Dynamical Decoupling Sequences Research Articles

Synergistic Dynamical Decoupling and Circuit Design for Enhanced Algorithm Performance on Near-Term Quantum Devices.

Dynamical decoupling (DD) is a promising technique for mitigating errors in near-term quantum devices. However, its effectiveness depends on both hardware characteristics and algorithm implementation details. This paper explores the synergistic effects of dynamical decoupling and optimized circuit design in maximizing the performance and robustness of algorithms on near-term quantum devices. By utilizing eight IBM quantum devices, we analyze how hardware features and algorithm design impact the effectiveness of DD for error mitigation. Our analysis takes into account factors such as circuit fidelity, scheduling duration, and hardware-native gate set. We also examine the influence of algorithmic implementation details, including specific gate decompositions, DD sequences, and optimization levels. The results reveal an inverse relationship between the effectiveness of DD and the inherent performance of the algorithm. Furthermore, we emphasize the importance of gate directionality and circuit symmetry in improving performance. This study offers valuable insights for optimizing DD protocols and circuit designs, highlighting the significance of a holistic approach that leverages both hardware features and algorithm design for the high-quality and reliable execution of near-term quantum algorithms.

Multi-qubit dynamical decoupling for enhanced crosstalk suppression

Dynamical decoupling (DD) is one of the simplest error suppression methods, aiming to enhance the coherence of qubits in open quantum systems. Moreover, DD has demonstrated effectiveness in reducing coherent crosstalk, one major error source in near-term quantum hardware, which manifests from two types of interactions. Static crosstalk exists in various hardware platforms, including superconductor and semiconductor qubits, by virtue of always-on qubit-qubit coupling. Additionally, driven crosstalk may occur as an unwanted drive term due to leakage from driven gates on other qubits. Here we explore a novel staggered DD protocol tailored for multi-qubit systems that suppresses the decoherence error and both types of coherent crosstalk. We develop two experimental setups—an ‘idle–idle’ experiment in which two pairs of qubits undergo free evolution simultaneously and a ‘driven-idle’ experiment in which one pair is continuously driven during the free evolution of the other pair. These experiments are performed on an IBM Quantum superconducting processor and demonstrate the significant impact of the staggered DD protocol in suppressing both types of coherent crosstalk. When compared to the standard DD sequences from state-of-the-art methodologies with the application of X2 sequences, our staggered DD protocol enhances circuit fidelity by 19.7% and 8.5%, respectively, in addressing these two crosstalk types.

Quantum double lock-in amplifier

Quantum lock-in amplifiers have been proposed to extract an alternating signal from a strong noise background. However, due to the typical target signal has unknown initial phase, it is challenging to extract complete information about the signal’s amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in amplifier by employing two quantum mixers operating under orthogonal pulse sequences. To demonstrate the practical implementation, we discuss the experimental feasibility using a five-level double-Λ coherent population trapping system with Rb atoms. Here, each Λ structure acts as a quantum mixer, and two applied dynamical decoupling sequences serve as orthogonal reference signals. Notably, the system significantly reduces the total measurement time by nearly half and mitigates time-dependent systematic errors compared to conventional two-level systems. Furthermore, our quantum double lock-in amplifier is robust against experimental imperfections. This study establishes a pathway to alternating signal measurement, thereby facilitating the development of practical quantum sensing technologies.

Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZM-like states with minimal cross-talk. We introduce the M-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZM-like states of up to M=10 qubits within time constraints that saturate bounds on M-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary M-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary M-tangling power which incorporates the impact of electronic dephasing errors on the M-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation.

Dissipative Dynamics of Graph-State Stabilizers with Superconducting Qubits.

We study experimentally and numerically the noisy evolution of multipartite entangled states, focusing on superconducting qubit devices accessible via the cloud. We find that a valid modeling of the dynamics requires one to properly account for coherent frequency shifts, caused by stochastic charge-parity fluctuations. We introduce an approach modeling the charge-parity splitting using an extended Markovian environment. This approach is numerically scalable to tens of qubits, allowing us to simulate efficiently the dissipative dynamics of some large multiqubit states. Probing the continuous-time dynamics of increasingly larger and more complex initial states with up to 12 coupled qubits in a ring-graph state, we obtain a good agreement of the experiments and simulations. We show that the underlying many-body dynamics generate decays and revivals of stabilizers, which are used extensively in the context of quantum error correction. Furthermore, we demonstrate the mitigation of 2-qubit coherent interactions (crosstalk) using tailored dynamical decoupling sequences. Our noise model and the numerical approach can be valuable to advance the understanding of error correction and mitigation and invite further investigations of their dynamics.

