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Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for achieving quantum advantage in combinatorial optimization. However, its variational framework presents a long-standing challenge in selecting circuit parameters. In this work, we prove that the energy expectation produced by QAOA can be expressed as a trigonometric function of the final-level mixer parameter. Leveraging this insight, we introduce Penta-O, a level-wise parameter-setting strategy that eliminates the classical outer loop, maintains minimal sampling overhead, and ensures non-decreasing performance. This method is broadly applicable to the generic quadratic unconstrained binary optimization formulated as the Ising model. For a $p$-level QAOA, Penta-O achieves an unprecedented quadratic time complexity of $\mathcal{O}(p^2)$ and a sampling overhead proportional to $5p+1$. Through experiments and simulations, we demonstrate that QAOA enhanced by Penta-O achieves near-optimal performance with exceptional circuit depth efficiency. Our work provides a versatile tool for advancing variational quantum algorithms., Comment: 13 pages, 4 figures

Flat-band systems provide an ideal platform for exploring exotic quantum phenomena, where the strongly suppressed kinetic energy in these flat energy bands suggests the potential for exotic phases driven by geometric structure, disorder, and interactions. While intriguing phenomena and physical mechanisms have been unveiled in theoretical models, synthesizing such systems within scalable quantum platforms remains challenging. Here, we present the experimental realization of a $\pi$-flux rhombic system using a two-dimensional superconducting qubit array with tunable coupling. We experimentally observe characteristic dynamics, e.g., $\pi$-flux driven destructive interference, and demonstrate the protocol for eigenstate preparation in this rhombic array with coupler-assisted flux. Our results provide future possibilities for exploring the interplay of geometry, interactions, and quantum information encoding in such degenerate systems., Comment: 7+7 pages, 4+2 figures

Large-scale superconducting quantum computers require massive numbers of high-performance cryogenic low-noise amplifiers (cryo-LNA) for qubit readout. Here we present a C-Band monolithic microwave integrated circuit (MMIC) cryo-LNA for this purpose. This cryo-LNA is based on 150 nm GaAs pseudomorphic high electron mobility transistor (pHEMT) process and implemented with a three-stage cascaded architecture, where the first stage adopts careful impedance match to optimize the noise and return loss. The integration of negative feedback loops adopted in the second and third-stage enhances the overall stability. Moreover, the pHEMT-self bias and current multiplexing circuitry structure facilitate the reduction of power consumption and require only single bias line. Operating at an ambient temperature of 3.6 K and consuming 15 mW, the cryo-LNA demonstrates good performance in the C-band, reaching a 5 K equivalent noise temperature and an average gain of 40 dB. We further benchmark this cryo-LNA with superconducting qubits, achieving an average single-shot dispersive readout fidelity of 98.3% without assistance from a quantum-limited parametric amplifier. The development of GaAs cryo-LNA diversifies technical support necessary for large-scale quantum applications.

Quantum metrology has emerged as a powerful tool for timekeeping, field sensing, and precision measurements within fundamental physics. With the advent of distributed quantum metrology, its capabilities have been extended to probing spatially distributed parameters across networked quantum systems. However, generating the necessary non-local entanglement remains a significant challenge, and the inherent incompatibility in multi-parameter quantum estimation affects ultimate performance. Here we use a superconducting quantum network with low-loss interconnects to estimate multiple distributed parameters associated with non-commuting generators. By employing high-fidelity non-local entanglement across network nodes and a sequential control strategy, we accurately estimate remote vector fields and their gradients. Our approach achieves an improvement of up to 6.86 dB over classical strategy for estimating all three components of a remote vector field in terms of standard deviation. Moreover, for the estimation of gradients along two distinct directions across distributed vector fields, our distributed strategy, which utilizes non-local entanglement, outperforms local entanglement strategies, leading to a 3.44 dB reduction in the sum of variances.

