We study the influence of a thermal environment on a non-adiabatic spin-flip driving protocol of spin-orbit qubits. The driving protocol operates by moving the qubit, trapped in a harmonic potential, along a nanowire in the presence of a time-dependent spin-orbit interaction. We consider the harmonic degrees of freedom to be weakly coupled to a thermal bath. We find an analytical expression for the Floquet states and derive the Lindblad equation for a strongly non-adiabatically driven qubit. The Lindblad equation corrects the dynamics of an isolated qubit with Lamb shift terms and a dissipative behaviour. Using the Lindblad equation, the influence of a thermal environment on the spin-flip protocol is analysed.
We demonstrate multipulse quantum control of a single electron charge qubit. The qubit is manipulated by applying nonadiabatic voltage pulses to a surface depletion gate and readout is achieved using a quantum point contact charge sensor. We observe Ramsey fringes in the excited state occupation in response to a pi/2 - pi/2 pulse sequence and extract T2* ~ 60 ps away from the charge degeneracy point. Simulations suggest these results may be extended to implement a charge-echo by reducing the interdot tunnel coupling and pulse rise time, thereby increasing the nonadiabaticity of the pulses.
We analyze the coupling of qubits mediated by a tunable and fast element beyond the adiabatic approximation. The nonadiabatic corrections are important and even dominant in parts of the relevant parameter range. As an example, we consider the tunable capacitive coupling between two charge qubits mediated by a gated Josephson junction, as suggested by Averin and Bruder. The nonadiabatic, inductive contribution persists when the capacitive coupling is tuned to zero. On the other hand, the total coupling can be turned off (in the rotating wave approximation) if the qubits are operated at symmetry…
An exact analytical solution is derived for the wavefunction of an electron in a one-dimensional moving quantum dot in a nanowire, in the presence of time-dependent spin-orbit coupling. For cyclic evolutions we show that the spin of the electron is rotated by an angle proportional to the area of a closed loop in the parameter space of the time-dependent quantum dot position and the amplitude of a fictitious classical oscillator driven by the time-dependent spin-orbit coupling. By appropriate choice of parameters, we show that arbitrary spin rotations may be performed on the Bloch sphere. Exact…
Implementing holonomic quantum computation is a challenging task as it requires complicated interaction among multilevel systems. Here we propose to implement nonadiabatic holonomic quantum computation based on dressed-state qubits in circuit QED. An arbitrary holonomic single-qubit gate can be conveniently achieved using external microwave fields and tuning their amplitudes and phases. Meanwhile, nontrivial two-qubit gates can be implemented in a coupled-cavities scenario assisted by a grounding SQUID with tunable interaction, where the tuning is achieved by modulating the ac flux threaded th…
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.
In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin shuttling in long chains of quantum dots in a n…
According to Clausius formulation of the second law of thermodynamics, for any thermal machine withdrawing heats $Q_{1,2}$ from two heat reservoirs at temperatures $T_{1,2}$, it holds $Q_1/T_1+Q_2/T_2 \leq 0$. Combined with the observation that the quantity $Q_1+Q_2$ is the work $W$ done by the system, that inequality tells that only 4 possible operation modes are possible for the thermal machine, namely heat engine [E], refrigerator [R], thermal accelerator [A] and heater [H]. We illustrate their emergence in the finite time operation of a quantum Otto engine realised with a single qubit. We …
A natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to the interaction with the quantized photon mode. One of the channels of such a process is the dynamical Lamb effect, induced by a nonadiabatic modulation of atomic level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (artificial macroscopic atom) provides a unique platform for the observation of the dynamical Lamb effe…
The flip-flop qubit, encoded in the states with antiparallel donor-bound electron and donor nuclear spins in silicon, showcases long coherence times, good controllability, and, in contrast to other donor-spin-based schemes, long-distance coupling. Electron spin control near the interface, however, is likely to shorten the relaxation time by many orders of magnitude, reducing the overall qubit quality factor. Here, we theoretically study the multilevel system that is formed by the interacting electron and nuclear spins and derive analytical effective two-level Hamiltonians with and without peri…
The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with standard semiconductor manufacturing. Here, we show that a quantum error correction code can be implemented using a four-qubit array in germanium. We demonstrate a resonant SWAP gate and by combining controlled-Z and controlled-$\text{S}^{-1}$ gates we construct a Toffoli-like three-qubit gate. We execute a two-qubit phase flip code and find that we can pres…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the smallest QEC codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Experimental demonstrations of QE…
Quantum information processing has greatly increased interest in the phenomenon of environmentally-induced decoherence. The spin boson model is widely used to study the interaction between a spin-modelling a quantum particle moving in a double well potential-and its environment-modelled by a heat bath of harmonic oscillators. This paper extends a previous analysis of the static spin boson study to the driven spin boson case, with the derivation of an exact integro-differential equation for the time evolution of the propagator of the reduced spin density matrix. This is the first main result. B…
The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here we circumvent this hurdle by operating a single-atom `flip-flop' qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulati…
