QOC — Dynamical decoupling

Dynamical Decoupling of Nonclassical States in a Biased-Noise Spin Qudit

2026-10-14T00:00:00Z

Encoding quantum information in $d$-dimensional systems (qudits) with $d>2$ offers appealing new directions for resource-efficient quantum computing. However, protecting the coherence of nonclassical qudit resource states remains an open challenge. Dynamical decoupling (DD) is a well-established technique for extending coherence, but its application to qudits is hindered by the quadratic scaling of the decoupling sequence overhead with the dimension $d$. As a result, demonstrations of qudit DD have so far been limited to low-dimensional qudits. Here, we show that noise-biased qudits enable a nontrivial reduction of this overhead, for example, from quadratic to linear. We perform qudit DD on a model $d=8$ qudit, the nuclear spin of an antimony donor in silicon. We benchmark DD performance on highly nonclassical states such as uniform superpositions, cat states, and Haar random states and measure coherence improvements up to a factor $5$ to $10$. For a spin-cat error correction code, continuous DD extends the coherence time of the logical superposition $|+\rangle_L$ to $225$~ms, compared to $19$~ms under free evolution and $85$~ms with a Hahn echo. This improvement shows that DD sequences tailored to a system's noise bias can significantly enhance the lifetime of encoded logical qubits.

Proposal for a multi-ion optical clock with hundreds of ions

2026-10-11T00:00:00Z

Scaling trapped-ion optical clocks to hundreds of ions remains a major challenge due to inhomogeneous frequency shifts in large ion crystals. Here, we propose a circular surface-trap architecture for a multi-ion optical clock with hundreds of ions. The rotational symmetry of the ion crystal suppresses the main sources of inhomogeneity, quadrupole shift.We investigate the feasibility of a clock based on a ring crystal of 400 $^{40}\mathrm{Ca}^{+}$ ions and propose a suitable experimental setup configuration. We have shown that circular configuration of ions leads to suppression by two orders of magnitude of the quadrupole shift comparing to the linear trap. Combined with stray-field compensation and dynamical decoupling techniques, this architecture provides a pathway toward multi-ion optical clocks with fractional frequency uncertainty at the $10^{-18}$ level and an expected 20-fold improvement in frequency stability compared to single ion clocks.

Continuous-wave AC magnetometry up to hundreds of megahertz using nitrogen-vacancy centers under a strong transverse magnetic field

2026-10-09T00:00:00Z

Nitrogen-vacancy (NV) centers in diamond are promising quantum sensors for AC magnetic fields. However, conventional dynamical-decoupling-based magnetometry becomes technically demanding at high frequencies because of the requirement for increasingly short and high-power microwave pulses. This paper describes an AC magnetometry technique based on continuous-wave optically detected magnetic resonance (CW-ODMR) measurements, which enables the detection of signals in the hundred-MHz range. By applying a strong static magnetic field transverse to the NV axis, the energy separation between the relevant electron-spin states was tuned and resonantly coupled with the target radiofrequency (RF) magnetic field, thereby forming RF-dressed states. Unlike pulsed dynamical-decoupling schemes, this approach does not require high-power microwave pulse sequences. The key feature of our method is that the detectable frequency can be tuned by controlling the bias magnetic field strength. Using this methodology, we have experimentally achieved the frequency-tunable detection of AC magnetic fields from 14.4-632 MHz. The sensitivity was 0.558 uT/Hz^(0.5) at 14.4 MHz and 24.4 uT/Hz^(0.5) at 632 MHz. We characterized the field-dependent ODMR contrast and linewidth, and found that their degradation at large transverse fields is a important factor limiting the high-frequency sensitivity. These results establish a simple CW-ODMR approach for widely tunable RF magnetic-field sensing without high-power pulsed spin control.

Investigating entanglement dynamics with dynamical decoupling together with initial qubit-reservoir correlations

2026-10-01T00:00:00Z

We study the exact entanglement dynamics of two qubits coupled to a common bosonic reservoir through a pure dephasing interaction. We ask how this dynamics changes when the qubits and the reservoir already share correlations before the qubit state is prepared. In that case the system and reservoir first interact for a long time and settle into a joint equilibrium state. Only afterward is the qubit pair projected onto the desired state by a local measurement. For an Ohmic spectral density we obtain the exact reduced two qubit dynamics. Using the Wootters concurrence we show that initial correlations always speed up entanglement sudden death relative to the factorized case, and that this gap grows quadratically with the coupling strength in the weak-to-moderate coupling regime. Finally we show that a symmetric sequence of periodic π pulses applied to both qubits extends the entanglement lifetime close to a factor of seven over the range of pulse numbers studied.