Fock-state lattices (FSLs), composed of photon number states with infinite Hilbert space, have emerged as a promising platform for simulating high-dimensional physics due to their potential to extend into arbitrarily high dimensions. Here, we demonstrate the construction of multi-dimensional FSLs using superconducting quantum circuits. By controlling artificial gauge fields within their internal structures, we investigate flux-induced extreme localization dynamics, such as Aharonov-Bohm caging, extending from 2D to 3D. We also explore the coherent interference of quantum superposition states, achieving extreme localization within specific subspaces assisted by quantum entanglement. Our findings pave the way for manipulating the behavior of a broad class of quantum states in higher-dimensional systems., Comment: 6+23 pages; 4+18 figures

Random fluctuations caused by environmental noise can lead to decoherence in quantum systems. Exploring and controlling such dissipative processes is both fundamentally intriguing and essential for harnessing quantum systems to achieve practical advantages and deeper insights. In this Letter, we first demonstrate the diffusive dynamics assisted by controlled dephasing noise in superconducting quantum circuits, contrasting with coherent evolution. We show that dephasing can enhance localization in a superconducting qubit array with quasiperiodic order, even in the regime where all eigenstates remain spatially extended for the coherent counterpart. Furthermore, by preparing different excitation distributions in the qubit array, we observe that a more localized initial state relaxes to a uniformly distributed mixed state faster with dephasing noise, illustrating another counterintuitive phenomenon called Mpemba effect, i.e., a far-from-equilibrium state can relax toward the equilibrium faster. These results deepen our understanding of diffusive dynamics at the microscopic level, and demonstrate controlled dissipative processes as a valuable tool for investigating Markovian open quantum systems., Comment: 7+10 pages, 4+9 figures

Superconducting transmon qubits have established as a leading candidate for quantum computation, as well as a flexible platform for exploring exotic quantum phases and dynamics. However, physical coupling naturally yields isotropic transverse interactions between qubits, restricting their access to diverse quantum phases that require spatially dependent interactions. Here, we demonstrate the simultaneous realization of both pairing (XX-YY) and hopping (XX+YY) interactions between transmon qubits by Floquet engineering. The coherent superposition of these interactions enables independent control over the XX and YY terms, yielding anisotropic transverse interactions. By aligning the transverse interactions along a 1D chain of six qubits, as calibrated via Aharonov-Bohm interference in synthetic space, we synthesize a transverse field Ising chain model and explore its dynamical phase transition under varying external field. The scalable synthesis of anisotropic transverse interactions paves the way for the implementation of more complex physical systems requiring spatially dependent interactions, enriching the toolbox for engineering quantum phases with superconducting qubits., Comment: 7+14 pages; 4+12 figures

Quantum simulators are ideal platforms to investigate quantum phenomena that are inaccessible through conventional means, such as the limited resources of classical computers to address large quantum systems or due to constraints imposed by fundamental laws of nature. Here, through a digitized adiabatic evolution, we report an experimental simulation of antiferromagnetic (AFM) and ferromagnetic (FM) phase formation induced by spontaneous symmetry breaking (SSB) in a three-generation Cayley tree-like superconducting lattice. We develop a digital quantum annealing algorithm to mimic the system dynamics, and observe the emergence of signatures of SSB-induced phase transition through a connected correlation function. We demonstrate that the signature of phase transition from classical AFM to quantum FM happens in systems undergoing zero-temperature adiabatic evolution with only nearest-neighbor interacting systems, the shortest range of interaction possible. By harnessing properties of the bipartite Renyi entropy as an entanglement witness, we observe the formation of entangled quantum FM and AFM phases. Our results open perspectives for new advances in condensed matter physics and digitized quantum annealing.

As superconducting quantum computing continues to advance at an unprecedented pace, there is a compelling demand for the innovation of specialized electronic instruments that act as crucial conduits between quantum processors and host computers. Here, we introduce a Microwave Measurement and Control System (M2CS) dedicated for large-scale superconducting quantum processors. M2CS features a compact modular design that balances overall performance, scalability, and flexibility. Electronic tests of M2CS show key metrics comparable to commercial instruments. Benchmark tests on transmon superconducting qubits further show qubit coherence and gate fidelities comparable to state-of-the-art results, confirming M2CS's capability to meet the stringent requirements of quantum experiments run on intermediate-scale quantum processors. The system's compact and scalable design offers significant room for further enhancements that could accommodate the measurement and control requirements of over 1000 qubits, and can also be adopted to other quantum computing platforms such as trapped ions and silicon quantum dots. The M2CS architecture may also be applied to wider range of scenarios, such as microwave kinetic inductance detectors, as well as phased array radar systems.

