The Toffoli gate is an important universal quantum gate, and will alongside the Clifford gates be available in future fault-tolerant quantum computing hardware. Many quantum algorithms rely on performing arbitrarily small single-qubit rotations for their function, and these rotations may also be used to construct any unitary from a limited (but universal) gate set. How to carry out such rotations is then of significant interest. In this work, we evaluate the performance of a recently proposed single-qubit rotation algorithm using the Clifford plus Toffoli gate set by implementation of a one-shot version on both a real and a simulated quantum computer. We test the algorithm under various simulated noise levels using a per-qubit depolarizing error noise model and examine how the probabilities and process fidelities are affected. We then conduct live runs and find that the results reasonably match the simulated results. We also attempt to model the hardware noise by combining a number of noise models, matching the results to results of the live runs to approximate the hardware noise. Our results suggest that the algorithm will perform well for up to $1\mathrm{\%}$ noise under the noise models we chose. We further posit the use of our algorithm as a benchmark for quantum processing units, given that it has a low complexity that is easy to fine-tune in small steps. We provide details for how to do this.

We propose a practical hybrid decoding scheme for the parity-encoding architecture. This architecture was first introduced by N. Sourlas [Phys. Rev. Lett. 94, 070601 (2005)] as a computational technique for tackling hard optimization problems, especially those modeled by spin systems such as the Ising model and spin glasses, and reinvented by W. Lechner, P. Hauke, and P. Zoller [Sci. Adv. 1, e1500838 (2015)] to develop quantum annealing devices. We study the specific model, called the SLHZ model, aiming to achieve a near-term quantum annealing device implemented solely through geometrically local spin interactions. Taking account of the close connection between the SLHZ model and a classical low-density parity-check (LDPC) code, two approaches can be chosen for the decoding: (1) finding the ground state of a spin Hamiltonian derived from the SLHZ model, which can be achieved via stochastic decoders such as a quantum annealer or a classical Monte Carlo sampler; or (2) using deterministic decoding techniques for the classical LDPC code, such as belief propagation and a bit-flip decoder. The proposed hybrid approach combines the two approaches by applying bit-flip decoding to the readout of the stochastic decoder based on the SLHZ model. We present simulations demonstrating that this approach can reveal the latent potential of the SLHZ model, realizing the soft-annealing concept proposed by Sourlas.

Semiconductor quantum dot (QD) devices have become central to advancements in spin-based quantum computing. However, the increasing complexity of modern QD devices makes calibration and control—particularly at elevated temperatures—a bottleneck to progress, highlighting the need for robust and scalable autonomous solutions. A major hurdle arises from trapped charges within the oxide layers, which induce random offset voltage shifts on gate electrodes, with a standard deviation of approximately 83 mV of variation within state-of-the-art present-day devices. Efficient characterization and tuning of large arrays of QD qubits depend on choices of automated protocols. Here we introduce a physically intuitive framework for a bootstrapping, autonomous testing, and initialization system (BATIS) designed to streamline QD device evaluation and calibration. BATIS navigates high-dimensional gate voltage spaces, automating essential steps such as leakage testing, formation of all current channels, and gate characterization in the presence of trapped charges. For forming the current channels, BATIS follows a nonstandard approach that requires a single set of measurements regardless of the number of channels. Demonstrated at 1.3 K on a quadruple QD $\mathrm{Si}/{\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}$ device, BATIS eliminates the need for deep cryogenic environments during initial device diagnostics, significantly increasing scalability and reducing setup times. By requiring only minimal prior knowledge of the device architecture, BATIS represents a platform-agnostic solution, adaptable to various QD systems, which bridges a critical gap in QD autotuning.

Quantum error-correcting codes (QECCs) require high encoding rates in addition to high thresholds unless a sufficiently large number of physical qubits are available. Many-hypercube (MHC) codes, defined as concatenations of the $[[6,4,2]]$ quantum error-detecting code, have been proposed as high-performance and high-encoding-rate QECCs. However, concatenated codes have the disadvantage that the syndrome weight grows exponentially with respect to the concatenation level. To address this issue, here we propose subsystem quantum codes based on MHC codes. In particular, we study the smallest subsystem MHC codes, namely, subsystem codes derived from concatenated $[[4,2,2]]$ error-detecting codes. The resulting codes have a constant syndrome-measurement weight of 4, while keeping high encoding rates. We build block-MAP and neural-network decoders and show that they demonstrate superior performance to the bounded-distance decoder.