Spin-exchange interactions between circular Rydberg atoms over long times

2026-09-29T00:00:00Z

Arrays of neutral atoms excited to Rydberg levels have emerged as one of the most promising platforms for quantum computation and simulation. With the hope to outperform classical devices, the number of atoms has been increased by orders of magnitude. However, the interaction time, i.e., the maximum accumulated time during which an atom interacts with its neighbours, has been limited to a few microseconds only. This restrains the number of gates per atom or prevents the simulation of long-time dynamics of quantum many-body systems. Here, we observe the spin-exchange interaction between two spin 1/2s encoded in laser-trapped circular Rydberg atoms over more than $60μs$ and 40 spin-oscillation periods, improving the state of the art by an order of magnitude. These unprecedented timescales allow us to record for weak atomic trapping a collapse and revival of the spin-exchange oscillation contrast induced by spin-motion coupling. Our results constitute the first observation of this coupling with laser-trapped Rydberg atoms. To counteract its detrimental effect for quantum simulation, we demonstrate a novel dynamical decoupling method that prevents the collapse of the spin oscillations. This method exploits the advantages of our recently developed hybrid platform that enables the measurement and the optical manipulation of long-lived circular Rydberg atoms with auxiliary Rydberg atoms. This work opens a direct route to long-duration quantum simulation of strongly-interacting many-body systems.

Phase-accumulating hyperfine strain sensing with rare-earth-ion phase memories

2026-09-25T00:00:00Z

Long-lived hyperfine coherences in rare-earth-ion crystals provide controlled phase evolution windows for metrology. We use this resource to propose an experimental protocol for accessing strain shifts of ground state hyperfine transitions in non-Kramers rare-earth-ion doped (REID) materials, a quantity that is difficult to access directly with conventional spectroscopic methods. Starting from the crystal field Hamiltonian, we relate the response to strain-dependent effective quadrupole and Zeeman tensors, including changes in electronic wave functions, virtual electronic admixtures, and the bare nuclear quadrupole interaction. The protocol optically prepares a selected hyperfine class, uses a phase-controlled rf $π/2$ pulse to create the sensing coherence, and applies synchronized dynamical decoupling pulses during the phase evolution interval so that a coherent ac strain drive accumulates phase rather than averaging away. The accumulated phase is then retrieved by Raman heterodyne readout. The resulting framework provides a route to understanding strain-induced hyperfine couplings in non-Kramers REID systems.

Trading Circuit Depth for Pulse Sparsity in Chromatic Dynamical Decoupling

2026-09-24T00:00:00Z

Suppressing decoherence and crosstalk systematically across large networks of qubits is a pressing concern as qubit counts increase rapidly. General multi-qubit dynamical decoupling (DD) has historically been based on Hadamard matrices and orthogonal arrays, with instantaneous-pulse sequences whose circuit depth scales linearly with the number of qubits. Chromatic-Hadamard DD (CHaDD) improves upon these methods by properly coloring the hardware graph and assigning to each color a row of a Hadamard matrix, resulting in a circuit depth that scales linearly with the number of colors $C$, which can be as low as the chromatic number of the graph. Here, we explore the tradeoff between circuit depth and the pulse repetition rate (PRR), the average fraction of time steps in which a qubit is pulsed, i.e., a measure of pulse density. We introduce two single-axis sequences based on binary and Gray matrices, Chromatic-Binary DD (CBDD) and Chromatic-Gray DD (CGDD), which, for $C>2$, are special cases of non-minimum-depth CHaDD and achieve PRR $<2/C$ and PRR $=1/C$, respectively, compared with a PRR above $1/4$ for CHaDD, at the price of a circuit depth of $2^C$. In state preservation experiments on a $127$-qubit IBM processor with $C=3$, the less dense sequences outperform CHaDD at short times when the pulses are not robust; this advantage is largely eliminated by robust versions designed to compensate for coherent pulse errors, and among the robust sequences, CGDD uses the fewest pulses over a fixed protection time. Across non-robust $C=3$ and $C=5$ schedules, equal PRR on a fixed qubit subset is empirically associated with similar state preservation. Thus, the PRR serves as a practical figure of merit for chromatic DD whenever coherent pulse errors dominate.

