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Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing are prominent approaches for solving combinatorial optimization problems, such as those formulated as Quadratic Unconstrained Binary Optimization (QUBO). These algorithms aim to minimize the objective function $x^T Q x$, where $Q$ is a QUBO matrix. However, the number of two-qubit CNOT gates in QAOA circuits and the complexity of problem embeddings in Quantum Annealing scale linearly with the number of non-zero couplings in $Q$, contributing to significant computational and error-related challenges. To address this, we introduce the concept of \textit{semi-symmetries} in QUBO matrices and propose an algorithm for identifying and factoring these symmetries into ancilla qubits. \textit{Semi-symmetries} frequently arise in optimization problems such as \textit{Maximum Clique}, \textit{Hamilton Cycles}, \textit{Graph Coloring}, and \textit{Graph Isomorphism}. We theoretically demonstrate that the modified QUBO matrix $Q_{\text{mod}}$ retains the same energy spectrum as the original $Q$. Experimental evaluations on the aforementioned problems show that our algorithm reduces the number of couplings and QAOA circuit depth by up to $45\%$. For Quantum Annealing, these reductions also lead to sparser problem embeddings, shorter qubit chains and better performance. This work highlights the utility of exploiting QUBO matrix structure to optimize quantum algorithms, advancing their scalability and practical applicability to real-world combinatorial problems., Comment: arXiv admin note: substantial text overlap with arXiv:2411.08824

Coupled optical cavities, which support normal modes, play a critical role in optical filtering, sensing, slow-light generation, and quantum state manipulation. Recent theoretical work has proposed incorporating nonlinear materials into these systems to enable novel quantum technologies. Here, we report the first experimental demonstration of squeezing generated in a quantum-enhanced coupled-cavity system, achieving a quantum noise reduction of 3.5 dB at a normal-mode splitting frequency of 7.47 MHz. We provide a comprehensive analysis of the system's loss mechanisms and performance limitations, validating theoretical predictions. Our results underscore the promise of coupled-cavity squeezers for advanced quantum applications, including gravitational wave detection and precision sensing.

Superconducting nanowire single-photon detectors (SNSPDs) are indispensable in fields such as quantum science and technology, astronomy, and biomedical imaging, where high detection efficiency, low dark count rates and high timing accuracy are required. Recently, helium (He) ion irradiation was shown to be a promising method to enhance SNSPD performance. Here, we study how changes in the underlying superconducting NbTiN film and the SiO2/Si substrate affect device performance. While irradiated and unirradiated NbTiN films show similar crystallinity, we observe He bubble formation below the SiO2/Si interface and an amorphization of the Si substrate. Both reduce the thermal conductance between the superconducting thin film and the substrate from 210 W/m^2/K^4 to 70 W/m^2/K^4 after irradiation with 2000 ions/nm^2. This effect, combined with the lateral straggle of He ions in the substrate, allows the modification of the superconductor-to-substrate thermal conductance of an SNSPD by selectively irradiating the regions around the nanowire. With this approach, we achieved an increased plateau width of saturating intrinsic detection efficiency of 9.8 uA compared to 3.7 uA after full irradiation. Moreover, the critical current remained similar to that of the unirradiated reference device (59 uA versus 60.1 uA), while full irradiation reduced it to 22.4 uA. Our results suggest that the irradiation-induced reduction of the thermal conductance significantly enhances SNSPD sensitivity, offering a novel approach to locally engineer substrate properties for improved detector performance., Comment: 18 pages, 11 figures

We investigate the impact of latent symmetries on the dynamics of photonic systems and their eigenmodes. Residing solely within the eigenspectral domain, latent symmetries are not visible in real space, yet promise intriguing new ways to engineer the functionality of photonic systems. We study the eigenmodes of a 9-site latent-symmetric photonic network and find that an anti-symmetric input state is fundamentally precluded from populating so-called singlet sites. Furthermore, arbitrary extensions of the system at these sites do not break its latent symmetry. Therefore anti-symmetric excitations cannot leave the initial system, which can be leveraged e.g. for the storage of information. This holds true for both single-photon states, or classical light, as well as both distinguishable and indistinguishable two-photon quantum states. Latent symmetries introduce a powerful new set of tools to the design of systems with desired functionality on any nanophotonic platform, paving the way for applications in photonic information processing., Comment: 10 pages, 4 figures

The transport of quantum states is a crucial aspect of information processing systems, facilitating operations such as quantum key distribution and inter-component communication within quantum computers. Most quantum networks rely on symmetries to achieve an efficient state transfer. A straightforward way to design such networks is to use spatial symmetries, which severely limits the design space. Our work takes a novel approach to designing photonic networks that do not exhibit any conventional spatial symmetries, yet nevertheless support an efficient transfer of quantum states. Paradoxically, while a perfect transfer efficiency is technically unattainable in these networks, a fidelity arbitrarily close to unity is always reached within a finite time of evolution. Key to this approach are so-called latent, or 'hidden', symmetries, which are embodied in the spectral properties of the network. Latent symmetries substantially expand the design space of quantum networks and hold significant potential for applications in quantum cryptography and secure state transfer. We experimentally realize such a nine-site latent-symmetric network and successfully observe state transfer between two sites with a measured fidelity of 75%. Furthermore, by launching a two-photon state, we show that quantum interference is preserved by the network. This demonstrates that the latent symmetries enable efficient quantum state transfer, while offering greater flexibility in designing quantum networks., Comment: 14 pages, 5 figures; Update: inserted arXiv identifier to related reference