Negatively charged silicon vacancy ($\mathrm{Si}$${\mathrm{V}}^{-}$) centers in diamond are leading candidates for solid-state quantum memory that can be controlled using electromagnetic or acoustic waves. The latter are particularly promising due to the strong strain response of $\mathrm{Si}$${\mathrm{V}}^{-}$, enabling large spin-phonon interaction strengths. Indeed, coherent spin control via surface acoustic waves (SAWs) has been demonstrated and is essential for developing on-chip phononic quantum networks. However, the absence of piezoelectricity in diamond requires an interface with a piezoelectric material for efficient transduction and delivery of acoustic waves to spins in diamonds. Here, we demonstrate a heterogeneously integrated phononic platform that combines thin-film lithium niobate with diamond to enable acoustic control of single $\mathrm{Si}$${\mathrm{V}}^{-}$ spins. Additionally, leveraging large SAW-induced strain at the location of $\mathrm{Si}$${\mathrm{V}}^{-}$, we achieve coherent acoustic control of an electron spin with more than twofold improvement in Rabi frequency compared to state-of-the-art devices based on aluminum nitride on diamond. This work represents a crucial step towards realizing phonon-based quantum information processing systems.

Superconducting qubits are often adversely affected by two-level systems (TLSs) within the Josephson junction, which contribute to decoherence and subsequently limit the performance of the qubit. By treating the TLS as a soft (i.e., low-frequency) bosonic mode localized in real space, we find that a single TLS in either the amorphous-oxide surface or the superconducting bulk may result in a localized “hot spot” of amplified Josephson energy. Such amplification is shown to have a non-negligible effect on the $T_1$ time of a simple phase qubit, regardless of whether or not the TLS is on resonance with the qubit frequency. With this study, we identify unique fingerprints of TLS defects in the Josephson current and qubit decoherence time.

Tailoring quantum-error-correction codes (QECCs) to biased noise has demonstrated significant benefits. However, most of the prior research on this topic has focused on code-capacity noise models. Furthermore, a no-go theorem prevents the construction of controlled-not (cnot) gates for two-level qubits in a bias-preserving manner which may, in principle, imply that noise bias cannot be leveraged in such systems. In this work, we show that a residual bias up to $\eta \sim 5$ can be maintained in cnot gates under certain conditions. Moreover, we employ controlled-Z (cz) gates in syndrome-extraction circuits and show how to natively implement these in a bias-preserving manner for a broad class of qubit platforms. This motivates the introduction of what we call a hybrid biased-depolarizing (HBD) circuit-level noise model that captures these features. We numerically study the performance of the $XZZX$ surface code and observe that bias-preserving cz gates are critical for leveraging biased noise. Accounting for the residual bias present in the cnot gates, we observe an increase in the code threshold up to a $1.27\mathrm{\%}$ physical error rate, representing a $90\mathrm{\%}$ improvement. Additionally, we find that the required qubit footprint can be reduced by up to $75\mathrm{\%}$ at relevant physical error rates.

The transmon, a fabrication-friendly superconducting qubit, remains a leading candidate for scalable quantum computing. Recent advances in tunable couplers have accelerated progress toward high-performance quantum processors. However, extending coherent interactions beyond millimeter scales to enhance quantum connectivity presents a critical challenge. Here we introduce a hybrid-mode coupler exploiting resonator-transmon hybridization to simultaneously engineer the two lowest-frequency modes, enabling high-contrast coupling between transmons spaced at a centimeter-scale distance. For a 1-cm coupler, we experimentally demonstrate flux-tunable hybrid modes and measure strong $XX$ and $ZZ$ couplings between qubits exceeding 23 and 10 MHz, respectively, under current conditions, in agreement with an effective two-channel model. Our theoretical model further suggests $ZZ$ coupling strengths reaching 100 MHz, with modulation contrasts exceeding ${10}^4$. This work provides an efficient pathway to mitigate the inherent connectivity constraints imposed by short-range interactions, enabling transmon-based architectures compatible with hardware-efficient quantum tasks.

Quantum random-number generators (QRNGs), based on the principles of quantum mechanics, are capable of producing truly unpredictable random numbers and have wide applications in many fields. As a key index, QRNGs with high generation speed across various scenarios are becoming increasingly needed. However, in conventional time-domain processing, the generation rate of high-speed QRNGs is limited by the bandwidth and sampling rate of electrical devices. In this work, we propose a quantum random-number generation scheme based on frequency-domain processing. By partitioning the power spectrum of phase noise into four nonoverlapping frequency bands for independent extraction and processing, we realize parallel multichannel output of random numbers. Finally, we experimentally validate our scheme and generate random numbers with rates of 44 and 52 Gbit/s in digital and analog processing, respectively. More importantly, for the generation rate of 52 Gbit/s, only devices with a bandwidth of 1 GHz and a sampling rate of $2\times {10}^9$ samples per second are used, which increases the random-bit generation rate 26 times. Thus, our method could significantly increase the generation rate with low bandwidth and low sampling rate.

