2QSS) in the parameter space of capacitively coupled EO qubits. Gate operations have the advantage of being all-electrical, but…
We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit. These results constitute a first proof of concept of spin-ensemb…
Superconducting spin qubits, also known as Andreev spin qubits, promise to combine the benefits of superconducting qubits and spin qubits defined in quantum dots. While most approaches to control these qubits rely on controlling the spin degree of freedom via the supercurrent, superconducting spin qubits can also be coupled to each other via the superconductor to implement two-qubit quantum gates. We theoretically investigate the interaction between superconducting spin qubits in the weak tunneling regime and concentrate on the effect of spin-orbit interaction (SOI), which can be large in semi…
We present an approximate analytical solution to the dynamic equation of two Ising-coupled qubits with oscillating classical control fields that are nonperpendicular to the static drift fields. This is a situation that has recently arisen in some solid-state experiments. With our solution we derive the analytical expressions for the local invariants as well as the local rotations needed to isolate a purely nonlocal gate. This determines the set of parameters that are required to generate any entangling gate. Moreover, we use our results to describe a recent experimental work on capacitively co…
In addition to magnetic field and electric charge noise adversely affecting spin qubit operations, performing single-qubit gates on one of multiple coupled singlet-triplet qubits presents a new challenge---crosstalk, which is inevitable (and must be minimized) in any multiqubit quantum computing architecture. We develop a set of dynamically-corrected pulse sequences that are designed to cancel the effects of both types of noise (i.e., field and charge) as well as crosstalk to leading order, and provide parameters for these corrected sequences for all 24 of the single-qubit Clifford gates. We t…
In order to enable semiconductor-based quantum computing with many qubits, issues like residual interqubit coupling and constraints from scalable control hardware need to be tackled to retain the high gate fidelities demonstrated in current single-qubit devices. Here, we focus on two exchange-coupled singlet-triplet spin qubits, considering realistic control hardware as well as Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we optimize realistic control pulses and show that two-qubit (single-qubit) gate fidelities of 99.90\% ($\ge 99.69\%$) can be …
Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform inter-qubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor due to their potential for scalability and miniaturization. However, their weak interactions with the environment, which leads to their long coherence times, makes inter-qubit operations challenging. We perform a controlled two-qubit operation between singlet-triplet qubits u…
A crucial requirement for scalable quantum-information processing is the realization of multiple-qubit quantum gates. Universal multiple-qubit gates can be implemented by a set of universal single qubit gates and any one kind of two-qubit gate, such as a controlled-NOT (CNOT) gate. Semiconductor quantum dot qubits are a leading approach for the physical implementation of quantum computation, due to their potential for large-scale integration. Two-qubit gate operations have been so far only demonstrated in individual electron spin-based quantum dot systems. Due to the relatively short de-cohere…
The quantum levels population behavior of the two coupled flux qubits depending on the external driving field characteristics is studied. The explicit expressions for the multiphoton transition probabilities at an arbitrary control field amplitude is obtained for the case of small tunnel splitting energies. We describe the controllable features of their formation and thereby creating or destroying entanglement by system bias tuning on the direct inter-level transition and during the transition through intermediate states. We found a feature of the qubits population inverting that ends in the i…
We investigate the dynamical purification of maximally entangled electron states by transport through coupled quantum dots. Under resonant ac driving and coherent tunneling, even-parity Bell states perform Rabi oscillations that decouple from the environment, leading to a dark state. The two electrons remain spatially separated, one in each quantum dot. We propose configurations where this effect will prove as antiresonances in transport spectroscopy experiments.
In this work we report on a new mechanism to generate dissipative steady state entanglement in two coupled qubits driven by strong periodic ac fields. We show that steady entanglement can be generated at one side of a multiphoton resonance between a non-entangled ground state and an entangled excited state. The degree of entanglement can be tuned as a function of the amplitude of the periodic drive. A rich dynamic behavior with creation, death and revival of entanglement can be observed for certain parameter regimes, accessible in current experimental devices.