Typically, the von Neumann entropy of a subsystem increases until it plateaus at the thermal value. Under some circumstances, however, the intermediate value can dwarf the final value, even if the subsystem starts in a pure state. A famous example in the context of the black hole information paradox is the entropy of the Hawking radiation, where this behaviour is dubbed the Page curve. More generally, this is the case for excited systems weakly coupled to cold reservoirs. Here we study the entropy dynamics for Lindbladian evolution, i.e. open quantum systems in weak contact with Markovian reservoirs. This allows us to study the non-equilibrium thermodynamics of the subsystem entropy decrease and link it to Landauer's principle: the entropy decrease must be accompanied by a heat flow out of the system. We give an analytic expression of the entanglement dynamics for a decaying excitation in a two-level system and study it under equilibration of a localised oscillator. In both cases the Page time occurs when half the initial energy has left the system., Comment: 5 pages, 2 figures, comments welcome

PAX (antiProtonic Atom X-ray spectroscopy) is a new experiment with the aim to test strong-field quantum electrodynamics (QED) effects by performing high-precision x-ray spectroscopy of antiprotonic atoms. By utilizing advanced microcalorimeter detection techniques and a low-energy antiproton beam provided by the ELENA ring at CERN, gaseous targets will be used for the creation of antiprotonic atoms, and the measurement of transitions between circular Rydberg states will be conducted with up to two orders of magnitude improved accuracy over previous studies using high-purity germanium detectors. Our approach eliminates the longstanding issue of nuclear uncertainties that have hindered prior studies using highly charged ions, thus enabling direct and purely QED-focused measurements. By precisely probing atomic systems with electric fields up to two orders of magnitude above the Schwinger limit, PAX will test vacuum polarization and second-order QED corrections, opening new frontiers in fundamental physics and uncovering potential pathways to physics beyond the Standard Model.

We formalize a rigorous connection between barren plateaus (BP) in variational quantum algorithms and exponential concentration of quantum kernels for machine learning. Our results imply that recently proposed strategies to build BP-free quantum circuits can be utilized to construct useful quantum kernels for machine learning. This is illustrated by a numerical example employing a provably BP-free quantum neural network to construct kernel matrices for classification datasets of increasing dimensionality without exponential concentration.

This paper presents a novel optimization approach for allocating grid operation costs in Peer-to-Peer (P2P) electricity markets using Quantum Computing (QC). We develop a Quadratic Unconstrained Binary Optimization (QUBO) model that matches logical power flows between producer-consumer pairs with the physical power flow to distribute grid usage costs fairly. The model is evaluated on IEEE test cases with up to 57 nodes, comparing Quantum Annealing (QA), hybrid quantum-classical algorithms, and classical optimization approaches. Our results show that while the model effectively allocates grid operation costs, QA performs poorly in comparison despite extensive hyperparameter optimization. The classical branch-and-cut method outperforms all solvers, including classical heuristics, and shows the most advantageous scaling behavior. The findings may suggest that binary least-squares optimization problems may not be suitable candidates for near-term quantum utility.

The ST2 center is an optically addressable point defect in diamond that facilitates spin initialization and readout. However, while this study presents the discovery of ST2 centers first observed in a natural diamond and provides a reliable technique for artificially creating them, its chemical structure remains unknown. To assess the potential of ST2, we map out its basic optical characteristics, reveal its electronic level structure, and quantify the intrinsic transition rates. Furthermore, we investigate its response to microwaves, static magnetic fields, and the polarization of excitation laser light, revealing twelve inequivalent orientations of the ST2 center. Simultaneous exposure to microwaves and static magnetic fields also reveals an exceptionally wide acceptance angle for sensing strong magnetic fields, unlike the well-established NV center, which is sensitive only within a narrow cone aligned with its symmetry axis. This finding establishes the ST2 center as a highly promising candidate for nanoscale quantum sensing., Comment: 8 Pages 3 Figures, Supplement: 9 Pages 4 (5) figures

It is advantageous for any quantum processor to support different classes of two-qubit quantum logic gates when compiling quantum circuits, a property that is typically not seen with existing platforms. In particular, access to a gate set that includes support for the CZ-type, the iSWAP-type, and the SWAP-type families of gates, renders conversions between these gate families unnecessary during compilation as any two-qubit Clifford gate can be executed using at most one two-qubit gate from this set, plus additional single-qubit gates. We experimentally demonstrate that a SWAP gate can be decomposed into one iSWAP gate followed by one CZ gate, affirming a more efficient compilation strategy over the conventional approach that relies on three iSWAP or three CZ gates to replace a SWAP gate. Our implementation makes use of a superconducting quantum processor design based on fixed-frequency transmon qubits coupled together by a parametrically modulated tunable transmon coupler, extending this platform's native gate set so that any two-qubit Clifford unitary matrix can be realized using no more than two two-qubit gates and single-qubit gates., Comment: 29 pages, 13 figures

A common trait of many machine learning models is that it is often difficult to understand and explain what caused the model to produce the given output. While the explainability of neural networks has been an active field of research in the last years, comparably little is known for quantum machine learning models. Despite a few recent works analyzing some specific aspects of explainability, as of now there is no clear big picture perspective as to what can be expected from quantum learning models in terms of explainability. In this work, we address this issue by identifying promising research avenues in this direction and lining out the expected future results. We additionally propose two explanation methods designed specifically for quantum machine learning models, as first of their kind to the best of our knowledge. Next to our pre-view of the field, we compare both existing and novel methods to explain the predictions of quantum learning models. By studying explainability in quantum machine learning, we can contribute to the sustainable development of the field, preventing trust issues in the future., Comment: 16+16 pages, 3+4 figures

This paper presents the development and implementation of a versatile ad-hoc metropolitan-range Quantum Key Distribution (QKD) network. The approach presented integrates various types of physical channels and QKD protocols, and a mix of trusted and untrusted nodes. Unlike conventional QKD networks that predominantly depend on either fiber-based or free-space optical (FSO) links, the testbed presented amalgamates FSO and fiber-based links, thereby overcoming some inherent limitations. Various network deployment strategies have been considered, including permanent infrastructure and provisional ad-hoc links to eradicate coverage gaps. Furthermore, the ability to rapidly establish a network using portable FSO terminals and to investigate diverse link topologies is demonstrated. The study also showcases the successful establishment of a quantum-secured link to a cloud server.