Thermometry in Near-Degenerate Nitrogen-Vacancy Ensembles Enabled by Bright-Dark-State Mixing

2026-09-19T00:00:00Z

Nitrogen-vacancy (NV) centers have emerged as a highly sensitive platform for spatially resolved temperature measurements. When the $\lvert0\rangle\to\lvert+1\rangle$ and $\lvert0\rangle\to\lvert-1\rangle$ transitions are nearly degenerate and the Rabi frequency is comparable to the transition splitting, the spin dynamics encountered during pulsed protocols for temperature measurement can significantly alter the intended accumulation of temperature-dependent phase. We investigate these triplet ($\lvert0\rangle$, $\lvert\pm1\rangle$) spin dynamics and their effect on pulsed thermometry protocols under these conditions. We find that the conventional thermal-echo timing produces negligible temperature-sensitive signal amplitudes at the common-mode detuning. However, we find that the nominal spin-echo timing produces resolvable oscillations at the common-mode detuning, leading to a strong temperature-sensitive carrier signal. This departure from the expected protocol behavior is qualitatively captured by an ensemble model of the triplet dynamics, which supports significant dark-state leakage as a plausible mechanism for the temperature-sensitive response. This mixing-enabled thermal echo uses a four-phase quadrature readout that resolves the signed oscillation frequency and is validated using independent sweeps of the microwave carrier frequency and fluid temperature. We further assess the ability of a four-refocusing-pulse (LDD4B) low-field dynamical-decoupling sequence to extend the NV coherence and find that while the echo retains a sensitivity to common-mode detuning, the effective phase-accumulation interval corresponds to approximately half the total evolution time. These findings could support the use of pulsed NV thermometry in biological or mobile applications where applying magnetic bias fields is impractical and microwave power may be limited.

Persistent Quantum-Enhanced Frequency Sensing with T^{-3/2} Scaling

2026-09-18T00:00:00Z

Quantum sensing uses nonclassical states to improve measurement sensitivity, but the same states that provide metrological gain also decohere more rapidly. This limits the usable interrogation time and, in practice, often precludes improvement in ultimate sensitivity - realized useful quantum advantage has consequently remained rare. Here, we restore persistent quantum advantage by embedding Fock-state enhancement within a quantum heterodyne (Qdyne) protocol, decoupling sensitivity from the decoherence-limited interrogation time τ. Measurements are acquired at short τ where the quantum-enhanced gain is optimal, while precision accumulates with the total measurement time. Demonstrated on the motional mode of a trapped 40Ca+ ion, we observe quantum-enhanced precision that persists to measurement times seven orders of magnitude beyond the dephasing limit, scaling as T^{-3/2} with no indication of saturation. Using the n=3 Fock state, we reach a frequency precision of 0.5uHz relative to an 86MHz carrier, achieving a fractional precision ~6x10^{-15}. This represents a quantum-enhanced gain of 7.1(10) dB over the n=0 state, in agreement with Fisher information predictions. This is the first demonstration of Qdyne beyond solid-state spin-defects. Further, by using the quantum harmonic oscillator to perform frequency mixing, we extend operation beyond 1GHz, two orders of magnitude above the ceiling of pulsed dynamical-decoupling implementations. These results recover quantum advantage at the long timescales required to improve ultimate sensitivity, with direct implications for nanoscale NMR and quantum logic spectroscopy.

Hamiltonian engineering via pulses: beyond group averaging

2026-09-16T00:00:00Z

We develop a geometric framework for Hamiltonian engineering in finite-dimensional quantum systems using ideal control pulses. Starting from a bilinear Schrödinger equation with unbounded control amplitudes, we construct the closed pulse group and use extensions of control systems and Filippov's relaxation theorem to obtain a family of effective Hamiltonians given by the convex hull of the drift's adjoint orbit plus the Lie algebra of the pulse group. The geometry of this orbitope describes possibilities beyond group averaging. Using the isotypic decomposition of the adjoint representation, we characterize its affine hull and show that the group average lies in its interior. This yields locally accessible families of effective Hamiltonians around the invariant part of the drift. We apply the framework to recover the necessary and sufficient condition for dynamical decoupling from arbitrary interactions with a finite-dimensional bath. For connected abelian pulse groups, we describe the relevant representation decomposition through restricted roots. Finally, for qubit networks with identical pairwise couplings, we give a qualitative characterization and quantitative estimation of effective Hamiltonians that can be generated using our framework.

A Case Study on Noise Resilient Operator Selection in Adaptive Variational Quantum Algorithms

2026-09-15T00:00:00Z

Hardware noise has been shown to significantly impact the accuracy of ADAPT-VQE, a ground state preparation algorithm. While previous work has studied the impact of noise on its parameter optimization step, its impact on the critical operator selection step remains comparatively unexplored. In this work, we examine the impact of a variety of noise channels on this step, using a linear H$_3$ molecule as a test case. We show that, despite the selection criterion's natural resilience to some noise, both coherent and incoherent noise can prevent convergence for sufficiently high noise rates. We employ quantum error mitigation techniques--dynamical decoupling, zero noise extrapolation, and Pauli twirling--and show that when combined appropriately, these techniques are capable of restoring a successful convergence profile. Our results highlight how error mitigation can improve the performance of ADAPT-VQE and enable convergence in the presence of hardware noise, offering valuable insights into the implementation of the algorithm on near-term quantum hardware.