We propose a circuit quantum electrodynamics (QED) realization of a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state for $N$ superconducting transmon qubits homogeneously coupled to a superconducting transmission line resonator in the dispersive limit. We derive an effective Hamiltonian with pairwise qubit exchange interactions of the XY type, $\tilde{g}(XX+YY)$, that can be globally controlled. Starting from a separable initial state, these interactions allow to generate a multi-qubit GHZ state within a time $t_{\text{GHZ}}\sim \tilde{g}^{-1}$. We discuss how to probe the non-lo…
Inter-qubit coupling and qubit connectivity in a processor are crucial for achieving high fidelity multi-qubit gates and efficient implementation of quantum algorithms. Typical superconducting processors employ relatively weak transverse inter-qubit coupling which are activated via frequency tuning or microwave drives. Here, we propose a class of multi-mode superconducting circuits which realize multiple transmon qubits with all-to-all longitudinal coupling. These "artificial molecules" directly implement a multi-dimensional Hilbert space that can be easily manipulated due to the always-on lon…
We theoretically describe the weak measurement of a two-level system (qubit) and quantify the degree to which such a qubit measurement has a quantum non-demolition (QND) character. The qubit is coupled to a harmonic oscillator which undergoes a projective measurement. Information on the qubit state is extracted from the oscillator measurement outcomes, and the QND character of the measurement is inferred by the result of subsequent measurements of the oscillator. We use the positive operator valued measure (POVM) formalism to describe the qubit measurement. Two mechanisms lead to deviations fr…
We report the parametric amplification of a microwave signal in a Kerr medium formed from superconducting qubits. Two mutually coupled flux qubits, embedded in the current antinode of a superconducting coplanar waveguide resonator, are used as a nonlinear element. Shared Josephson junctions provide the qubit-resonator coupling, resulting in a device with a measured gain of about 20 dB. We argue, that this arrangement represents a unit cell which can be straightforwardly extended to a quasi one-dimensional quantum metamaterial with a large tunable Kerr nonlinearity.
For some cavity-quantum-electrodynamics systems, such as a single electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can …
We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit.
We present a theory describing the semiclassical dynamics of a superconducting flux qubit inductively coupled to a nanomechanical oscillator. Focusing on the influence of the qubit on the mechanical element, and on the nonlinear phenomena displayed by this device, we show that it exhibits retardation effects and self-excited oscillations. These can be harnessed for the generation of non-classical states of the mechanical oscillator. In addition, we find that this system shares several fundamental properties with cavity optomechanical systems, and elucidate the analogy between these two classes…
We study phonon statistics in a nanomechanical resonator (NAMR) which is resonantly coupled to a qubit. We find that there are two different mechanisms for phonon blockade in such a resonantly coupled NAMR-qubit system. One is due to the strong anharmonicity of the NAMR-qubit system with large coupling strength; the other one is due to the destructive interference between different paths for two-phonon excitation in the NAMR-qubit system with a moderate coupling strength. We find that the phonon blockade is fragile towards thermal mode occupations and can only be observed for NAMR being at ult…
For a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation $L$. We study the correlations by calculating the second-order correlation function $g_2(t)$ in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calcula…
Using recently proposed measures for non-Markovianity [H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. {\bf 103}, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism. We show the existence of a point, in the parameter space of the system, where the qubit dynamics is effectively Markovian and that such a point separates two regions with completely different dynamical behaviors. Indeed, our study demonstrates that the qubit evolution can in principle be tuned from a perfectly forgetful one to a deep non-Markovian regime where …
We apply the quantum optimal control theory based on the Krotov method to implement single-qubit $X$ and $Z$ gates and two-qubit CNOT gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off-diagonal qubit-qubit coupling. Our scheme that shares the same advantage of other directly coupling schemes requires no additional coupler subcircuit and control lines. The control lines needed are only for the manipulation of individual qubits (e.g., a time-dependent magnetic flux or field applied on each qubit). The qubits are operated at the optimal…
Recent achievements in the field of gate defined semiconductor quantum dots reinforce the concept of a spin-based quantum computer consisting of nodes of locally connected qubits which communicate with each other via superconducting circuit resonator photons. In this work we theoretically demonstrate a versatile set of quantum gates between adjacent spin qubits defined in semiconductor quantum dots situated within the same node of such a spin-based quantum computer. The electric dipole acquired by the spin of an electron that moves across a double quantum dot potential in a magnetic field grad…
Designing coherent processes is essential for developing quantum information technologies. We study coherent dynamics of two spatially separated electrons in a coupled semiconductor double quantum dot (DQD), in which various two-qubit operations are demonstrated just by adjusting the gate voltages. Especially, second-order correlated coherent oscillations provide functional quantum processes for making quantum correlation of separated particles. The results encourage searching quantum entanglement in electronic devices.
We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons. These patterns are in excellent agreement with a simulation using the Tavis-Cummings model, and allow us to readily identify different parameter regimes for both qubits in the detuning space. This method could potentially be an important component in the overall spectrosc…