Graph states are fundamental objects in the theory of quantum information due to their simple classical description and rich entanglement structure. They are also intimately related to IQP circuits, which have applications in quantum pseudorandomness and quantum advantage. For us, they are a toy model to understand the relation between circuit connectivity, entanglement structure and computational complexity. In the worst case, a strict dichotomy in the computational universality of such graph states appears as a function of the degree $d$ of a regular graph state [GDH+23]. In this paper, we initiate the study of the average-case complexity of simulating random graph states of varying degree when measured in random product bases and give distinct evidence that a similar complexity-theoretic dichotomy exists in the average case. Specifically, we consider random $d$-regular graph states and prove three distinct results: First, we exhibit two families of IQP circuits of depth $d$ and show that they anticoncentrate for any $2 < d = o(n)$ when measured in a random $X$-$Y$-plane product basis. This implies anticoncentration for random constant-regular graph states. Second, in the regime $d = \Theta(n^c)$ with $c \in (0,1)$, we prove that random $d$-regular graph states contain polynomially large grid graphs as induced subgraphs with high probability. This implies that they are universal resource states for measurement-based computation. Third, in the regime of high degree ($d\sim n/2$), we show that random graph states are not sufficiently entangled to be trivially classically simulable, unlike Haar random states. Proving the three results requires different techniques--the analysis of a classical statistical-mechanics model using Krawtchouck polynomials, graph theoretic analysis using the switching method, and analysis of the ranks of submatrices of random adjacency matrices, respectively., Comment: many pages, lots of counting, lovely figures

The two-qubit controlled-not (C-NOT) gate is an essential component in the construction of a gate-based quantum computer. In fact, its operation, combined with single qubit rotations allows to realise any quantum circuit. Several strategies have been adopted in order to build quantum gates, among them the photonic one offers the dual advantage of excellent isolation from the external environment and ease of manipulation at the single qubit level. Here we adopt a scalable time-multiplexed approach in order to build a fully reconfigurable architecture capable of implementing a post-selected interferometric scheme that implements the C-NOT operation with a fidelity of $(93.8\pm1.4)\%$. We use our experimental platform to generate the four Bell states., Comment: 9 pages, 4 figures

QAOA is a quantum algorithm for solving combinatorial optimization problems. It is capable of searching for the minimizing solution vector $x$ of a QUBO problem $x^TQx$. The number of two-qubit CNOT gates in the QAOA circuit scales linearly in the number of non-zero couplings of $Q$ and the depth of the circuit scales accordingly. Since CNOT operations have high error rates it is crucial to develop algorithms for reducing their number. We, therefore, present the concept of \textit{semi-symmetries} in QUBO matrices and an algorithm for identifying and factoring them out into ancilla qubits. \textit{Semi-symmetries} are prevalent in QUBO matrices of many well-known optimization problems like \textit{Maximum Clique}, \textit{Hamilton Cycles}, \textit{Graph Coloring}, \textit{Vertex Cover} and \textit{Graph Isomorphism}, among others. We theoretically show that our modified QUBO matrix $Q_{mod}$ describes the same energy spectrum as the original $Q$. Experiments conducted on the five optimization problems mentioned above demonstrate that our algorithm achieved reductions in the number of couplings by up to $49\%$ and in circuit depth by up to $41\%$.

Fast entangling gate operations are a fundamental prerequisite for quantum simulation and computation. We propose an entangling scheme for arbitrary pairs of ions in a linear crystal, harnessing the high electric polarizability of highly excited Rydberg states. An all-to-all quantum gate connectivity is based on an initialization of a pair of ions to a superposition of ground- and Rydberg-states by laser excitation, followed by the entangling gate operation which relies on a state-dependent frequency shift of collective vibrational modes of the crystal. This gate operation requires applying an electric waveform to trap electrodes. Employing transverse collective modes of oscillation, we reveal order of $\mu s$ operation times within any of the qubit pairs in a small crystal. In our calculation, we are taking into account realistic experimental conditions and feasible electric field ramps. The proposed gate operation is ready to be combined with a scalable processor architecture to reconfigure the qubit register, either by shuttling ions or by dynamically controlling optical tweezer potentials., Comment: 9 pages, 4 figures

The quest for a global quantum internet is based on the realization of a scalable network which requires quantum hardware with exceptional performance. Among them are quantum light sources providing deterministic, high brightness, high-fidelity entangled photons and quantum memories with coherence times in the millisecond range and above. To operate the network on a global scale, the quantum light source should emit at telecommunication wavelengths with minimum propagation losses. A cornerstone for the operation of such a quantum network is the demonstration of quantum teleportation. Here we realize full-photonic quantum teleportation employing one of the most promising platforms, i.e. semiconductor quantum dots, which can fulfill all the aforementioned requirements. Two remote quantum dots are used, one as a source of entangled photon pairs and the other as a single-photon source. The frequency mismatch between the triggered sources is erased using two polarization-preserving quantum frequency converters, enabling a Bell state measurement at telecommunication wavelengths. A post-selected teleportation fidelity of up to 0.721(33) is achieved, significantly above the classical limit, demonstrating successful quantum teleportation between light generated by distinct sources. These results mark a major advance for the semiconductor platform as a source of quantum light fulfilling a key requirement for a scalable quantum network. This becomes particularly relevant after the seminal breakthrough of addressing a nuclear spin in semiconductor quantum dots demonstrating long coherence times, thus fulfilling another crucial step towards a scalable quantum network.