Accurate noise spectroscopy using quantum sensing ensembles

2026-09-15T00:00:00Z

Noise spectroscopy with quantum sensors is a powerful tool for characterising the properties of the sensor environment and detecting critical magnetic phenomena. While replacing single sensors with large ensembles promises substantial gains in measurement sensitivity and field of view, the output becomes difficult to interpret when there is a variable coupling to targets across the sensing ensemble. In this work we present an analysis procedure for accessing the true source noise spectrum using ensemble coherence from dynamical decoupling measurements. We show that sequence timing plays a dual role in ensemble noise spectroscopy, setting both the frequency selectivity and the weighted collection of signal across the ensemble, and demonstrate how incorporation of the coupling distribution allows accurate parameter extraction of the noise. We apply this procedure to a model system, shallow nitrogen-vacancy centres in diamond, and show that consistent information about the spectral character of MHz-range surface noise can be obtained from two sensing ensembles featuring distinct depth distributions. Our results pave the way for using large quantum sensor ensembles for quantitative, broadband noise spectroscopy, with straightforward extension to other solid-state and molecular sensing platforms.

Quantum Sensing of Non-Repeatable Events Enhanced by In-Sensor Quantum Reservoir Computing

2026-09-05T00:00:00Z

High-density nitrogen-vacancy (NV) ensembles in diamond enable sensitive magnetometry. Many quantum-sensing protocols rely on reproducible target fields, allowing repeated measurements under different sensing conditions. In dynamical decoupling (DD) magnetometry, sweeping the interval between $π$ pulses across repeated measurements enables estimation of the frequency and amplitude of an unknown alternating field. For non-repeatable events, however, the same field waveform cannot be reproduced for measurements under different settings. Here we propose NV-based in-sensor quantum reservoir computing (NV-QRC) for sensing such events. Field-driven many-body dynamics and simultaneous fluorescence readout from multiple spatial regions provide a classical classifier with multiple features from a single event. For binary phase classification, we benchmark NV-QRC against DD magnetometry using a single pulse sequence fixed in advance. We show that NV-QRC can retain class-dependent information in regimes where the fixed-DD protocol fails to capture it. These results identify non-repeatable-event sensing as a promising application of quantum reservoir computing.

Shuttling-aware dynamical decoupling for quantum charge-coupled devices

2026-09-02T00:00:00Z

Dynamical decoupling (DD) helps maintain high-fidelity quantum computations by suppressing dephasing noise through carefully timed refocusing pulses. In quantum charge-coupled device (QCCD) architectures, however, where ions are shuttled throughout the device, transport constrains when pulses can be applied and affects the phase accumulated by an ion. Conventional DD methods do not account for shuttling and may therefore schedule pulses that must be omitted or shifted after transport scheduling, weakening the protection from dephasing. We therefore introduce shuttling-aware dynamical decoupling (SADD), an offline compiler pass that jointly selects refocusing pulses and local ion rerouting while preserving logical-gate timings and the total schedule length. In benchmark simulations, SADD improves average final-state fidelity over both the original schedules and a simple nearest-feasible Hahn-echo baseline when dephasing dominates control and transport errors and varies slowly enough for DD. Rerouting enables otherwise infeasible pulse timings, while spatial information about the noise can provide further gains. These benefits disappear, however, when the added transport introduces too much error. Overall, our results show that coordinating DD with ion transport is an effective compiler strategy for reducing dephasing in QCCD processors.

Tuning Boron-Vacancy Qubit Coherence through Layer Number in hBN

2026-09-01T00:00:00Z

The negatively charged boron vacancy ($\VB$) in hexagonal boron nitride (\hBN{}) was the first optically addressable spin qubit identified inside a van der Waals crystal, allowing atomically defined placement relative to a target. Its coherence in bulk \hBN{} is limited by the boron nuclei of the layers flanking the defect plane, which a thin flake removes. Here, we use a generalized cluster-correlation expansion with an extended central-spin block to calculate the Hahn-echo coherence time of $\VB$ in h$^{11}$B$^{15}$N as a function of layer number. Our results show that $T_2$ rises from $199\ns$ in the bulk limit to $653\ns$ in a monolayer, a factor of $3.3$ that is already saturated at three layers and that a sublattice decomposition attributes entirely to boron. The enhancement is confined to low field, is insensitive to stacking registry and twist angle, and requires alignment to within about two degrees, an onset we reproduce with no free parameters. Under dynamical decoupling, a $1/e$ threshold returns $206\ns$ for every thickness, but this is a zero of the first-shell modulation rather than a decay: measured without a threshold, the layer contrast survives and reaches a factor of $170$. Layer number thus emerges as a design parameter for $\VB$-based sensing.