Amplified nanoscale detection of labeled molecules via surface electrons on diamond

The detection of individual molecules and their dynamics is a long-standing challenge in the field of nanotechnology. In this work, we present a method that utilizes a nitrogen vacancy (NV) center and a dangling bond on the diamond surface to measure the coupling between two electronic targets tagged on a macromolecule. To achieve this, we design a multi-tone dynamical decoupling sequence that leverages the strong interaction between the nitrogen vacancy center and the dangling bond. In addition, this sequence minimizes the impact of decoherence finally resulting in an increased signal-to-noise ratio. This proposal has the potential to open up avenues for fundamental research and technological innovation in distinct areas such as biophysics and biochemistry.

Frequency Limits of Sequential Readout for Sensing AC Magnetic Fields Using Nitrogen-Vacancy Centers in Diamond.

The nitrogen-vacancy (NV) centers in diamond have the ability to sense alternating-current (AC) magnetic fields with high spatial resolution. However, the frequency range of AC sensing protocols based on dynamical decoupling (DD) sequences has not been thoroughly explored experimentally. In this work, we aimed to determine the sensitivity of the ac magnetic field as a function of frequency using the sequential readout method. The upper limit at high frequency is clearly determined by Rabi frequency, in line with the expected effect of finite DD-pulse width. In contrast, the lower frequency limit is primarily governed by the duration of optical repolarization rather than the decoherence time (T2) of NV spins. This becomes particularly crucial when the repetition (dwell) time of the sequential readout is fixed to maintain the acquisition bandwidth. The equation we provide successfully describes the tendency in the frequency dependence. In addition, at the near-optimal frequency of 1 MHz, we reached a maximum sensitivity of 229 pT/Hz by employing the XY4-(4) DD sequence.

Measuring the environment of a Cs qubit with dynamical decoupling sequences

We report the experimental implementation of dynamical decoupling on a small, non-interacting ensemble of up to 25 optically trapped, neutral Cs atoms. The qubit consists of the two magnetic-insensitive Cs clock states and , which are coupled by microwave radiation. We observe a significant enhancement of the coherence time when employing Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. A CPMG sequence with ten refocusing pulses increases the coherence time of 16.2(9) ms by more than one order of magnitude to 178(2) ms. In addition, we make use of the filter function formalism and utilise the CPMG sequence to measure the background noise floor affecting the qubit coherence, finding a power-law noise spectrum with . This finding is in very good agreement with an independent measurement of the noise in the intensity of the trapping laser. Moreover, the measured coherence evolutions also exhibit signatures of low-frequency noise originating at distinct frequencies. Our findings point toward noise spectroscopy of engineered atomic baths through single-atom dynamical decoupling in a system of individual Cs impurities immersed in an ultracold 87Rb bath.

Coherent dynamics of strongly interacting electronic spin defects in hexagonal boron nitride

Optically active spin defects in van der Waals materials are promising platforms for modern quantum technologies. Here we investigate the coherent dynamics of strongly interacting ensembles of negatively charged boron-vacancy ({{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-}) centers in hexagonal boron nitride (hBN) with varying defect density. By employing advanced dynamical decoupling sequences to selectively isolate different dephasing sources, we observe more than 5-fold improvement in the measured coherence times across all hBN samples. Crucially, we identify that the many-body interaction within the {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-} ensemble plays a substantial role in the coherent dynamics, which is then used to directly estimate the concentration of {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-}. We find that at high ion implantation dosage, only a small portion of the created boron vacancy defects are in the desired negatively charged state. Finally, we investigate the spin response of {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-} to the local charged defects induced electric field signals, and estimate its ground state transverse electric field susceptibility. Our results provide new insights on the spin and charge properties of {{{{{{{{rm{V}}}}}}}}}_{{{{{{{{rm{B}}}}}}}}}^{-}, which are important for future use of defects in hBN as quantum sensors and simulators.