Neutral atoms have emerged as a promising technology for implementing quantum computers due to their scalability and long coherence times. However, the execution frequency of neutral atom quantum computers is constrained by image processing procedures, particularly the assembly of defect-free atom arrays, which is a crucial step in preparing qubits (atoms) for execution. To optimize this assembly process, we propose a novel quadrant-based rearrangement algorithm that employs a divide-and-conquer strategy and also enables the simultaneous movement of multiple atoms, even across different columns and rows. We implement the algorithm on FPGA to handle each quadrant independently (hardware-level optimization) while maximizing parallelization. To the best of our knowledge, this is the first hardware acceleration work for atom rearrangement, and it significantly reduces the processing time. This achievement also contributes to the ongoing efforts of tightly integrating quantum accelerators into High-Performance Computing (HPC) systems. Tested on a Zynq RFSoC FPGA at 250 MHz, our hardware implementation is able to complete the rearrangement process of a 30$\times$30 compact target array, derived from a 50$\times$50 initial loaded array, in approximately 1.0 $\mu s$. Compared to a comparable CPU implementation and to state-of-the-art FPGA work, we achieved about 54$\times$ and 300$\times$ speedups in the rearrangement analysis time, respectively. Additionally, the FPGA-based acceleration demonstrates good scalability, allowing for seamless adaptation to varying sizes of the atom array, which makes this algorithm a promising solution for large-scale quantum systems., Comment: The paper is accepted by Design, Automation and Test in Europe Conference (DATE), 2025

Fe$^{\mathrm{II}}$ spin-crossover (SCO) complexes are materials that change their magnetic properties upon temperature variation, exhibiting a thermal hysteresis. Particularly interesting for magnetic-memory applications are thin layers of SCO complexes, where practical magnetic probing techniques are required. While conventional magnetometry on SCO complexes employs cryogenic temperatures, nitrogen-vacancy (NV) centers are quantum magnetometers that can operate at room temperature with high spatial resolution and magnetic-field sensitivity. In this work, we apply thin layers of Fe-triazole SCO complexes directly onto a single-crystal diamond with shallow NV centers working as magnetic sensors and probe the fluctuating magnetic field. Using temperature-dependent NV-center $T_1$ measurements and a widefield technique, we find that the complexes are paramagnetic in the investigated temperature range from 20 {\deg}C to 80 {\deg}C. We quantitatively describe the $T_1$ time by a model considering the fluctuating magnetic field of the Fe$^{\mathrm{II}}$ ions. We see signatures of a local change of spin state in the $T_1$ relaxometry data, but structural changes in the SCO material dominate the local magnetic environment of the NV centers. Moreover, we conduct a Hahn echo to measure the $T_2$ time, which contrasts the findings of the $T_1$ times for the SCO complexes. We attribute this to different NV detection sensitivities towards Fe$^{\mathrm{II}}$ and Fe$^{\mathrm{III}}$ of the protocols. Our results on the magnetic properties of SCO materials highlight the capabilities of the NV center as a susceptible sensor for fluctuating magnetic fields. At the same time, a spin switching of the complexes cannot be observed due to the systematic challenges when working on nanometer distances to the SCO thin layers., Comment: 6 + 21 figures, 12 + 11 pages

This paper explores communication over a two-sender, two-receiver classical interference channel, enhanced by the availability of entanglement resources between transmitters. The central contributions are an inner and outer bound on the capacity region for a general interference channel with entangled transmitters. It addresses the persistent challenge of the lack of a general capacity formula, even in the purely classical case, and highlights the striking similarities in achievable rate expressions when assessing quantum advantages. Through a concrete example, it is shown that entanglement can significantly boost performance in certain types of channels.

Finding reliable approximations to the quantum many-body problem is one of the central challenges of modern physics. Elemental to this endeavor is the development of advanced numerical techniques pushing the limits of what is tractable. One such recently proposed numerical technique are neural quantum states. This new type of wavefunction based Ans\"atze utilizes the expressivity of neural networks to tackle fundamentally challenging problems, such as the Mott transition. In this paper we aim to gauge the universalness of one representative of neural network Ans\"atze, the hidden-fermion slater determinant approach. To this end, we study five different fermionic models each displaying volume law scaling of the entanglement entropy. For these, we correlate the effectiveness of the Ansatz with different complexity measures. Each measure indicates a different complexity in the absence of which a conventional Ansatz becomes efficient. We provide evidence that whenever one of the measures indicates proximity to a parameter region in which a conventional approach would work reliable, the neural network approach also works reliable and efficient. This highlights the great potential, but also challenges for neural network approaches: Finding suitable points in theory space around which to construct the Ansatz in order to be able to efficiently treat models unsuitable for their current designs., Comment: 20 pages, 25 figures

We study the convergence properties of Variational Quantum Circuits (VQCs) to investigate how they can differ from their classical counterparts. It is known that a VQC is a linear model in a feature map determined by its architecture. Learning a classical model on the same feature map will lead to a solution called the Minimum Norm Least Square (MNLS) estimator. In this work, we characterize the separation between quantum and classical models by their respective weight vector. We show that a necessary condition for a quantum model to avoid dequantization by its classical surrogate is to have a large weight vector norm. Furthermore, we suggest that this can only happen with a high dimensional feature map.Through the study of some common quantum architectures and encoding schemes, we obtain bounds on the norms of the quantum weight vector and the corresponding MNLS weight vector. It is possible to find instances allowing for such separation, but in these cases, concentration issues become another concern. We finally prove that there exists a linear model with large weight vector norm and without concentration, potentially achievable by a quantum circuit.