Hardware-Efficient Error Mitigation and Shot-Efficient Sampling on IBM Quantum Hardware

2026-08-28T00:00:00Z

We experimentally study error mitigation and finite-shot sampling on superconducting quantum hardware under a constrained execution budget. The study combines calibration-aware qubit selection, circuit-depth scaling, zero-noise extrapolation, dynamical decoupling, readout-error mitigation, and repeated-shot estimation on an IBM Quantum processor. Experiments are organized across ideal simulation, noise-model simulation, and physical-device execution to separate sampling uncertainty from device-induced error. We investigate how mitigation performance changes with circuit depth, effective noise scale, qubit connectivity, and measurement budget, and quantify accuracy using expectation-value error, mean-squared error, statistical uncertainty, and mitigation gain. A fixed hardware-execution budget is used to evaluate shot allocation strategies and repeated measurements without relying on unlimited sampling. The resulting analysis provides a hardware-aware characterization of when mitigation improves expectation-value estimation and when finite-shot fluctuations offset the benefit of additional mitigation overhead. The implementation uses contemporary Qiskit and IBM Quantum Runtime workflows and is designed to provide reproducible experimental evidence for error-mitigation studies on current quantum processors.

A Cavity-Interfaced Register of Trapped-Ion Qubits with Multi-Second Coherence

2026-08-22T00:00:00Z

Scalable quantum networks require generating remote entanglement faster than decoherence erases it, calling for nodes that combine efficient light-matter interfaces with long coherence times. Cavity-coupled trapped ions are a promising platform for network nodes, offering high-efficiency extraction of photons. Here, we report multi-second coherence for a qubit register in a cavity-integrated ion trap. First, using dynamical decoupling on spin ground states, the coherence times of five co-trapped ion qubits are extended into the multi-second regime. Second, cavity-collected ion-photon entanglement is faithfully stored in these protected ion-memory states for multiple seconds. Third, we show that ion-memory qubits can be robust to the generation of over a thousand cavity photons by a co-trapped ion, with decoherence limited by laser crosstalk. Finally, we estimate that a modestly improved and duplicated ion-cavity system could enable the simultaneous establishment of multiple remote Bell pairs between two remote ion registers, representing a step toward networking multi-qubit prototype trapped-ion quantum processors.

Hybrid dynamical decoupling and coherent driving for high-fidelity nuclear-spin control in diamond

2026-08-21T00:00:00Z

Nitrogen-vacancy (NV) centers in diamond provide room-temperature electron-nuclear spin registers for quantum sensing and quantum information processing, with surrounding 13C nuclear spins serving as long-lived quantum memories. However, coherent control of large nuclear-spin registers is limited by finite electron-spin coherence and spectral addressability. Existing approaches follow two complementary strategies: dynamical-decoupling (DD) gates exploit filter-function resonances to realize selective conditional evolution but permit only discrete rotation angles, whereas dynamical-decoupling radio-frequency (DDrf) control restores continuous tunability at the cost of stringent hyperfine-geometry and RF-power requirements. Here, we introduce hybrid dynamical-decoupling and radio-frequency (H-DDrf) control, which preserves the DD-induced conditional evolution and employs a geometrically phase-matched RF drive to complete the target operation. This approach reduces both RF power and gate duration while maintaining high-fidelity control, thereby expanding the accessible 13C nuclear-spin register for room-temperature NV-based quantum memories and quantum processors.

Quantum sensors that compute: quantum computational magnetic-field sensing using a superconducting qubit

2026-08-18T00:00:00Z

A measurement of a single-qubit quantum sensor reveals at most 1 bit of information about the signal that was sensed. To perform a classification task on the signal, the conventional approach is to repeat a sensing protocol many times, averaging the measurement results to obtain a high-precision estimate of the sensed signal, and then to apply classical postprocessing. Quantum computational sensing (QCS) is an alternative approach that breaks with the paradigm of first obtaining a classical estimate of the signal and then computing a function of the estimated signal in postprocessing. QCS instead combines quantum sensing with quantum computing to concentrate information about the signal relevant to the task into the solitary bit revealed by each measurement. Here, we report on the experimental demonstration of QCS where sensing and computing were both performed by the same single superconducting transmon qubit. We consider various binary classification tasks based on static and oscillating magnetic fields induced by current through a flux line. The fields were sensed through a double-junction superconducting quantum interference device (SQUID) loop that was part of the qubit. We used a protocol based on quantum signal processing to preprocess the sensed signals in the quantum domain prior to measurement. For tasks on static magnetic fields, our protocol outperformed the conventional baseline of Ramsey-based phase estimation by as much as 15 percentage points. For tasks on oscillating magnetic fields, we classified signal amplitude and frequency with up to 20 and 15 percentage points higher accuracy, respectively, compared to the conventional baseline of optimized dynamical-decoupling protocols. Our results illustrate how quantum computing can enhance quantum sensing even with a minimally sized quantum system subject to the practical limitations of decoherence and error-prone operations.

