Dense ensembles of spin qubits are valuable for quantum applications, even though their coherence protection remains challenging. Continuous dynamical decoupling can protect ensemble qubits from noise while allowing gate operations, but it is hindered by the additional noise introduced by the driving. Concatenated continuous driving (CCD) techniques can, in principle, mitigate this problem. Here we provide deeper insights into the dynamics under CCD, based on Floquet theory, that lead to optimized state protection by adjusting driving parameters in the CCD scheme to induce mode evolution control. We experimentally demonstrate the improved control by simultaneously addressing a dense Nitrogen-vacancy (NV) ensemble with $10^{10}$ spins. We achieve an experimental 15-fold improvement in coherence time for an arbitrary, unknown state, and a 500-fold improvement for an arbitrary, known state, corresponding to driving the sidebands and the center band of the resulting Mollow triplet, respectively. We can achieve such coherence time gains by optimizing the driving parameters to take into account the noise affecting our system. By extending the generalized Bloch equation approach to the CCD scenario, we identify the noise sources that dominate the decay mechanisms in NV ensembles, confirm our model by experimental results, and identify the driving strengths yielding optimal coherence. Our results can be directly used to optimize qubit coherence protection under continuous driving and bath driving, and enable applications in robust pulse design and quantum sensing.
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure.
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct against phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error-correcting codes offers a practical tool to handle realistic noise contributed by both ind…
In this paper, we present a realistic application of the coherence protection method proposed in the previous article. A qubit of information encoded on the two spin states of a Rubidium isotope is protected from the action of electric and magnetic fields.
The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence ti…
In this paper, we investigate coherence protection of a quantum system coupled to a hierarchical environment by utilizing noise. As an example, we solve the Jaynes-Cummings (J-C) model in presence of both a classical and a quantized noise. The master equation is derived beyond the Markov approximation, where the influence of memory effects from both noises is taken into account. More importantly, we find that the performance of the coherence protection sensitively depends on the non-Markovian properties of both noises. By analyzing the mathematical mechanism of the coherence protection, we sho…
We show that the effects of decoherence on quantum steering ellipsoids can be controlled by a specific reservoir manipulating, in both Markovian and non-Markovian realms. Therefore, the so-called maximal steered coherence could be protected through reservoir engineering implemented by coupling auxiliary qubits to the reservoir.
In this paper, we present a coherence protection method based upon a multidimensional generalization of the Quantum Zeno Effect, as well as ideas from the coding theory. The non-holonomic control technique is employed as a physical tool which allows its effective implementation. The two limiting cases of small and large quantum systems are considered.
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be arbitrarily suppressed. By concatenating the 7-qubit Steane and 15-qubit Reed-Muller codes, the 105-qubit code enables a universal set of fault-tolerant gates despite not all of them being transversal. Importantly, the CNOT gate remains transversal in both codes, and as such has increased error protection relative to the other single qubit logical gates. We show…
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed.
In this letter, we investigate the effects of non-Hermitian driving on quantum coherence in a bipartite system. The results that the dynamical localization destroyed by the Hermitian interaction revives are an evidence of the restoration of quantum coherence by non-Hermitian driving. Besides, the entanglement between the two subsystems also decays with the boosting of non-hermitian driving strength, which provides another evidence that non-Hermitian driving will protect quantum coherence. The physics behind this phenomenon is the domination of the quasieigenstate with maximum imaginary value o…
The interaction of a quantum system with its environment causes decoherence, setting a fundamental limit on the suitability of a system for quantum information processing. However, we show that if the quantum system consists of coupled parts with different internal energy scales then the interaction of one part with a thermal bath need not lead to loss of coherence from the other. Remarkably, we find that the protected part can become more coherent when the coupling to the bath becomes stronger or the temperature is raised. Our theory will enable the design of decoherence-resistant hybrid quan…
We experimentally emulate, in a controlled fashion, the non-Markovian dynamics of a pure dephasing spin-boson model at zero temperature. Specifically, we use a randomized set of external radio-frequency fields to engineer a desired noise power-spectrum to effectively realize a non-Markovian environment for a single NMR qubit. The information backflow, characteristic to the non-Markovianity, is captured in the nonmonotonicity of the decoherence function and von Neumann entropy of the system. Using such emulated non-Markovian environments, we experimentally study the efficiency of the Carr-Purce…
We consider finite sized atomic systems with varying number of particles which have dipolar interactions among them and also under the collective driving and dissipative effect of thermal photon environment. Focusing on the simple case of two atoms, we investigate the impact of different parameters of the model on the coherence contained in the system. We observe that even though the system is initialized in a completely incoherent state, it evolves to a state with a finite amount of coherence and preserve that coherence in the long-time limit in the presence of thermal photons. We propose a n…