In this work we investigate the computational complexity of the pure consistency of local density matrices ($\mathsf{PureCLDM}$) and pure $N$-representability ($\mathsf{Pure}$-$N$-$\mathsf{Representability}$) problems. In these problems the input is a set of reduced density matrices and the task is to determine whether there exists a global \emph{pure} state consistent with these reduced density matrices. While mixed $\mathsf{CLDM}$, i.e. where the global state can be mixed, was proven to be $\mathsf{QMA}$-complete by Broadbent and Grilo [JoC 2022], almost nothing was known about the complexity of the pure version. Before our work the best upper and lower bounds were $\mathsf{QMA}(2)$ and $\mathsf{QMA}$. Our contribution to the understanding of these problems is twofold. Firstly, we define a pure state analogue of the complexity class $\mathsf{QMA}^+$ of Aharanov and Regev [FOCS 2003], which we call $\mathsf{PureSuperQMA}$. We prove that both $\mathsf{Pure}$-$N$-$\mathsf{Representability}$ and $\mathsf{PureCLDM}$ are complete for this new class. Along the way we supplement Broadbent and Grilo by proving hardness for 2-qubit reduced density matrices and showing that mixed $N$-$\mathsf{Representability}$ is $\mathsf{QMA}$ complete. Secondly, we improve the upper bound on $\mathsf{PureCLDM}$. Using methods from algebraic geometry, we prove that $\mathsf{PureSuperQMA} \subseteq \mathsf{PSPACE}$. Our methods, and the $\mathsf{PSPACE}$ upper bound, are also valid for $\mathsf{PureCLDM}$ with exponential or even perfect precision, hence $\mathsf{precisePureCLDM}$ is not $\mathsf{preciseQMA}(2) = \mathsf{NEXP}$-complete, unless $\mathsf{PSPACE} = \mathsf{NEXP}$. We view this as evidence for a negative answer to the longstanding open question whether $\mathsf{PureCLDM}$ is $\mathsf{QMA}(2)$-complete., Comment: 42 pages, 1 figure

We study the long-standing open question of the power of unique witness in quantum protocols, which asks if UniqueQMA, a variant of QMA whose accepting witness space is 1-dimensional, is equal to QMA. We show a quantum oracle separation between UniqueQMA and QMA via an extension of the Aaronson-Kuperberg's QCMA vs QMA oracle separation. In particular, we show that any UniqueQMA protocol must make $\Omega(\sqrt{D})$ queries to a subspace phase oracle of unknown dimension $\leq D$ to "find" the subspace. This presents an obstacle to relativizing techniques in resolving this question (unlike its classical analogue - the Valiant-Vazirani theorem - which is essentially a black-box reduction) and suggests the need to study the structure of the ground space of local Hamiltonians in distilling a potential unique witness. Our techniques also yield a quantum oracle separation between QXC, the class characterizing quantum approximate counting, and QMA. Very few structural properties are known that place the complexity of local Hamiltonians in UniqueQMA. We expand this set of properties by showing that the ground energy of local Hamiltonians that satisfy the eigenstate thermalization hypothesis (ETH) can be estimated through a UniqueQMA protocol. Specifically, our protocol can be viewed as a quantum expander test in a low energy subspace of the Hamiltonian and verifies a unique entangled state in two copies of the subspace. This allows us to conclude that if UniqueQMA $\neq$ QMA, then QMA-hard Hamiltonians must violate ETH under adversarial perturbations (more accurately, under the quantum PCP conjecture if ETH only applies to extensive energy subspaces). Our results serve as evidence that chaotic local Hamiltonians, such as the SYK model, contain polynomial verifiable quantum states in their low energy regime and may be simpler than general local Hamiltonians if UniqueQMA $\neq$ QMA.

The first artificial quantum neuron models followed a similar path to classic models, as they work only with discrete values. Here we introduce an algorithm that generalizes the binary model manipulating the phase of complex numbers. We propose, test, and implement a neuron model that works with continuous values in a quantum computer. Through simulations, we demonstrate that our model may work in a hybrid training scheme utilizing gradient descent as a learning algorithm. This work represents another step in the direction of evaluation of the use of artificial neural networks efficiently implemented on near-term quantum devices., Comment: 11 pages, 7 figures, to be published in Ci\^encia e Natura (ISSN 2179-460X, DOI: 10.5902/2179460X)

The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the development of a quantum algorithm for the calculation of internal products between vectors of continuous values. In order for this to be possible, it was necessary to make adaptations to the classic kernel method, since it is necessary to consider the limitations imposed by the Hilbert space of the quantum processor. As a test case, we applied this new algorithm to learn to classify whether new points generated randomly, in a finite square located under a plane, were found inside or outside a circle located inside this square. It was found that the algorithm was able to correctly detect new points in 99% of the samples tested, with a small difference due to considering the radius slightly larger than the ideal. However, the kernel method was able to perform classifications correctly, as well as the internal product algorithm successfully performed the internal product calculations using quantum resources. Thus, the present work represents a contribution to the area, proposing a new model of machine learning accessible to both physicists and computer scientists., Comment: 14 pages, in Portuguese language, 1 figure

We prove a conjecture of Arunachalam & Dutt ([AD24]) on the existence of a tolerant stabilizer testing algorithm, and achieve an exponential improvement in the parameters of the tester. Key to our argument is a generalized uncertainty relation for sets of Pauli operators, based on the Lovasz theta function., Comment: 9 pages, several really large powers. Comments welcome!