Mixers play a crucial role in superconducting quantum computing, primarily by facilitating frequency conversion of signals to enable precise control and readout of quantum states. However, imperfections, particularly carrier leakage and unwanted sideband signal, can significantly compromise control fidelity. To mitigate these defects, regular and precise mixer calibrations are indispensable, yet they pose a formidable challenge in large-scale quantum control. Here, we introduce an in situ calibration technique and outcome-focused mixer calibration scheme using superconducting qubits. Our method leverages the qubit's response to imperfect signals, allowing for calibration without modifying the wiring configuration. We experimentally validate the efficacy of this technique by benchmarking single-qubit gate fidelity and qubit coherence time., Comment: 9 pages, 7 figures

Random fluctuations can lead to cooperative effects in complex systems. We here report the experimental observation of noise-induced quantum synchronization in a chain of superconducting transmon qubits with nearest-neighbor interactions. The application of Gaussian white noise to a single site leads to synchronous oscillations in the entire chain. We show that the two synchronized end qubits are entangled, with nonzero concurrence, and that they belong to a class of generalized Bell states known as maximally entangled mixed states, whose entanglement cannot be increased by any global unitary. We further demonstrate the stability against frequency detuning of both synchronization and entanglement by determining the corresponding generalized Arnold tongue diagrams. Our results highlight the constructive influence of noise in a quantum many-body system and uncover the potential role of synchronization for mixed-state quantum information science.

Superconducting qubits are a promising platform for building fault-tolerant quantum computers, with recent achievement showing the suppression of logical error with increasing code size. However, leakage into non-computational states, a common issue in practical quantum systems including superconducting circuits, introduces correlated errors that undermine QEC scalability. Here, we propose and demonstrate a leakage reduction scheme utilizing tunable couplers, a widely adopted ingredient in large-scale superconducting quantum processors. Leveraging the strong frequency tunability of the couplers and stray interaction between the couplers and readout resonators, we eliminate state leakage on the couplers, thus suppressing space-correlated errors caused by population propagation among the couplers. Assisted by the couplers, we further reduce leakage to higher qubit levels with high efficiency (98.1%) and low error rate on the computational subspace (0.58%), suppressing time-correlated errors during QEC cycles. The performance of our scheme demonstrates its potential as an indispensable building block for scalable QEC with superconducting qubits., Comment: 25 pages, 15 figures

As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting their performance in realistic circuits. To overcome this problem, we must improve their robustness against pertinent error models besides isolated fidelity. Here we report the experimental realization of robust quantum gates in superconducting quantum circuits based on a geometric framework for diagnosing and correcting various gate errors. Using quantum process tomography and randomized benchmarking, we demonstrate robust single-qubit gates against quasi-static noise and spatially-correlated noise in a broad range of strengths, which are common sources of coherent errors in large-scale quantum circuit. We also apply our method to non-static noises and to realize robust two-qubit gates. Our work provides a versatile toolbox for achieving noise-resilient complex quantum circuits., Comment: 6 pages, 4 figures plus Supplementary Information

Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device. Variational quantum-classical algorithms have emerged as a promising approach for achieving such tasks on near-term quantum simulators, despite facing significant quantum and classical resource overheads. Here, we experimentally demonstrate multi-level variational spectroscopy for fundamental many-body Hamiltonians using a superconducting programmable digital quantum simulator. By exploiting symmetries, we effectively reduce circuit depth and optimization parameters allowing us to go beyond the ground state. Combined with the subspace search method, we achieve full spectroscopy for a 4-qubit Heisenberg spin chain, yielding an average deviation of 0.13 between experimental and theoretical energies, assuming unity coupling strength. Our method, when extended to 8-qubit Heisenberg and transverse-field Ising Hamiltonians, successfully determines the three lowest energy levels. In achieving the above, we introduce a circuit-agnostic waveform compilation method that enhances the robustness of our simulator against signal crosstalk. Our study highlights symmetry-assisted resource efficiency in variational quantum algorithms and lays the foundation for practical spectroscopy on near-term quantum simulators, with potential applications in quantum chemistry and condensed matter physics.

Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multi-dimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this work, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low cross talk between qutrits, thus being friendly for scaling up. Our work constitutes an important step towards scalable qutrit-based quantum computation., Comment: 15 pages, 12 figures

Scalable quantum information processing requires that modular gate operations can be executed in parallel. The presence of crosstalk decreases the individual addressability, causing erroneous results during simultaneous operations. For superconducting qubits which operate in the microwave regime, electromagnetic isolation is often limited due to design constraints, leading to signal crosstalk that can deteriorate the quality of simultaneous gate operations. Here, we propose and demonstrate a method based on AC Stark effect for calibrating the microwave signal crosstalk. The method is suitable for processors based on fixed-frequency qubits which are known for high coherence and simple control. The optimal compensation parameters can be reliably identified from a well-defined interference pattern. We implement the method on an array of 7 superconducting qubits, and show its effectiveness in removing the majority of crosstalk errors.