We study the dynamics of a two-level system described by a slowly varying Hamiltonian and weakly coupled to the Ohmic environment. We follow the Bloch--Redfield perturbative approach to include the effect of the environment on qubit evolution and take into account modification of the spectrum and matrix elements of qubit transitions due to time-dependence of the Hamiltonian. This formalism is applied to two problems. (1) We consider a qubit, or a spin-1/2, in a rotating magnetic field. We show that once the rotation starts, the spin has a component perpendicular to the rotation plane of the fi…
We study spin transfer torques induced by a spin-triplet supercurrent in a magnet with the superconducting proximity effect. By a perturbative approach, we show that spin-triplet correlations realize new types of torques, which are analogous to the adiabatic and non-adiabatic ($β$) torques, without extrinsic spin-flip scattering. Remarkable advantages compared to conventional spin-transfer torques are highlighted in domain wall manipulation. Oscillatory motions of a domain wall do not occur for a small Gilbert damping, and the threshold current density to drive its motion becomes zero in the a…
In this study, we examine decoherence of qubits system coupled independently by using influence functional. We especially concentrated on the effect of qubit flip process. We examine the zero-dimensional qubit and one-dimensional qubits system coupled with multi-band one-dimensional system. The qubit flip process leads to oscillation and self-excitation. We also obtained the time evolution of von Neumann entropy.The pure dephasing channel indicates entropy. These results show quantum brown motion. We present the numerical calculation of the entropy for random telegraph noise. This indicates th…
An important goal in quantum information processing is to reduce the duration of quantum-logical operations. Motivated by this, we provide a theoretical analysis of electrically induced fast dynamics of a single-electron spin-orbit qubit. We study the example of a one-dimensional quantum dot with Rashba spin-orbit interaction and harmonic driving, and focus on the case of strong driving, when the real-space oscillation amplitude of the driven electron is comparable to the width of its wave function. We provide simple approximate analytical relations between the qubit Larmor frequency, the shor…
Gate control of donor electrons near interfaces is a generic ingredient of donor-based quantum computing. Here, we address the question: how is the phonon-assisted qubit relaxation time $T_1$ affected as the electron is shuttled between the donor and the interface? We focus on the example of the `flip-flop qubit' [Tosi et al., arXiv:1509.08538v1], defined as a combination of the nuclear and electronic states of a phosphorous donor in silicon, promising fast electrical control and long dephasing times when the electron is halfway between the donor and the interface. We theoretically describe or…
Large-scale quantum computers rely on quantum error correction to protect the fragile quantum information. Among the possible candidates of quantum computing devices, silicon-based spin qubits hold a great promise due to their compatibility to mature nanofabrication technologies for scaling up. Recent advances in silicon-based qubits have enabled the implementations of high quality one and two qubit systems. However, the demonstration of quantum error correction, which requires three or more coupled qubits and often involves a three-qubit gate, remains an open challenge. Here, we demonstrate a…
We study single-qubit gates performed via stimulated Raman adiabatic passage (STIRAP) on a spin qubit implemented in a quantum dot system in the presence of phonons. We analyze the interplay of various kinds of errors resulting from the carrier-phonon interaction as well as from quantum jumps related to nonadiabaticity and calculate the fidelity as a function of the pulse parameters. We give quantitative estimates for an InAs/GaAs system and identify the parameter values for which the error is considerably minimized, even to values below $10^{-4}$ per operation.
We provide insight into the qubit measurement process involving a switching type of detector. We study the switching-induced decoherence during escape events. We present a simple method to obtain analytical results for the qubit dephasing and bit-flip errors, which can be easily adapted to various systems. Within this frame we investigate potential of switching detectors for a fast but only weakly invasive type of detection. We show that the mechanism that leads to strong dephasing, and thus fast measurement, inverts potential bit flip errors due to an intrinsic approximate time reversal symme…
Realizable spin models are investigated in a two superconducting flux qubit system. It is shown that a specific adjustment of system parameters in the two flux qubit system makes it possible to realize an artificial two-spin system that cannot be found naturally. For the artificial two-spin systems, time evolution of a prepared quantum state is discussed to quantify quantum entanglement dynamics. The concurrence and fidelity as a function of time are shown to reveal a characteristic entanglement dynamics of the artificial spin systems. It is found that the unentangled input state can evolute t…
We consider a CNOT gate operation under the influence of quantum bit-flip noise and demonstrate that ac fields can change bit-flip noise into phase noise and thereby improve coherence up to several orders of magnitude while the gate operation time remains unchanged. Within a high-frequency approximation, both purity and fidelity of the gate operation are studied analytically. The numerical treatment with a Bloch-Redfield master equation confirms the analytical results.
Josephson junctions based on semiconductor nanowires are potential building blocks for electrically tunable qubit structures, e.g. the gatemon or the Andreev qubit. However, an actual realization requires the thorough investigation of the intrinsic excitation spectrum. Here, we demonstrate the fabrication of low-loss superconducting microwave circuits that combine high quality factors with a well-controlled gate architecture by utilizing a flip-chip approach. This platform is then used to perform single-tone and two-tone experiments on Andreev states in in-situ grown InAs/Al core/half-shell na…