A Quantum Dynamics Tutorial: Visualising Dynamical Decoupling Sequences on the Bloch Sphere

2026-08-11T00:00:00Z

Dynamical decoupling protocols provide a versatile toolbox for robust control of quantum systems, suppressing noise that would otherwise limit their performance. This tutorial aims to provide an intuitive interpretation of these protocols. Written from an experimentalist's perspective, we use the Bloch sphere picture to visualise quantum dynamics for a range of sequences. Here each dynamical decoupling operation can be viewed as an "effective field vector", whilst the phase and population of the two-level system is encoded into a "Bloch vector". The two-level dynamics are calculated by the cross product between these two vectors, such that the quantum state represented by the Bloch vector rotates around the effective field vector. Several prominent control schemes are simulated using this picture, starting with a Rabi oscillation, followed by the Ramsey sequence and a selection of pulsed and continuous dynamical decoupling techniques. These sequences are engineered to preserve control of the quantum system for as long as possible, with their efficacy often quantified by a coherence time. We clarify the definition of the longitudinal $T_1$, transverse $T_2$ and inhomogeneous $T_2^*$ coherence times, which are used across the literature. Each simulation has an accompanying animation to illustrate the protocol's two-level dynamics on the Bloch sphere. The custom simulation and Bloch sphere plotting scripts are also provided in an open access repository to allow the reader to reproduce, modify, and explore these results. Dynamical decoupling sequences have established themselves as an invaluable tool across the entire quantum technologies remit; by providing an open framework alongside this tutorial, we aim to make these protocols more accessible to new researchers discovering this thriving field.

An ionic clock qubit inside a circular Rydberg atom

2026-08-07T00:00:00Z

Neutral atoms trapped in optical tweezers and excited to Rydberg states, together with trapped ions, are among the most advanced platforms for quantum simulation and quantum computing. Current experiments often rely on additional atoms in neighboring traps to encode ancilla qubits for local manipulation and readout. Here, we demonstrate a dual ion-Rydberg system comprising two qubits encoded in two individually controlled electrons of the same alkaline-earth atom. The first, a microwave qubit, is encoded in a pair of circular Rydberg states, while the second, an optical qubit, is encoded on a narrow quadrupole transition of the Rydberg atom's ionic core. We demonstrate coherent control of the optical qubit and achieve coherence times of several hundred microseconds under dynamical decoupling. Furthermore, we realize coherent coupling between the two electrons via electrostatic quadrupole interactions over the large separation between the Rydberg electron and the ionic core, and map out its angular tunability. Finally, we demonstrate a two-qubit operation, reminiscent of a Mølmer-Sørensen gate, that evolves through an entangled state of the two qubits driven by the quadrupole coupling. Our work opens a pathway to exploit a pair of individually controlled electronic qubits with tunable coupling for quantum simulation and quantum metrology.

Hadamard sensing channel: deterministic artifact suppression for quantum sensors

2026-08-06T00:00:00Z

Dynamical decoupling sequences are essential for nanoscale quantum sensing, but the finite duration of microwave pulses generates spurious responses. While phase randomization (PR) protocol can suppress these artifacts, they rely on probabilistic averaging. This introduces an inherent statistical variance that demands excessive sequence lengths and stringent hardware capabilities for true random phase generation. Here, we propose Hadamard sensing channel (HSC), a deterministic phase-design framework based on Hadamard matrices. HSC completely eliminates the statistical variance of PR by exactly and deterministically canceling spurious signals using a finite set of orthogonal phase patterns. Simulations confirm that HSC matches the ideal suppression of PR but exhibits superior robustness against control errors. HSC offers a mathematically exact and hardware-friendly solution for reliable high-resolution nanoscale nuclear magnetic resonance.