Controlling the flow of quantum information is a fundamental task for quantum computers, which is unfeasible to realize on classical devices. Coherent devices which can process quantum states are thus required to route the quantum states that encode information. In this paper we demonstrate experimentally the smallest quantum transistor with a superconducting quantum processor which is composed of a collector qubit, an emitter qubit, and a coupler (transistor gate). The interaction strength between the collector and emitter qubits is controlled by the frequency and state of the coupler, effectively implementing a quantum switch. Through the coupler-state-dependent Heisenberg (inherent) interaction between the qubits, a single-step (native) conditional $i$SWAP operation can be applied. To this end, we find that it is important to take into consideration higher energy level for achieving a native and high-fidelity transistor operation. By reconstructing the Quantum Process Tomography, we obtain an operation fidelity of $92.36\%$ when the transistor gate is open ($i$SWAP implementation) and $95.23 \%$ in the case of closed gate (identity gate implementation). The architecture has strong potential in quantum information processing applications with superconducting qubits., Comment: 10 pages and 6 figures, including Appendix Section

Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in connectivity and gate alphabets, often result in unacceptable implementation costs. To enable successful near-term applications, it is crucial to optimize compilation by exploiting the potential capabilities of existing hardware. Here, we implement a resource-efficient construction for a quantum version of AND logic that can reduce the cost, enabling the execution of key quantum circuits. On a high-scalability superconducting quantum processor, we demonstrate low-depth synthesis of high-fidelity generalized Toffoli gates with up to 8 qubits and Grover's search algorithm in a search space of up to 64 entries; both are the largest such implementations in scale to date. Our experimental demonstration illustrates a scalable implementation of simplifying quantum algorithms, paving the way for larger, more meaningful quantum applications on noisy devices.

Unwanted $ZZ$ interaction is a quantum-mechanical crosstalk phenomenon which correlates qubit dynamics and is ubiquitous in superconducting qubit systems. It adversely affects the quality of quantum operations and can be detrimental in scalable quantum information processing. Here we propose and experimentally demonstrate a practically extensible approach for complete cancellation of residual $ZZ$ interaction between fixed-frequency transmon qubits, which are known for long coherence and simple control. We apply to the intermediate coupler that connects the qubits a weak microwave drive at a properly chosen frequency in order to noninvasively induce an ac Stark shift for $ZZ$ cancellation. We verify the cancellation performance by measuring vanishing two-qubit entangling phases and $ZZ$ correlations. In addition, we implement a randomized benchmarking experiment to extract the idling gate fidelity which shows good agreement with the coherence limit, demonstrating the effectiveness of $ZZ$ cancellation. Our method allows independent addressability of each qubit-qubit connection, and is applicable to both nontunable and tunable couplers, promising better compatibility with future large-scale quantum processors., Comment: Main text: 6 pages, 4 figures; Supplement: 7 pages, 6 figures

Quantum batteries are miniature energy storage devices and play a very important role in quantum thermodynamics. In recent years, quantum batteries have been extensively studied, but limited in theoretical level. Here we report the experimental realization of a quantum battery based on superconducting qubits. Our model explores dark and bright states to achieve stable and powerful charging processes, respectively. Our scheme makes use of the quantum adiabatic brachistochrone, which allows us to speed up the {battery ergotropy injection. Due to the inherent interaction of the system with its surrounding, the battery exhibits a self-discharge, which is shown to be described by a supercapacitor-like self-discharging mechanism. Our results paves the way for proposals of new superconducting circuits able to store extractable work for further usage., Comment: 5 pages and 3 figures + Supplemental material

High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502; Phys. Rev. Lett. 125, 240503] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, preventing us from fully exploiting its potential. Here we present a comprehensive theoretical study, explaining the origin of the high-contrast ZZ interaction. Based on improved understanding, we develop a general yet convenient method for shaping an adiabatic pulse in a multilevel system, and identify how to optimize the gate performance from design. Given state-of-the-art coherence properties, we expect the scheme to potentially achieve a two-qubit gate error rate near $10^{-5}$, which would drastically speed up the progress towards fault-tolerant quantum computation., Comment: 22 pages, 11 figures

