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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

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.

We report new experimental results on the search for dark photons based on a near-quantum-limited haloscope equipped with a superconducting cavity. The loaded quality factor of the superconducting cavity is $6\times10^{5}$, so that the expected signal from dark photon dark matter can be enhanced by more than one order compared to a copper cavity. A Josephson parametric amplifier with a near-quantum-limited noise temperature has been utilized to minimize the noise during the search. Furthermore, a digital acquisition card based on field programmable gate arrays has been utilized to maximize data collection efficiency with a duty cycle being 100$\%$. This work has established the most stringent constraints on dark photons at around 26.965 $\mu$eV. In the future, our apparatus can be extended to search for other dark matter candidates, such as axions and axion-like particles, and scrutinize new physics beyond the Standard Model.

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

Superconducting qubits have emerged as a premier platform for large-scale quantum computation, yet the fidelity of state readout is often hindered by random noise and crosstalk, especially in multi-qubit systems. While neural networks trained on labeled data have shown promise in reducing crosstalk effects during readout, their current capabilities are limited to binary discrimination of joint-qubit states due to architectural constraints. Here we introduce a time-resolved modulated neural network capable of full-state tomography for individual qubits, enabling detailed time-resolved measurements like Rabi oscillations. This scalable approach, with a dedicated module per qubit, mitigated readout error by an order of magnitude under low signal-to-noise ratios and substantially reduced variance in Rabi oscillation measurements. This advancement bolsters quantum state discrimination with neural networks, and propels the development of next-generation quantum processors with enhanced performance and scalability.

As the basis for generating multi-particle quantum correlations, inter-particle interaction plays a crucial role in collective quantum phenomena, quantum phase transitions, and quantum information processing. It can profoundly alter the band structure of quantum many-body systems and give rise to exotic topological phenomena. Conventional topological pumping, which has been well demonstrated in driven linear or noninteracting systems, may break down in the presence of strong interaction. However, the interplay between band topology and interaction could also induce emergent topological pumping of interacting particles, but its experimental realization has proven challenging. Here we demonstrate interaction-induced topological pumping in a solid-state quantum system comprising an array of 36 superconducting qubits. With strong interaction inherent in the qubits and site-resolved controllability of the lattice potential and hopping strength, we realize the topological Thouless pumping of single and two bounded particles. Beyond these topological phenomena with linear or noninteracting counterparts, we also observe topologically resonant tunneling and asymmetric edge-state transport of interacting particles. Our work creates a paradigm for multi-particle topological effects, and provides a new pathway to the study of exotic topological phenomena, many-body quantum transport, and quantum information transfer., Comment: 8+29 pages, 4+24 figures

Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.

Quantum teleportation~\cite{Bennett1993} is of both fundamental interest and great practical importance in quantum information science. To date, quantum teleportation has been implemented in various physical systems~\cite{Pirandola2015}, among which superconducting qubits are of particular practical significance as they emerge as a leading system to realize large-scale quantum computation~\cite{Arute2019,Wu2021}. Nevertheless, the number of superconducting qubits on the same chip is severely limited by the available chip size, the cooling power, and the wiring complexity. Realization of quantum teleportation and remote computation over qubits on distant superconducting chips is a key quantum communication technology to scaling up the system through a distributed quantum computational network~\cite{Gottesman1999,Eisert2000,Jiang2007,Kimble2008,Monroe2014}. However, this goal has not been realized yet in experiments due to the technical challenge of making a quantum interconnect between distant superconducting chips and the inefficient transfer of flying microwave photons over the lossy interconnects~\cite{Kurpiers2018,Axline2018,Campagne2018,Magnard2020}. Here we demonstrate deterministic teleportation of quantum states and entangling gates between distant superconducting chips connected by a 64-meter-long cable bus featuring an ultralow loss of 0.32~dB/km at cryogenic temperatures, where high fidelity remote entanglement is generated via flying microwave photons utilizing time-reversal-symmetry~\cite{Cirac1997,Korotkov2011}. Apart from the fundamental interest of teleporting macroscopic superconducting qubits over a long distance, our work lays a foundation to realization of large-scale superconducting quantum computation through a distributed computational network~\cite{Gottesman1999,Eisert2000,Jiang2007,Kimble2008,Monroe2014}.

Scaling is now a key challenge in superconducting quantum computing. One solution is to build modular systems in which smaller-scale quantum modules are individually constructed and calibrated, and then assembled into a larger architecture. This, however, requires the development of suitable interconnects. Here, we report low-loss interconnects based on pure aluminium coaxial cables and on-chip impedance transformers featuring quality factors up to $8.1 \times 10^5$, which is comparable to the performance of our transmon qubits fabricated on single-crystal sapphire substrate. We use these interconnects to link five quantum modules with inter-module quantum state transfer and Bell state fidelities up to 99\%. To benchmark the overall performance of the processor, we create maximally-entangled, multi-qubit Greenberger-Horne-Zeilinger (GHZ) states. The generated inter-module four-qubit GHZ state exhibits 92.0\% fidelity. We also entangle up to 12 qubits in a GHZ state with $55.8 \pm 1.8\%$ fidelity, which is above the genuine multipartite entanglement threshold of 1/2. These results represent a viable modular approach for large-scale superconducting quantum processors.