Motional refocusing for trap-off Rydberg gates

2026-08-05T00:00:00Z

Rydberg entangling gates in optical-tweezer arrays are commonly executed with the trapping light switched off, so every gate contains a release--and--recapture cycle that heats the atomic motion and can ultimately limit circuit depth. We develop a motional refocusing protocol that exactly removes this heating in the harmonic approximation using only programmable intensity switching of the trapping light. The protocol closes the release--and--recapture cycle for every matched harmonic mode, returning arbitrary motional populations and coherences exactly up to ordinary evolution under the static trap. We derive the recovery sequence in closed form for arbitrary catch depth and prove that, within the experimentally relevant regime, it is the unique globally time-optimal solution under bounded trap intensity. The harmonic theory is then extended in two directions. First, we construct exact common-intensity recovery sequences that simultaneously refocus several nondegenerate harmonic modes, including radial--axial and fully anisotropic three-dimensional traps. Second, we derive a composite sequence that suppresses the leading anharmonic correction of weakly anharmonic traps by canceling all first-order motional transitions induced by the quartic anharmonicity, changing the residual heating law from $U_0^{-2}$ to $U_0^{-4}$. Wave-packet simulations in realistic Gaussian tweezers validate the analytic theory and quantify the residual effects of anharmonicity, finite switching ramps, trap ellipticity, and control errors. Applied to representative cesium Rydberg gates, the protocol suppresses the dominant recapture heating to the anharmonic floor and prevents the associated motional Doppler contribution from increasing with circuit depth. The resulting framework provides a practical route toward heating-free trap-off neutral-atom gates using only trap-intensity modulation.

Dissipation Enables Strongly Detuning-Dependent Interference in Pulsed Dynamical Decoupling

2026-07-28T00:00:00Z

One of the defining features of pulsed dynamical decoupling is its suppression of a driven qubit's sensitivity to static detuning errors between the drive field and qubit resonance. In this paper, we show that dissipation, in the form of excited-state decay, can change this behavior entirely, producing an interference signal with a strong detuning dependence. This signal arises from decay during driven evolution and relies on coherence retained by the qubit after such a decay event. We develop analytical and numerical models that capture the underlying mechanism and observe this same dissipation-induced detuning dependence experimentally in both a free-space strontium atom interferometer and a superconducting transmon qubit system. We also use this dissipation-induced detuning dependence as the basis for a new spectroscopic technique called Dissipative Carr-Purcell Spectroscopy (DCPS) and compare it with a traditional Ramsey sequence. Our results establish a regime of pulsed dynamical decoupling in which dissipation reshapes, rather than merely degrades, coherent control, and we expect these dynamics to be relevant to a wide range of quantum systems.

Correlated Coherent Errors in Stabilizer Codes: A General Cumulant Framework and Interference-Based Error Suppression

2026-07-24T00:00:00Z

Coherent errors in stabilizer codes are often correlated across qubits and QEC cycles. Having a general analytical treatment of such noise would thus be extremely valuable. We derive here the exact logical channel induced by repeated QEC cycles under correlated coherent $Z$ noise, and develop a broadly general cumulant-expansion framework that yields a tractable expression for the noise-averaged logical infidelity. Crucially, this expression is non-perturbative in the noise, and applies to arbitrary stabilizer codes and correlation structures. It reveals a feature with no analogue in standard stochastic Pauli error models: the induced channel depends on which stabilizer eigenspace is chosen as the codespace. Exploiting this, we introduce protected stabilizer eigenspace (PROSE) encoding, an error-suppression strategy that selects the optimal codespace. We show that this eigenspace can be efficiently identified in many relevant situations. Further, when combined with logical Pauli twirling, PROSE matches or outperforms standard error suppression techniques (dynamical decoupling, Pauli twirling of physical qubits). We also show that noise correlations, usually assumed to be harmful to QEC, can instead be a resource: with the right encoding, even positive correlations reduce the logical infidelity below the uncorrelated baseline. Our results offer a new, broadly applicable lens on correlated coherent noise in stabilizer codes.

Statevector-to-Hardware Reconstruction of a Four-Qubit ZZ Quantum Kernel: A Single-Backend Case Study of Three Execution Jobs

2026-07-22T00:00:00Z

Hardware noise and finite sampling perturb the fidelity estimates forming a quantum-kernel Gram matrix. We measured how far three hardware-reconstructed Gram matrices depart from an exact statevector reference for one frozen four-qubit ZZ feature map on N=24 indoor air-quality windows, executed on ibm_fez at 1024 shots per circuit in three single, non-interleaved jobs: baseline, dynamical decoupling alone, and gate twirling alone. All were complete, finite, and positive-semidefinite. Off-diagonal root-mean-squared error (RMSE) against the reference was 0.0878, 0.0864, and 0.0427; full-matrix centered kernel alignment (CKA) ranged 0.933-0.989 and the post hoc diagonal-excluded (U-centered) CKA 0.816-0.986. The gate-twirled job deviated least on every reported geometry axis; its baseline contrasts are deletion-stable for the Spearman, mean-absolute-error, RMSE, and full-matrix CKA diagnostics, while the Pearson and diagonal-excluded contrasts fall just below that convention. Dynamical decoupling was not separated from the baseline. The observed error exceeded both finite-shot reference scales, so, under those sampling-only models, sampling does not explain it. Centered kernel-target alignment did not track reconstruction fidelity and stayed at or below each label-permutation reference: implementation fidelity and task relevance are distinct diagnostic axes. All configuration-level statements describe three realized jobs on one backend; no mitigation-efficacy, classifier-superiority, forecasting, or quantum-advantage claim is made.