We consider topological protection mechanisms in dissipative quantum systems in the presence of quenched disorder, with the intent to prolong coherence times of qubits. The physical setting is a network of qubits and dissipative cavities whose coupling parameters are tunable, such that topological edge states can be stabilized. The evolution of a fiducial qubit is entirely determined by a non-Hermitian Hamiltonian which thus emerges from a bona-fide physical process. It is shown how even in the presence of disorder winding numbers can be defined and evaluated in real space, as long as certain …
Concatenated dynamical decoupling (CDD) pulse sequences hold much promise as a strategy to mitigate decoherence in quantum information processing. It is important to investigate the actual performance of these dynamical decoupling strategies in real systems that are promising qubit candidates. In this Rapid Communication, we compute the echo decay of concatenations of the Hahn echo sequence for a solid-state electronic spin qubit in a nuclear spin bath using a cluster expansion technique. We find that each level of concatenation reverses the effect of successive levels of intrabath fluctuation…
The protection of qubit coherence is an essential task in order to build a practical quantum computer able to manipulate, store and read quantum information with a high degree of fidelity. Recently, it has been proposed to increase the operation time of a qubit by means of strong pulses to achieve a dynamical decoupling of the qubit from its environment. We propose and demonstrate a simple and highly efficient alternative pulse protocol based on Floquet modes, which increases the decoherence time in a number of materials with different spin Hamiltonians and environments. We demonstrate the reg…
Decoherence largely limits the physical realization of qubits and its mitigation is critical to quantum science. Here, we construct a robust qubit embedded in a decoherence-protected subspace, obtained by hybridizing an applied microwave drive with the ground-state electron spin of a silicon carbide divacancy defect. The qubit is protected from magnetic, electric, and temperature fluctuations, which account for nearly all relevant decoherence channels in the solid state. This culminates in an increase of the qubit's inhomogeneous dephasing time by over four orders of magnitude (to > 22 millise…
Understanding fully the dynamics of coupled electron-nuclear spin systems, which are important for the development of long-lived qubits based on solid-state systems, remains a challenge. We show that in a singly charged semiconductor quantum dot with inhomogeneous hyperfine coupling, the nuclear spins relatively strongly coupled to the electron spin form a polarized core during the dynamical polarization process. The polarized core provides a protection effect against the electron spin relaxation, reducing the decay rate by a factor of $N_1$, the number of the nuclear spins in the polarized co…
We experimentally investigate the protection of electron spin coherence of nitrogen vacancy (NV) center in diamond by dynamical nuclear polarization. The electron spin decoherence of an NV center is caused by the magnetic ield fluctuation of the $^{13}$C nuclear spin bath, which contributes large thermal fluctuation to the center electron spin when it is in equilibrium state at room temperature. To address this issue, we continuously transfer the angular momentum from electron spin to nuclear spins, and pump the nuclear spin bath to a polarized state under Hartman-Hahn condition. The bath pola…
One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases to non-Hermitian systems, a finite system in a non-trivial topological phase displays surface states with exponentially long life times. In this work we explore the possibility of exploiting such non-Hermitian topological phases to enhance the quantum coherence of a fiducial qubit embedded in a dissipative environment. We first show that a network of qubits interacting with lossy cavities can be represented, in a suitable super-one-par…
We re-examine a scheme generalized by [R. Finkelstein et al, Phys. Rev. X 11, 011008 (2021)], whose original purpose was to remove the effects of static Doppler broadening from an ensemble of non-interacting two-level systems (qubits). This scheme involves the simultaneous application of red and blue detuned drives between a qubit level and an auxiliary level, and by carefully choosing the drive amplitudes and detunings, the drive-induced energy shifts can exactly compensate the inhomogeneous static Doppler-induced frequency shifts - effectively removing the inhomogeneous Doppler broadening. W…
All-mechanical coherence protection and fast control of a spin qubit
John A. Paulson School for Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；IonQ；Q-CTRL；Nubis Communications；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（巴伐利亚科学院瓦尔特·迈斯纳研究所）
There are several important solid-state systems, such as defects in solids, superconducting circuits and molecular qubits, for attractive candidates of quantum computations. Molecular qubits, which benefit from the power of chemistry for the tailored and inexpensive synthesis of new systems, face the challenge from decoherence effect. The decoherence effect is due to the molecular qubits' inevitable interactions to their environment. Strategies to overcome decoherence effect have been developed, such as designing a nuclear spin free environment and working at atomic clock transitions. These ch…
Quantum coherence and non-Markovianity of an atom in dissipative cavity under weak measurement are investigated in this work. We find that, the quantum coherence obviously depends on the atomic initial state, the strength of the weak measurement and its reversal, the atom-cavity coupling constant and the non-Markovian effecct. The more obvious the weak measurement effect is, the better the protection of coherence is. The quantum coherence is preserved more efficiently for lager the atom-cavity coupling. The stronger the non-Markovian effect, the more slowly the coherence reduces. This is, the …
In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities such as quantum gates. Here we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretati…
In this paper we study an error correcting protocol that specifically derives its error correcting properties from elementary units of coherence. The entire protocol from beginning to end is performed using non-coherence increasing operations, resulting in the consumption of the input coherence, thus necessitating further quantum resources if one wishes to perform the protocol again. We show that even when the input quantum resource is just 1 coherent qubit, one may acquire partial protection from phase flip errors, and that this can be scaled up to protect against arbitrary qubit errors with …