The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical simulations, it has been suggested that the addition of non-linear elements to the experiment will help retain the quantum advantage. We propose a classical simulation tool for general continuous variable sampling problems, including Gaussian Boson Sampling and beyond. We reformulate the sampling problem as that of finding the ground state of a simple few-body Hamiltonian. This allows us to employ powerful variational methods based on tensor networks and to read off the simulation error directly from the expectation value of the Hamiltonian. We validate our method by simulating Gaussian Boson Sampling, where we achieve results comparable to the state of the art. We also consider a non-Gaussian sampling problem, for which we develop novel local basis optimization techniques based on a non-linear parameterization of the implicit basis, resulting in high effective cutoffs with diminished computational overhead.

We study the sample complexity of the prototypical tasks quantum purity estimation and quantum inner product estimation. In purity estimation, we are to estimate $tr(\rho^2)$ of an unknown quantum state $\rho$ to additive error $\epsilon$. Meanwhile, for quantum inner product estimation, Alice and Bob are to estimate $tr(\rho\sigma)$ to additive error $\epsilon$ given copies of unknown quantum state $\rho$ and $\sigma$ using classical communication and restricted quantum communication. In this paper, we show a strong connection between the sample complexity of purity estimation with bounded quantum memory and inner product estimation with bounded quantum communication and unentangled measurements. We propose a protocol that solves quantum inner product estimation with $k$-qubit one-way quantum communication and unentangled local measurements using $O(median\{1/\epsilon^2,2^{n/2}/\epsilon,2^{n-k}/\epsilon^2\})$ copies of $\rho$ and $\sigma$. Our protocol can be modified to estimate the purity of an unknown quantum state $\rho$ using $k$-qubit quantum memory with the same complexity. We prove that arbitrary protocols with $k$-qubit quantum memory that estimate purity to error $\epsilon$ require $\Omega(median\{1/\epsilon^2,2^{n/2}/\sqrt{\epsilon},2^{n-k}/\epsilon^2\})$ copies of $\rho$. This indicates the same lower bound for quantum inner product estimation with one-way $k$-qubit quantum communication and classical communication, and unentangled local measurements. For purity estimation, we further improve the lower bound to $\Omega(\max\{1/\epsilon^2,2^{n/2}/\epsilon\})$ for any protocols using an identical single-copy projection-valued measurement. Additionally, we investigate a decisional variant of quantum distributed inner product estimation without quantum communication for mixed state and provide a lower bound on the sample complexity., Comment: 33 pages, 1 figure

Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to realize on realistic quantum hardware. In this work, we seek to make progress on both of these fronts simultaneously -- by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z-rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate $t$-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys., Comment: 64 pages, 1 figure

We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that $\Omega(\sqrt{n})$ copies are required for any algorithm. The main observation behind our algorithm is that when repeatedly measuring in a randomly chosen stabilizer basis, stabilizer states are the most likely among the set of all pure states to exhibit linear dependencies in measurement outcomes. Our algorithm is designed to probe deviations from this extremal behavior. For the lower bound, we first reduce stabilizer testing to the task of distinguishing random stabilizer states from the maximally mixed state. We then argue that, without loss of generality, it is sufficient to consider measurement strategies that a) lie in the commutant of the tensor action of the Clifford group and b) satisfy a Positive Partial Transpose (PPT) condition. By leveraging these constraints, together with novel results on the partial transposes of the generators of the Clifford commutant, we derive the lower bound on the sample complexity., Comment: 38 pages, no figures. Comments welcome

In this note we prove a necessary set of conditions which must be satisfied by any controlled gate in the qubit Clifford Hierarchy. These conditions are straightforward to derive yet quite restricting. We also extend our proofs to gates composed of certain direct sums of unitaries. Finally, we provide some evidence that these conditions are also sufficient., Comment: 9 pages, comments welcome

In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral method, which involves encoding the solution functions in the amplitudes of the quantum states generated by different parametrized circuits and transforms the task of solving the differential equations into an optimization problem. We first describe the principle of the algorithm from a theoretical point of view. We provide a detailed pseudo-code of the algorithm, on which we conduct a complexity analysis to highlight its scaling properties. We apply it to a set of examples, showcasing its applicability across diverse sets of differential equations. We discuss the advantages of our method and potential avenues for further exploration and refinement., Comment: The algorithm described in this paper is subject to a patent submission (EP24306601). Use of this method requires a license, which can be obtained from ColibriTD

Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can offer polynomial speed-up and can be used to mimic classical machine learning algorithms. In this work, we propose a novel convolutional neural network architecture model based on Hamming weight preserving quantum circuits. In particular, we introduce convolutional layers, and measurement based pooling layers that preserve the symmetries of the quantum states while realizing non-linearity using gates that are not subspace preserving. Our proposal offers significant polynomial running time advantages over classical deep-learning architecture. We provide an open source simulation library for Hamming weight preserving quantum circuits that can simulate our techniques more efficiently with GPU-oriented libraries. Using this code, we provide examples of architectures that highlight great performances on complex image classification tasks with a limited number of qubits, and with fewer parameters than classical deep-learning architectures.