Depth Determination of Individual Shallow NV-Centers via Spin-Lock NMR

2026-07-20T00:00:00Z

Quantitative quantum sensing with shallow electron spins, such as those hosted by nitrogen-vacancy (NV) centers in diamond, requires accurate knowledge of the spin's depth below the host material's surface. A widely used approach infers this depth from the 1H nuclear magnetic resonance (NMR) signal of immersion oil on the diamond surface that can be detected using dynamical decoupling sequences such as XY8. However, finite-width pulses make XY8 sensitive to subharmonic responses, including unwanted contributions from nearby 13C spins, and its instrument-limited spectral resolution provides only sparse sampling of the narrow 1H NMR lineshape. Here, we introduce Spin-Lock NMR as an alternative approach to single-NV depth determination. By tuning the Spin-Lock Rabi frequency to the 1H Larmor frequency, the NV probes the 1H NMR signal through the Hartmann-Hahn resonance without the harmonic ambiguities of pulsed decoupling sequences and with substantially higher instrument-limited spectral resolution. We derive a quantitative Spin-Lock NMR fit function from a Markovian master equation that directly relates the measured spectrum to the NV depth. Our approach yields NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers and establishes Spin-Lock NMR as a robust alternative for quantitative single-NV depth determination. To demonstrate its applicability, we employ our method to investigate the 1H nuclear spin signal that is regularly reported to be present on diamond, even in the absence of immersion oil.

Improving Dynamical Decoupling for Trapped-Ion QCCD Quantum Computers

2026-07-16T00:00:00Z

We examine the impact of scheduling errors on dynamical decoupling (DD) in trapped-ion quantum charge-coupled devices (QCCDs) and develop better strategies for reducing memory errors. In the QCCD architecture, qubit transport and control introduce stochastic pulse delays that impact the efficiency of DD. Using the filter-function formalism, we analyze the performance of DD in the presence of scheduling-induced timing errors, showing that they increase the sensitivity of standard DD to low-frequency fluctuations. For typical memory errors in trapped-ion platforms, we numerically demonstrate that increasing the DD pulse frequency beyond 2 Hz is generally counterproductive due to scheduling-induced timing errors. Furthermore, we introduce a real-time DD protocol that inserts refocusing pulses opportunistically during idle periods. We demonstrate our methods on Quantinuum H2-1 with Ramsey delay-type experiments.

Heisenberg-limited metrology in the presence of non-Markovian noise with finite control rates

2026-07-14T00:00:00Z

Recently, it has been shown that protocols utilizing infinitely fast controls, such as quantum error correction, can in principle restore Heisenberg-limited frequency estimation in the presence of a broad class of non-Markovian noise models arising from coupling to finite-dimensional environments. However, these controls differ substantially from those used to address Markovian noise, and their underlying physical mechanism remains unclear. In this work, we establish a direct connection between these protocols and the quantum Zeno effect, and extend the framework to infinite-dimensional environments. We delineate three types of constructions: (a) protocols that rely solely on measurements, (b) protocols using an active recovery after measurements and (c) protocols using dynamical decoupling and rigorously analyze the performance of each when controls can be applied at only a finite rate. While protocols relying purely on measurements can be engineered for noise models where active recoveries are fundamentally impossible, they result in the quantum Fisher information exhibiting a quadratically worse dependence on the control frequency. Surprisingly, while dynamical decoupling protocols are possible whenever protocols relying only on measurements can be engineered, the quantum Fisher information has the same dependence on control frequency as the active recovery protocols. Numerical simulations suggest that the improvement offered by dynamical decoupling may work in regimes beyond the perturbative setting where our rigorous theorems apply.

Control Protocols for Entangling Gates for Group-IV Color-Centers in Diamond

2026-07-08T00:00:00Z

Accurately controlling entangling gates remains a major challenge for quantum technology applications with solid-state spin qubits. Here, we study a group-IV color-center with a strongly-coupled nuclear spin and approach the problem from a quantum control perspective. We show that there are three different types of entangling gates where the entanglement is mediated by the parallel hyperfine-coupling component, the orthogonal one or both. We derive the respective quantum speed limits (QSL) and show by means of dynamical decoupling, resonant driving of single- and double-quantum transitions, quantum optimal control and algebraic gate decomposition how these gates can be realized. We finally discuss the experimental applicability.