We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols offer superior convergence and stability as compared to deterministic counterparts. In addition, we show how randomization always allows to outperform purely deterministic schemes at long times, including combinatorial and concatenated methods. General criteria for optimally interpolating between deterministic and stochastic design are proposed and illustrated in explicit decoupling scenarios relevant to quantum information storage.
We introduce a task that we call partial decoupling, in which a bipartite quantum state is transformed by a unitary operation on one of the two subsystems and then is subject to the action of a quantum channel. We assume that the subsystem is decomposed into a direct-sum-product form, which often appears in the context of quantum information theory. The unitary is chosen at random from the set of unitaries having a simple form under the decomposition. The goal of the task is to make the final state, for typical choices of the unitary, close to the averaged final state over the unitaries. We co…
The present thesis deals with various methods of quantum error correction. It is divided into two parts. In the first part, dynamical decoupling methods are considered which have the task of suppressing the influence of residual imperfections in a quantum memory. The suppression is achieved by altering the dynamics of an imperfect quantum memory with the help of a sequence of local unitary operations applied to the qudits. Whereas up to now the operations of such decoupling sequences have been constructed in a deterministic fashion, strategies are developed in this thesis which construct the o…
We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences [Physical Review Letters 122, 200403 (2019)] can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to $π$ pulse imperfections and spurious responses due to finite-width $π$ pulses. This enhances selectivity of quantum sensors such as those based on NV centers in diamond.
We consider a system with general decoherence and a quadratic dynamical decoupling sequence (QDD) for the coherence control of a qubit coupled to a bath of spins. We investigate the influence of the geometry and of the initial conditions of the bath on the performance of the sequence. The overall performance is quantified by a distance norm $d$. It is expected that $d$ scales with $T$, the total duration of the sequence, as $T^{\min \{N_x,N_z\}+1}$, where $N_x$ and $N_z$ are the number of pulses of the outer and of the inner sequence, respectively. We show both numerically and analytically tha…
Evolution of homonuclear J-coupling during t1 period creates Zero Quantum artefacts which seriously degrade the performance of 2D NOESY. In our previous work [28], it is demonstrated that creation of such artefacts can be prevented by incorporation of a perfect echo based broadband homo-nuclear decoupling technique during t1 period that also allows chemical shift encoding. However, such experiments have limited F1 resolution as the perfect echo based decoupling remains efficient for interpulse delay 2τ (=t1) short compared to 1/J. A solution to this problem is provided in the present work wher…
We use multi-pulse dynamical decoupling to increase the coherence lifetime (T2) of large numbers of nitrogen-vacancy (NV) electronic spins in room temperature diamond, thus enabling scalable applications of multi-spin quantum information processing and metrology. We realize an order-of-magnitude extension of the NV multi-spin T2 for diamond samples with widely differing spin environments. For samples with nitrogen impurity concentration <~1 ppm, we find T2 > 2 ms, comparable to the longest coherence time reported for single NV centers, and demonstrate a ten-fold enhancement in NV multi-spin se…
Entanglement-enhanced fluctuation-free daemonic ergotropy with random measurements
TCG CREST；Seoul National University（首尔大学）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里斯-钱德拉研究所，霍米·巴巴国立学院成员机构）；Slovak Academy of Sciences（斯洛伐克科学院）
One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is quickly lost due to such dephasing, and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through a communication channel. We propose a dynamical decoupling sequence to protect photonic qubits from dephasing by integrating wave plates into optical fiber at prescribed locations. We simulate random birefringent noise along…
We present a method to reduce the variance of stochastic trace estimators used in quantum typicality (QT) methods via a randomized low-rank approximation of the finite-temperature density matrix $e^{-βH}$. The trace can be evaluated with higher accuracy in the low-rank subspace while using the QT estimator to approximate the trace in the complementary subspace. We present two variants of the trace estimator and demonstrate their efficacy using numerical experiments. The experiments show that the low-rank approximation outperforms the standard QT trace estimator for moderate- to low-temperature…
Methods that preserve coherence broadly impact all quantum information processing and metrology applications. Dynamical decoupling methods accomplish this by protecting qubits in noisy environments but are typically constrained to the limit where the qubits themselves are non-interacting. Here we consider the alternate regime wherein the inter-qubit couplings are of the same order as dephasing interactions with the environment. We propose and demonstrate a multi-pulse protocol that protects transverse spin states by suitably Hamiltonian engineering the inter-spin coupling while simultaneously …
Nuclear magnetic resonance (NMR) schemes can be applied to micron-, and nanometer-sized samples by the aid of quantum sensors such as nitrogen-vacancy (NV) color centers in diamond. These minute devices allow for magnetometry of nuclear spin ensembles with high spatial and frequency resolution at ambient conditions, thus having a clear impact in different areas such as chemistry, biology, medicine, and material sciences. In practice, NV quantum sensors are driven by microwave (MW) control fields with a twofold objective: On the one hand, MW fields bridge the energy gap between NV and nearby nu…
Robust Spin Polarization by Adiabatic Dynamical Decoupling
Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；Department of Physical Chemistry, University of the Basque Country UPV/EHU（巴斯克大学物理化学系）；EHU Quantum Center, University of the Basque Country UPV/EHU（巴斯克大学EHU量子中心）；Department of Physical and Astronomy, University College London（伦敦大学学院物理与天文学系）；Leibniz Institute of Surface Engineering (IOM)（莱布尼茨表面工程研究所）
Scalable quantum error mitigation for dynamical decoupling
Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）；Anhui Province Key Laboratory of Scientific（安徽省科学重点实验室）；New York University Abu Dhabi（阿布扎比纽约大学）；University of Science（科技大学）
Minimal-Energy Optimal Control of Tunable Two-Qubit Gates in Superconducting Platforms Using Continuous Dynamical Decoupling
Sao Carlos Institute of Physics, University of Sao Paulo（圣卡洛斯物理研究所，圣保罗大学）；Departamento de Física, Universidade Federal de São Carlos (UFSCar)（圣卡洛斯联邦大学物理系）
Nuclear magnetic resonance (NMR) has enormous applications. Two-dimensional NMR is an essential technique to characterize correlations between nuclei and, hence, molecule structures. Towards the ultimate goal of single-molecule NMR, dynamical-decoupling- (DD) enhanced diamond quantum sensing enables the detection of single nuclear spins and nanoscale NMR. However, there is still the lack of a standard method in DD-based quantum sensing to characterize correlations between nuclear spins in single molecules. Here we present a scheme of two-dimensional DD-based quantum sensing, as a universal met…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop covers applications as diverse as consensus on probability distributions (either classical or quantum), uniform random state generation, and open-loop disturbance rejection by quantum dynamical decoupling. Robust convergence results are explicitly provided in a group-theoretic formulation, both for deterministic and for randomized dynamics. This indicates a way t…
Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We dramatically suppress the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence is preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement is found to follow a general scaling with the number of decoupling pulses. No limit is observed for the decoupling action up to 136 pulses, for which the coherence time is enhanced …
We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our $1/f$ noise model. The results are applic…
As quantum computers grow in size and scope, a question of great importance is how best to benchmark performance. Here we define a set of characteristics that any benchmark should follow -- randomized, well-defined, holistic, device independent -- and make a distinction between benchmarks and diagnostics. We use Quantum Volume (QV) [1] as an example case for clear rules in benchmarking, illustrating the implications for using different success statistics, as in Ref. [2]. We discuss the issue of benchmark optimizations, detail when those optimizations are appropriate, and how they should be rep…
When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful way to complement usual refocusing techniques. Relaxation imposes a fundamental limit on the sensitivity of state of the art quantum sensors which cannot be overcome by dynamical decoupling. The only way to overcome this is to utilize quantum error correcting codes. We present a superconducting magnetometry design that incorporates approximate quantum error…
The ability to design quantum systems that decouple from environmental noise sources is highly desirable for development of quantum technologies with optimal coherence. The chemical tunability of electronic states in magnetic molecules combined with advanced electron spin resonance techniques provides excellent opportunities to address this problem. Indeed, so-called clock transitions (CTs) have been shown to protect molecular spin qubits from magnetic noise, giving rise to significantly enhanced coherence. Here we conduct a spectroscopic and computational investigation of this physics, focusi…
Sensing, localising and identifying individual nuclear spins or frequency components of a signal in the presence of a noisy environments requires the development of robust and selective methods of dynamical decoupling. An important challenge that remains to be addressed in this context are spurious higher order resonances in current dynamical decoupling sequences as they can lead to the misidentification of nuclei or of different frequency components of external signals. Here we overcome this challenge with engineered quantum sensing sequences that achieve both, enhanced robustness and the sim…
In the field of quantum metrology and sensing, a collection of quantum systems (e.g. spins) are used as a probe to estimate some physical parameter (e.g. magnetic field). It is usually assumed that there are no interactions between the probe systems. We show that strong interactions between them can increase robustness against thermal noise, leading to enhanced sensitivity. In principle, the sensitivity can scale exponentially in the number of probes -- even at non-zero temperatures -- if there are long-range interactions. This scheme can also be combined with other techniques, such as dynamic…
The sensitivity of classical and quantum sensing is impaired in a noisy environment. Thus, one of the main challenges facing sensing protocols is to reduce the noise while preserving the signal. State of the art quantum sensing protocols that rely on dynamical decoupling achieve this goal under the restriction of long noise correlation times. We implement a proof-of-principle experiment of a protocol to recover sensitivity by using an error correction for photonic systems that does not have this restriction. The protocol uses a protected entangled qubit to correct a single error. Our results s…
Persistent Quantum-Enhanced Frequency Sensing with T^{-3/2} Scaling
Department of Physics and Astronomy, University of California Los Angeles（加州大学洛杉矶分校物理与天文系）；Challenge Institute for Quantum Computation, University of California Los Angeles（加州大学洛杉矶分校挑战量子计算研究所）；Center for Quantum Science and Engineering, University of California Los Angeles（加州大学洛杉矶分校量子科学与工程中心）
We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve a factor of 30 improvement in signal-to-noise ratio, translating to a sensitivity enhancement exceeding an order of magnitude. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous bias and control fields, ensuring that all of the ${\sim}10^9$ two-qubit sensors are sufficiently identical to permit global control of the NV en…
We demonstrate fluorescence thermometry techniques with sensitivities approaching 10 mK Hz^(-1/2) based on the spin-dependent photoluminescence of nitrogen vacancy (NV) centers in diamond. These techniques use dynamical decoupling protocols to convert thermally induced shifts in the NV center's spin resonance frequencies into large changes in its fluorescence. By mitigating interactions with nearby nuclear spins and facilitating selective thermal measurements, these protocols enhance the spin coherence times accessible for thermometry by 45x, corresponding to a 7x improvement in the NV center'…