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

High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel however degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these non-idealities, by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconducting quantum nodes connected by a moderately lossy, 1-meter long superconducting communication cable. We use a purification process to correct the dominant amplitude damping errors caused by transmission through the cable, with fractional increases in fidelity as large as $25\%$, achieved for higher damping errors. The best final fidelity the purification achieves is $94.09\pm 0.98\%$. In addition, we use both dynamical decoupling and Rabi driving to protect the entangled states from local noise, increasing the effective qubit dephasing time by a factor of 4, from $3~\rm \mu s$ to $12~\rm\mu s$. These methods demonstrate the potential for the generation and preservation of very high-fidelity entanglement in a superconducting quantum communication network.

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

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

Quantum entanglement is a key resource for quantum computation and quantum communication \cite{Nielsen2010}. Scaling to large quantum communication or computation networks further requires the deterministic generation of multi-qubit entanglement \cite{Gottesman1999,Duan2001,Jiang2007}. The deterministic entanglement of two remote qubits has recently been demonstrated with microwave photons \cite{Kurpiers2018,Axline2018,Campagne2018,Leung2019,Zhong2019}, optical photons \cite{Humphreys2018} and surface acoustic wave phonons \cite{Bienfait2019}. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily due to limited state transfer fidelities. Here, we report a quantum network comprising two separate superconducting quantum nodes connected by a 1 meter-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the coaxial cable to one qubit in each node, we can transfer quantum states between the nodes with a process fidelity of $0.911\pm0.008$. Using the high-fidelity communication link, we can prepare a three-qubit Greenberger-Horne-Zeilinger (GHZ) state \cite{Greenberger1990,Neeley2010,Dicarlo2010} in one node and deterministically transfer this state to the other node, with a transferred state fidelity of $0.656\pm 0.014$. We further use this system to deterministically generate a two-node, six-qubit GHZ state, globally distributed within the network, with a state fidelity of $0.722\pm0.021$. The GHZ state fidelities are clearly above the threshold of $1/2$ for genuine multipartite entanglement \cite{Guhne2010}, and show that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers \cite{Monroe2014,Chou2018}.

Variable microwave-frequency couplers are highly useful components in classical communication systems, and likely will play an important role in quantum communication applications. Conventional semiconductor-based microwave couplers have been used with superconducting quantum circuits, enabling for example the in situ measurements of multiple devices via a common readout chain. However, the semiconducting elements are lossy, and furthermore dissipate energy when switched, making them unsuitable for cryogenic applications requiring rapid, repeated switching. Superconducting Josephson junction-based couplers can be designed for dissipation-free operation with fast switching and are easily integrated with superconducting quantum circuits. These enable on-chip, quantum-coherent routing of microwave photons, providing an appealing alternative to semiconductor switches. Here, we present and characterize a chip-based broadband microwave variable coupler, tunable over 4-8 GHz with over 1.5 GHz instantaneous bandwidth, based on the superconducting quantum interference device (SQUID) with two parallel Josephson junctions. The coupler is dissipation-free, features large on-off ratios in excess of 40 dB, and the coupling can be changed in about 10 ns. The simple design presented here can be readily integrated with superconducting qubit circuits, and can be easily generalized to realize a four- or more port device., Comment: 11 pages, 8 figures

Effective quantum communication between remote quantum nodes requires high fidelity quantum state transfer and remote entanglement generation. Recent experiments have demonstrated that microwave photons, as well as phonons, can be used to couple superconducting qubits, with a fidelity limited primarily by loss in the communication channel. Adiabatic protocols can overcome channel loss by transferring quantum states without populating the lossy communication channel. Here we present a unique superconducting quantum communication system, comprising two superconducting qubits connected by a 0.73 m-long communication channel. Significantly, we can introduce large tunable loss to the channel, allowing exploration of different entanglement protocols in the presence of dissipation. When set for minimum loss in the channel, we demonstrate an adiabatic quantum state transfer protocol that achieves 99% transfer efficiency as well as the deterministic generation of entangled Bell states with a fidelity of 96%, all without populating the intervening communication channel, and competitive with a qubit-resonant mode-qubit relay method. We also explore the performance of the adiabatic protocol in the presence of significant channel loss, and show that the adiabatic protocol protects against loss in the channel, achieving higher state transfer and entanglement fidelities than the relay method., Comment: 27 pages, 14 figures

Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface-acoustic-wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later re-capture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel, or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit's final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signalling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon's self-interference, or erased., Comment: 16 pages, 8 figures