Scalable quantum information processing requires the ability to tune multi-qubit interactions. This makes the precise manipulation of quantum states particularly difficult for multi-qubit interactions because tunability unavoidably introduces sensitivity to fluctuations in the tuned parameters, leading to erroneous multi-qubit gate operations. The performance of quantum algorithms may be severely compromised by coherent multi-qubit errors. It is therefore imperative to understand how these fluctuations affect multi-qubit interactions and, more importantly, to mitigate their influence. In this study, we demonstrate how to implement dynamical-decoupling techniques to suppress the two-qubit analogue of the dephasing on a superconducting quantum device featuring a compact tunable coupler, a trending technology that enables the fast manipulation of qubit--qubit interactions. The pure-dephasing time shows an up to ~14 times enhancement on average when using robust sequences. The results are in good agreement with the noise generated from room-temperature circuits. Our study further reveals the decohering processes associated with tunable couplers and establishes a framework to develop gates and sequences robust against two-qubit errors., Comment: 19 pages, 14 figures

High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces crosstalk effect, simplifies calibration procedures, yet produces a controlled-Z gate in 30ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.

Based on the geometrical nature of quantum phases, non-adiabatic holonomic quantum control (NHQC) has become a standard technique for enhancing robustness in constructing quantum gates. However, the conventional approach of NHQC is sensitive to control instability, as it requires the driving pulses to cover a fixed pulse area. Furthermore, even for small-angle rotations, all operations need to be completed with the same duration of time. Here we experimentally demonstrate a time-optimal and unconventional approach of NHQC (called TOUNHQC), which can optimize the operation time of any holonomic gate. Compared with the conventional approach, TOUNHQC provides an extra layer of robustness to decoherence and control errors. The experiment involves a scalable architecture of superconducting circuit, where we achieved a fidelity of 99.51% for a single qubit gate using interleaved randomized benchmarking. Moreover, a two-qubit holonomic control-phase gate has been implemented where the gate error can be reduced by as much as 18% compared with NHQC.

For building a scalable quantum processor with superconducting qubits, ZZ interaction is of great concern because its residual has a crucial impact to two-qubit gate fidelity. Two-qubit gates with fidelity meeting the criterion of fault-tolerant quantum computationhave been demonstrated using ZZ interaction. However, as the performance of quantum processors improves, the residual static-ZZ can become a performance-limiting factor for quantum gate operation and quantum error correction. Here, we introduce a superconducting architecture using qubits with opposite-sign anharmonicity, a transmon qubit and a C-shunt flux qubit, to address this issue. We theoretically demonstrate that by coupling the two types of qubits, the high-contrast ZZ interaction can be realized. Thus, we can control the interaction with a high on/off ratio to implement two-qubit CZ gates, or suppress it during two-qubit gate operation using XY interaction (e.g., an iSWAP gate). The proposed architecture can also be scaled up to multi-qubit cases. In a fixed coupled system, ZZ crosstalk related to neighboring spectator qubits could also be heavily suppressed.

Fast robust two-qubit gate operation with low susceptibility to crosstalk are the key to scalable quantum information processing. Parametrically driven gate is inherently insensitive to crosstalk while superadiabatic control can speed up the gate without losing accuracy. We propose and experimentally implement superadiabatic two-qubit gates using parametric modulation on superconducting quantum circuits. Our results demonstrate the preservation of adiabaticity at a gate speed close to the quantum limit, in addition to robustness against control instability. We demonstrate a CZ gate with error rate of 5.8$\%$, limited largely by qubit decoherence, promising future improvement and scalable implementation.

Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum-metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system, which is characterized by the Euler characteristic number instead of the Chern number. The work opens up a unique approach to explore the topology of quantum states with the QGT., Comment: 6 pages, 4 figures; newly cited two experimental references

We consider a scenario with only one sterile neutrino $ N $, negligible mixing with the active neutrinos $ \nu_{L} $, where its interactions with ordinary particles could be described in a model independent approach based on an effective theory. Under such a framwork, we consider the contributions of the sterile neutrino $N$ to the pure leptonic decays $ M \rightarrow l\nu $ and $ \nu \overline{\nu} $, and the radiative leptonic decays $ M \rightarrow l\nu\gamma $ with $M$ denoting the pseudoscalar mesons $ B $, $ D $ and $ K$. We find that it can produce significant effects on some of these rare decay processes., Comment: 20 pages, 7 figures, references added and typos are corrected