Experiments in the field of quantum optics often require very low concentrations of dust particles in the laboratory, but the complexity of working routines precludes operation within a proper clean room. Research teams have established a multitude of different approaches, precaution measures, and habits to keep the delicate optics setups free of contamination. Here, we systematically quantify dust particle concentration during day-to-day operation of a quantum optics lab, assess the effectiveness of various measures, and give practical recommendations., Comment: 4 pages, 4 figures, comments welcome!

Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer separated components. In this article, we present QuForge, a Python-based library designed to simulate quantum circuits with qudits. This library provides the necessary quantum gates for implementing quantum algorithms, tailored to any chosen qudit dimension. Built on top of differentiable frameworks, QuForge supports execution on accelerating devices such as GPUs and TPUs, significantly speeding up simulations. It also supports sparse operations, leading to a reduction in memory consumption compared to other libraries. Additionally, by constructing quantum circuits as differentiable graphs, QuForge facilitates the implementation of quantum machine learning algorithms, enhancing the capabilities and flexibility of quantum computing research., Comment: 18 pages, 7 figures

In neutral atom quantum computers, readout and preparation of the atomic qubits are usually based on fluorescence imaging and subsequent analysis of the acquired image. For each atom site, the brightness or some comparable metric is estimated and used to predict the presence or absence of an atom. Across different setups, we can see a vast number of different approaches used to analyze these images. Often, the choice of detection algorithm is either not mentioned at all or it is not justified. We investigate several different algorithms and compare their performance in terms of both precision and execution run time. To do so, we rely on a set of synthetic images across different simulated exposure times with known occupancy states. Since the use of simulation provides us with the ground truth of atom site occupancy, we can easily state precise error rates and variances of the reconstructed property. To also rule out the possibility of better algorithms existing, we calculated the Cram\'er-Rao bound in order to establish an upper limit that even a perfect estimator cannot outperform. As the metric of choice, we used the number of photonelectrons that can be contributed to a specific atom site. Since the bound depends on the occupancy of neighboring sites, we provide the best and worst cases, as well as a half filled one. Our comparison shows that of our tested algorithms, a global non-linear least-squares solver that uses the optical system's PSF to return a each sites' number of photoelectrons performed the best, on average crossing the worst-case bound for longer exposure times. Its main drawback is its huge computational complexity and, thus, required calculation time. We manage to somewhat reduce this problem, suggesting that its use may be viable. However, our study also shows that for cases where utmost speed is required, simple algorithms may be preferable., Comment: 10 pages, 11 figures

The realization of fault-tolerant quantum computing requires the execution of quantum error-correction (QEC) schemes, to mitigate the fragile nature of qubits. In this context, to ensure the success of QEC, a protocol capable of implementing both qubit reset and leakage reduction is highly desirable. We demonstrate such a protocol in an architecture consisting of fixed-frequency transmon qubits pair-wise coupled via tunable couplers -- an architecture that is compatible with the surface code. We use tunable couplers to transfer any undesired qubit excitation to the readout resonator of the qubit, from which this excitation decays into the feedline. In total, the combination of qubit reset, leakage reduction, and coupler reset takes only 83ns to complete. Our reset scheme is fast, unconditional, and achieves fidelities well above 99%, thus enabling fixed-frequency qubit architectures as future implementations of fault-tolerant quantum computers. Our protocol also provides a means to both reduce QEC cycle runtime and improve algorithmic fidelity on quantum computers.

As contemporary quantum computers do not possess error correction, any calculation performed by these devices can be considered an involuntary approximation. To solve a problem on a quantum annealer, it has to be expressed as an instance of Quadratic Unconstrained Binary Optimization (QUBO). In this work, we thus study whether systematically approximating QUBO representations of the MAX-3SAT problem can improve the solution quality when solved on contemporary quantum hardware, compared to using exact, non-approximated QUBO representations. For a MAX-3SAT instance consisting of a 3SAT formula with n variables and m clauses, we propose a method of systematically creating approximate QUBO representations of dimension (n x n), which is significantly smaller than the QUBO matrices of any exact, non-approximated MAX-3SAT QUBO transformation. In an empirical evaluation, we demonstrate that using our QUBO approximations for solving MAX-3SAT problems on D-Wave's quantum annealer Advantage_System6.4 can yield better results than using state-of-the-art exact QUBO transformations. Furthermore, we demonstrate that using naive QUBO approximation methods, based on removing values from exact (n+m)x(n+m)-dimensional QUBO representations of MAX-3SAT instances is ineffective.

Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well-known provided that the quantum channels are completely characterized. In this work, we consider the inverse problem, i.e., the estimation of channel parameters employing probes in which quantum coherence is used as a resource. Two paradigmatic bosonic Gaussian channels are treated, the thermal attenuator and the thermal amplifier. We also consider the degradation of the coherence due to a Markovian bath. The quantum Fisher information for each relevant parameter is computed and we observed that the rate of change of coherence concerning the channel parameter, rather than the amount of coherence, can produce a parameter estimation gain. Finally, we obtain a direct relation between the quantum Fisher information and the relative entropy or coherence, allowing in principle an experimental implementation based on the measurement of the covariance matrix of the probe system.