Robust two-qubit gates using pulsed dynamical decoupling

We present the experimental implementation of a two-qubit phase gate, using a radio frequency (RF) controlled trapped-ion quantum processor. The RF-driven gate is generated by a pulsed dynamical decoupling sequence applied to the ions’ carrier transitions only. It allows for a tunable phase shift with high-fidelity results. The conditional phase shift is measured using a Ramsey-type measurement with an inferred fringe contrast of up to . We also prepare a Bell state using this laser-free gate. The phase gate is robust against common sources of error. We investigate the effect of the excitation of the center-of-mass (COM) mode, errors in the axial trap frequency, pulse area errors and errors in sequence timing. The contrast of the phase gate is not significantly reduced up to a COM mode excitation 20 phonons, trap frequency errors of +10%, and pulse area errors of −8%. The phase shift is not significantly affected up to 10 phonons and pulse area errors of −2%. Both, contrast and phase shift are robust to timing errors up to −30% and +15%. The gate implementation is resource efficient, since only a single driving field is required per ion. Furthermore, it holds the potential for fast gate speeds (gate times on the order of 100 µs) by using two axial motional modes of a two-ion crystal through improved setups.

Learning noise via dynamical decoupling of entangled qubits

Understanding noise in entangled systems is a prerequisite for developing scalable quantum computers. Here, we propose and apply multiqubit dynamical decoupling sequences that characterize noise during two-qubit gates. This noise is qualitatively different from the well-studied noise that leads to single-qubit dephasing; it simultaneously affects the two qubits, inducing fluctuations in their entangling parameter. In our superconducting system, the experimentally observed noise comes from coupler flux fluctuations and is observed to be non-Gaussian, leading to the stepwise decay of signals.

Deep learning enhanced noise spectroscopy of a spin qubit environment

The undesired interaction of a quantum system with its environment generally leads to a coherence decay of superposition states in time. A precise knowledge of the spectral content of the noise induced by the environment is crucial to protect qubit coherence and optimize its employment in quantum device applications. We experimentally show that the use of neural networks (NNs) can highly increase the accuracy of noise spectroscopy, by reconstructing the power spectral density that characterizes an ensemble of carbon impurities around a nitrogen-vacancy (NV) center in diamond. NNs are trained over spin coherence functions of the NV center subjected to different Carr–Purcell sequences, typically used for dynamical decoupling (DD). As a result, we determine that deep learning models can be more accurate than standard DD noise-spectroscopy techniques, by requiring at the same time a much smaller number of DD sequences.

Protection of noisy multipartite entangled states of superconducting qubits via universally robust dynamical decoupling schemes

In this paper, we demonstrate the efficacy of the universally robust dynamical decoupling (URDD) sequence to preserve multipartite maximally entangled quantum states on a cloud-based quantum computer via the IBM platform. URDD is a technique that can compensate for experimental errors and simultaneously protect the state against environmental noise. To further improve the performance of the URDD sequence, phase randomization (PR) as well as correlated PR (CPR) techniques are added to the basic URDD sequence. The performance of the URDD sequence is quantified by measuring the entanglement in several noisy entangled states (two-qubit triplet state, three-qubit Greenberger–Horne–Zeilinger (GHZ) state, four-qubit GHZ state and four-qubit cluster state) at several time points. Our experimental results demonstrate that the URDD sequence is successfully able to protect noisy multipartite entangled states and its performance is modestly improved by adding the PR and CPR sequences.

Coherent Control of a Nuclear Spin via Interactions with a Rare-Earth Ion in the Solid State

Individually addressed Er$^{3+}$ ions in solid-state hosts are promising resources for quantum repeaters, because of their direct emission in the telecom band and compatibility with silicon photonic devices. While the Er$^{3+}$ electron spin provides a spin-photon interface, ancilla nuclear spins could enable multi-qubit registers with longer storage times. In this work, we demonstrate coherent coupling between the electron spin of a single Er$^{3+}$ ion and a single $I=1/2$ nuclear spin in the solid-state host crystal, which is a fortuitously located proton ($^1$H). We control the nuclear spin using dynamical decoupling sequences applied to the electron spin, implementing one- and two-qubit gate operations. Crucially, the nuclear spin coherence time exceeds the electron coherence time by several orders of magnitude, because of its smaller magnetic moment. These results provide a path towards combining long-lived nuclear spin quantum registers with telecom-wavelength emitters for long-distance quantum repeaters.