We put forward a scheme based on reservoir engineering to protect quantum coherence from leaking to bath, in which we intensely disturb the Lorentzian bath by N harmonic oscillators. We show that the intense disturbance changes the spectrum of the bath and reduces the qubit-bath interaction. Furthermore, we give the exact time evolution with the Lorentzian spectrum by a master equation, and calculate the concurrence and survival probability of the qubits to demonstrate the effect of the intense bath disturbance on the protection of coherence. Meanwhile, we reveal the dynamic effects of counter…
Superconducting circuits rank among the most interesting architectures for the implementation of quantum information processing devices. The recently proposed 0-$π$ qubit [Brooks et al., Phys. Rev. A ${\bf 87}$, 52306 (2013)] promises increased protection from spontaneous relaxation and dephasing. In practice, this ideal behavior is only realized if the parameter dispersion among nominally identical circuit elements vanishes. In this paper we present a theoretical study of the more realistic scenario of slight variations in circuit elements. We discuss how the coupling to a spurious, low-energ…
We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to $77$ K suppresses longitudinal spin relaxation $T_1$ effects and DD microwave pulses are used to increase the transverse coherence time $T_2$ from $\sim 0.7$ ms up to $\sim 30$ ms. We extend previous work of single-axis (CPMG) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance o…
In this paper, we investigate preservation of quantum coherence of a single-qubit interacting with a zero-temperature thermal reservoir through the addition of noninteracting qubits in the reservoir. Moreover, we extend this scheme to preserve quantum entanglement between two and three distant qubits, each of which interacts with a dissipative reservoir independently. At the long time limit, we obtained analytical expressions for the coherence measure and the concurrence of two and three qubits in terms of the number of additional qubits. It is observed that, by increasing the number of additi…
Modern quantum technologies rely crucially on techniques to mitigate quantum decoherence; these techniques can be either passive, achieved for example via materials engineering, or active, typically achieved via pulsed monochromatic driving fields applied to the qubit. Using a solid-state defect spin coupled to a microwave-driven spin bath, we experimentally demonstrate a decoherence mitigation method based on spectral engineering of the environmental noise with a polychromatic drive waveform, and show that it outperforms monochromatic techniques. Results are in agreement with quantitative mod…
We investigate the effectiveness of different dynamical decoupling protocols for storage of a single qubit in the presence of a purely dephasing bosonic bath, with emphasis on comparing quantum coherence preservation under uniform vs. non-uniform delay times between pulses. In the limit of instantaneous bit-flip pulses, this is accomplished by establishing a new representation of the controlled qubit evolution, where the resulting decoherence behaviour is directly expressed in terms of the free evolution. Simple analytical expressions are given to approximate the long- and short- term coherenc…
We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare performance of Hahn, CP, concatenated dynamical decoupling (CDD) and Uhrig dynamical decoupling (UDD) for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T2 ~ 80 microseconds.
Although the Gaussian-noise assumption is widely adopted in the study of qubit decoherence, non-Gaussian noise sources, especially the strong discrete fluctuators, have been detected in many qubits. It remains an important task to further understand and mitigate the distinctive decoherence effect of the non-Gaussian noise. Here, we study the qubit dephasing caused by the non-Gaussian fluctuators, and predict a symmetry-breaking effect that is unique to the non-Gaussian noise. This broken symmetry results in an experimentally measurable mismatch between the extremum points of the dephasing rate…
Symmetry considerations are key towards our understanding of the fundamental laws of Nature. The presence of a symmetry implies that a physical system is invariant under specific transformations and this invariance may have deep consequences. For instance, symmetry arguments state that a system will remain in its initial state if incentives to actions are equally balanced. Here, we apply this principle to a chain of qubits and show that it is possible to engineer the symmetries of its Hamiltonian in order to keep quantum information intrinsically protected from both relaxation and decoherence.…
Entanglement and coherence protection are investigated using the dynamical map of three non-interacting qubits that are initially prepared as maximally entangled GHZ-like states coupled to external fields in solid-state and superconducting materials. Thermal fluctuations and resistance in these materials produce power-law (PL) noise, which we assume controls external fields in three different configurations with single or multiple noise sources. The genuine response of isolated environments to entanglement and coherence retention is analyzed. We also briefly discuss the initial purity and rela…
We address entanglement, coherence, and information protection in a system of four non-interacting qubits coupled with different classical environments, namely: common, bipartite, tripartite, and independent environments described by Ornstein-Uhlenbeck (ORU) noise. We show that quantum information preserved by the four qubit state is more dependent on the coherence than the entanglement using time-dependent entanglement witness, purity, and Shannon entropy. We find these two quantum phenomena directly interrelated and highly vulnerable in environments with ORU noise, resulting in the pure expo…
Under the Born--Markov approximation, a qubit system, such as a two-level atom, is known to undergo a memoryless decay of quantum coherence or excitation when weakly coupled to a featureless environment. Recently, it has been shown that unavoidable disorder in the environment is responsible for non-Markovian effects and information backflow from the environment into the system owing to Anderson localization. This~turns disorder into a resource for enhancing non-Markovianity in the system--environment dynamics, which could be of relevance in cavity quantum electrodynamics. Here we consider the …