Quantum transduction is essential for connecting quantum technologies across varied frequencies. Achieving a positive quantum capacity of a traditional quantum transduction channel is a long-pursued goal in the field. However, to overcome the high threshold remains a major challenge, owing to practical limitations. Recently, an entanglement-assisted transducer was proposed based on a cavity-optic system [Opt. Quantum 2, 475 (2024)], where a modified bosonic loss channel was obtained, and the transduction efficiency could be enhanced by properly tuning the squeezing parameters. In this paper, we further identify three types of quantum channel enabled by this design, offering additional options for implementing the proposed transduction schemes. Compared with transducers without entanglement assistance, the scheme also shows a great enhancement in the conversion bandwidth for achieving high quantum capacity, further increasing its value in practical applications.

Parameter-shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evaluate the cost function at different parameter shifts, then use specific coefficients to combine them linearly to obtain the exact derivatives. In this work, we propose an extended PRS (EPSR), which generalizes a broad range of existing PSRs and has the following two advantages. First, EPSR offers an infinite number of possible parameter shifts, allowing the selection of the optimal parameter shifts to minimize the final derivative variance and thereby obtaining the more accurate derivative estimates with limited quantum resources. Second, EPSR extends the scope of the PSRs in the sense that EPSR can handle arbitrary Hermitian operator $H$ in gate $U(x)=\exp (iHx)$ in the parameterized quantum circuits, while existing PSRs are valid only for simple Hermitian generators $H$ such as simple Pauli words. Additionally, we show that the widely used “general PSR”, introduced by Wierichs et al. (2022), is a special case of our EPSR, and we prove that it yields globally optimal shifts for minimizing the derivative variance under the weighted-shot scheme. Finally, through numerical simulations, we demonstrate the effectiveness of EPSR and show that the usage of the optimal parameter shifts indeed leads to more accurate derivative estimates.

Quantum physics-informed neural networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach has recently been implemented in both the gate model and continuous-variable quantum computing architecture, where it has been demonstrated capable of solving ordinary differential equations. Here, we aim to extend the method to effectively address a wider range of equations, such as the Poisson equation and the heat equation. To achieve this goal, we introduce an architecture specifically designed to compute second-order (and higher-order) derivatives without relying on nested automatic differentiation methods. This approach mitigates the unwanted side effects associated with nested gradients in simulations, paving the way for more efficient and accurate implementations. By leveraging such an approach, the quantum circuit addresses partial differential equations—a challenge not yet tackled using this approach on continuous-variable quantum computers. As a proof of concept, we solve a one-dimensional instance of the heat equation, demonstrating its effectiveness in handling partial differential equations in both ideal and a noisy regime. We report our experiment on photonic hardware to address a realistic noise scenario for our simulations. Such a framework paves the way for further developments in continuous-variable quantum computing and underscores its potential contributions to advancing quantum machine learning.

Coupling microwave cavity modes with spin qubit transitions is crucial for enabling efficient qubit readout and control, long-distance qubit coupling, quantum memory implementation, and entanglement generation. We experimentally observe the coupling of different spin qubit transitions in silicon carbide ($\mathrm{Si}\mathrm{C}$) material to a three-dimensional microwave (MW) resonator mode around 12.6 GHz at a temperature of 10 mK. Tuning the spin resonances across the cavity resonance via magnetic field sweeps, we perform microwave cavity transmission measurements. We observe spin transitions of different spin defects that are detuned from each other by around 60–70 MHz. By optically exciting the $\mathrm{Si}\mathrm{C}$ sample placed in the MW cavity with an 810-nm laser, we observe the coupling of an additional spin resonance to the MW cavity, also detuned by around 60–70 MHz from the center resonance. We perform complementary confocal optical spectroscopy as a function of temperature from 4 to 200 K, using a part of the same sample used for the cavity measurements. Combining the confocal spectroscopy results and a detailed analysis of the MW-resonator-based experiments, we attribute the observed spin resonances to two different paramagnetic defects, the negatively charged silicon-vacancy spins located at the $V_1$ and $V_2$ lattice sites. The $V_1$ and $V_2$ lines in $\mathrm{Si}\mathrm{C}$ are interesting qubit transitions since they are known to be robust to decoherence. Consequently, the demonstration of the joint coupling of these spin qubits to a MW cavity mode could lead to interesting new modalities: The microwave cavity could act as an information bus and mediate long-range coupling between the spins, with potential applications in quantum computing and quantum communication, which is an especially attractive proposition in a complementary metal-oxide semiconductor–compatible material such as $\mathrm{Si}\mathrm{C}$.