Spinsim: A GPU optimized python package for simulating spin-half and spin-one quantum systems

Spinsim simulates the quantum dynamics of unentangled spin-1/2 and spin-1 systems evolving under time-dependent control. While other solvers for the time-dependent Schrödinger equation optimize for larger state spaces but less temporally-rich control, spinsim is optimized for intricate time evolution of a minimalist system. Efficient simulation of individual or ensemble quanta driven by adiabatic sweeps, elaborate pulse sequences, complex signals and non-Gaussian noise is the primary target application. We achieve fast and robust evolution using a geometric integrator to bound errors over many steps, and split the calculation parallel-in-time on a GPU using the numba just-in-time compiler. Speed-up is three orders of magnitude over QuTip's sesolve and Mathematica's NDSolve, and four orders over SciPy's ivp_solve for equal accuracy. Interfaced through python, spinsim should be useful for simulating robust state preparation, inversion and dynamical decoupling sequences in NMR and MRI, and in quantum control, memory and sensing applications with two- and three-level quanta. Program summaryProgram Title: SpinsimCPC Library link to program files:https://doi.org/10.17632/f6rdk4gyxr.1Developer's repository link:https://github.com/alexander-tritt-monash/spinsimLicensing provisions: BSD 3-clauseProgramming language: Python (3.7 or greater)Nature of problem: Quantum sensing is a domain of quantum technology where the dynamics of quantum systems are used to infer properties of the systems' environments. The development of quantum sensing protocols is greatly sped-up by software simulations of the new techniques. Quantum sensing simulation benefits from temporally-rich control of individual quanta. However, current specialized time-dependent Schrödinger equation solvers are instead optimized only for simple pulses in large Hilbert spaces. Thus, there is a need for efficient simulation of individual or ensemble quanta driven by adiabatic sweeps, elaborate pulse sequences, complex signals and non-Gaussian noise.Solution method: Spinsim simulates the quantum dynamics of spin-1/2 and spin-1 systems evolving under time-dependent control. We first speed up the integration of the time-dependent Schrödinger equation by splitting the calculation parallel-in-time on a GPU using the numba [1] just-in-time compiler. We achieve fast and robust evolution using a geometric integrator to bound errors over many steps. A dynamic rotating frame transformation and Lie-Trotter decomposition are used to decrease effective step sizes on long and short time scales, respectively. Hence, each individual step is more accurate. Spinsim is interfaced via a python package, meaning it can be used by researchers inexperienced with geometric integrators and GPU parallelism.Additional comments including restrictions and unusual features: To use the (default) Nvidia cuda GPU parallelization, one needs to have a cuda compatible Nvidia GPU [2]. For cuda mode to function, one also needs to install the Nvidia cuda toolkit [3]. If cuda is not available on the system, the simulator will automatically parallelize over multicore CPUs instead. Developed and tested on Windows 10; tested on Windows 11. CPU functionality tested on MacOS 10.16 Big Sur (note that MacOS 10.14 Mojave and higher are not compatible with cuda hardware and software). The package (including cuda functionality) is in principle compatible with Linux, but functionality has not been tested.

Monte Carlo simulation of the nuclear spin decoherence process in Eu3+ : Y2SiO5 crystals

${\mathrm{Eu}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ crystals are promising candidates for quantum memories because their nuclear spin coherence lifetime can be extended to 47 seconds at a particular magnetic field. Although an extended coherence lifetime of 6 hours can be achieved with a large number of dynamic decoupling sequences, these pulses will also introduce unwanted noise. To realize quantum storage with a lifetime of hours, it is necessary to quantitatively characterize the spin decoherence process of ${\mathrm{Eu}}^{3+}$ ions to guide the experimental efforts. In practice, a number of limiting factors could impose a limit on the achievable spin coherence lifetime, which includes the spin inhomogeneous broadening of the ${\mathrm{Eu}}^{3+}$ ensemble and the homogeneity and stability of the external magnetic field. Here, we provide a Monte Carlo simulation model of the nuclear spin decoherence process of ${\mathrm{Eu}}^{3+}$ ions in ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ crystals, and these limiting factors are considered to provide an accurate prediction of the spin coherence lifetimes. This method is universal and can be applied to other rare-earth-ion-doped crystals.

Robust Dynamical Decoupling for the Manipulation of a Spin Network Via a Single Spin

High-fidelity control of quantum systems is crucial for quantum information processing, but is often limited by perturbations from the environment and imperfections in the applied control fields. Here, we investigate the combination of dynamical decoupling (DD) and robust optimal control (ROC) to address this problem. In this combination, ROC is employed to find robust shaped pulses, wherein the directional derivatives of the controlled dynamics with respect to control errors are reduced to a desired order. Then, we incorporate ROC pulses into DD sequences, achieving a remarkable improvement of robustness against multiple error channels. We demonstrate this method in the example of manipulating nuclear spin bath via an electron spin in the nitrogen-vacancy center system. Simulation results indicate that ROC-based DD sequences outperform the state-of-the-art robust DD sequences. Our work has implications for robust quantum control on near-term noisy quantum devices.

Suppression of Crosstalk in Superconducting Qubits Using Dynamical Decoupling

Currently available superconducting quantum processors with interconnected transmon qubits are noisy and prone to various errors. The errors can be attributed to sources such as open quantum system effects and spurious inter-qubit couplings (crosstalk). The ZZ-coupling between qubits in fixed frequency transmon architectures is always present and contributes to both coherent and incoherent crosstalk errors. Its suppression is therefore a key step towards enhancing the fidelity of quantum computation using transmons. Here we propose the use of dynamical decoupling to suppress the crosstalk, and demonstrate the success of this scheme through experiments performed on several IBM quantum cloud processors. In particular, we demonstrate improvements in quantum memory as well as the performance of single-qubit and two-qubit gate operations. We perform open quantum system simulations of the multi-qubit processors and find good agreement with the experimental results. We analyze the performance of the protocol based on a simple analytical model and elucidate the importance of the qubit drive frequency in interpreting the results. In particular, we demonstrate that the XY4 dynamical decoupling sequence loses its universality if the drive frequency is not much larger than the system-bath coupling strength. Our work demonstrates that dynamical decoupling is an effective and practical way to suppress crosstalk and open system effects, thus paving the way towards higher-fidelity logic gates in transmon-based quantum computers.

Five-second coherence of a single spin with single-shot readout in silicon carbide.

An outstanding hurdle for defect spin qubits in silicon carbide (SiC) is single-shot readout, a deterministic measurement of the quantum state. Here, we demonstrate single-shot readout of single defects in SiC via spin-to-charge conversion, whereby the defect’s spin state is mapped onto a long-lived charge state. With this technique, we achieve over 80% readout fidelity without pre- or postselection, resulting in a high signal-to-noise ratio that enables us to measure long spin coherence times. Combined with pulsed dynamical decoupling sequences in an isotopically purified host material, we report single-spin T2 > 5 seconds, over two orders of magnitude greater than previously reported in this system. The mapping of these coherent spin states onto single charges unlocks both single-shot readout for scalable quantum nodes and opportunities for electrical readout via integration with semiconductor devices.

Effects of Dynamical Decoupling and Pulse-Level Optimizations on IBM Quantum Computers

Currently available quantum computers are prone to errors. Circuit optimization and error mitigation methods are needed to design quantum circuits to achieve better fidelity when executed on NISQ hardware. Dynamical decoupling (DD) is generally used to suppress the decoherence error and different DD strategies have been proposed. Moreover, the circuit fidelity can be improved by pulse-level optimization, such as creating hardware-native pulse-efficient gates. This paper implements all the popular DD sequences and evaluates their performances on IBM quantum chips with different characteristics for various well-known quantum applications. Also, we investigate combining DD with pulse-level optimization method and apply them to QAOA to solve Max-Cut problem. Based on the experimental results, we found that DD can be a benefit for only certain types of quantum algorithms, while the combination of DD and pulse-level optimization methods always has a positive impact. Finally, we provide several guidelines for users to learn how to use these noise mitigation methods to build circuits for quantum applications with high fidelity on IBM quantum computers.