We introduce ExcitationSolve, a fast globally-informed gradient-free optimizer for physically-motivated ans\"atze constructed of excitation operators, a common choice in variational quantum eigensolvers. ExcitationSolve is to be classified as an extension of quantum-aware and hyperparameter-free optimizers such as Rotosolve, from parameterized unitaries with generators $G$ of the form $G^2=I$, e.g., rotations, to the more general class of $G^3=G$ exhibited by the physically-inspired excitation operators such as in the unitary coupled cluster approach. ExcitationSolve is capable of finding the global optimum along each variational parameter using the same quantum resources that gradient-based optimizers require for a single update step. We provide optimization strategies for both fixed- and adaptive variational ans\"atze, as well as a multi-parameter generalization for the simultaneous selection and optimization of multiple excitation operators. Finally, we demonstrate the utility of ExcitationSolve by conducting electronic ground state energy calculations of molecular systems and thereby outperforming state-of-the-art optimizers commonly employed in variational quantum algorithms. Across all tested molecules in their equilibrium geometry, ExcitationSolve remarkably reaches chemical accuracy in a single sweep over the parameters of a fixed ansatz. This sweep requires only the quantum circuit executions of one gradient descent step. In addition, ExcitationSolve achieves adaptive ans\"atze consisting of fewer operators than in the gradient-based adaptive approach, hence decreasing the circuit execution time., Comment: 45 pages, 10 figures

The performance of the Variational Quantum Eigensolver (VQE) is promising compared to other quantum algorithms, but also depends significantly on the appropriate design of the underlying quantum circuit. Recent research by Bowles, Ahmend \& Schuld, 2024 [1] raises questions about the effectiveness of entanglement in circuits for quantum machine learning algorithms. In our paper we want to address questions about the effectiveness of state preparation via Hadamard gates and entanglement via CNOT gates in the realm of quantum optimisation. We have constructed a total of eight different circuits, varying in implementation details, solving a total of 100 randomly generated MaxCut problems. Our results show no improvement with Hadamard gates applied at the beginning of the circuits. Furthermore, also entanglement shows no positive effect on the solution quality in our small scale experiments. In contrast, the investigated circuits that used entanglement generally showed lower, as well as deteriorating results when the number of circuit layers is increased. Based on our results, we hypothesise that entanglement can play a coordinating role, such that changes in individual parameters are distributed across multiple qubits in quantum circuits, but that this positive effect can quickly be overdosed and turned negative. The verification of this hypothesis represents a challenge for future research and can have a considerable influence on the development of new hybrid algorithms., Comment: 7 pages, 3 figures

The Quantum Approximate Optimization Algorithm (QAOA) is a prominent quantum algorithm designed to find approximate solutions to combinatorial optimization problems, which are challenging for classical computers. In the current era, where quantum hardware is constrained by noise and limited qubit availability, simulating the QAOA remains essential for research. However, existing state-of-the-art simulation frameworks suffer from long execution times or lack comprehensive functionality, usability, and versatility, often requiring users to implement essential features themselves. Additionally, these frameworks are primarily restricted to Python, limiting their use in safer and faster languages like Rust, which offer, e.g., advanced parallelization capabilities. In this paper, we develop a GPU accelerated QAOA simulation framework utilizing the NVIDIA CUDA toolkit. This framework offers a complete interface for QAOA simulations, enabling the calculation of (exact) expectation values, direct access to the statevector, fast sampling, and high-performance optimization methods using an advanced state-of-the-art gradient calculation technique. The framework is designed for use in Python and Rust, providing flexibility for integration into a wide range of applications, including those requiring fast algorithm implementations leveraging QAOA at its core. The new framework's performance is rigorously benchmarked on the MaxCut problem and compared against the current state-of-the-art general-purpose quantum circuit simulation frameworks Qiskit and Pennylane as well as the specialized QAOA simulation tool QOKit. Our evaluation shows that our approach outperforms the existing state-of-the-art solutions in terms of runtime up to multiple orders of magnitude. Our implementation is publicly available at https://github.com/JFLXB/cuaoa and Zenodo., Comment: 6 pages, 3 figures

Benchmarking the performance of quantum optimization algorithms is crucial for identifying utility for industry-relevant use cases. Benchmarking processes vary between optimization applications and depend on user-specified goals. The heuristic nature of quantum algorithms poses challenges, especially when comparing to classical counterparts. A key problem in existing benchmarking frameworks is the lack of equal effort in optimizing for the best quantum and, respectively, classical approaches. This paper presents a comprehensive set of guidelines comprising universal steps towards fair benchmarks. We discuss (1) application-specific algorithm choice, ensuring every solver is provided with the most fitting mathematical formulation of a problem; (2) the selection of benchmark data, including hard instances and real-world samples; (3) the choice of a suitable holistic figure of merit, like time-to-solution or solution quality within time constraints; and (4) equitable hyperparameter training to eliminate bias towards a particular method. The proposed guidelines are tested across three benchmarking scenarios, utilizing the Max-Cut (MC) and Travelling Salesperson Problem (TSP). The benchmarks employ classical mathematical algorithms, such as Branch-and-Cut (BNC) solvers, classical heuristics, Quantum Annealing (QA), and the Quantum Approximate Optimization Algorithm (QAOA).

In this project summary paper, we summarize the key results and use-cases explored in the German Federal Ministry of Education and Research (BMBF) funded project "Q-GRID" which aims to assess potential quantum utility optimization applications in the electrical grid. The project focuses on two layers of optimization problems relevant to decentralized energy generation and transmission as well as novel energy transportation/exchange methods such as Peer-2-Peer energy trading and microgrid formation. For select energy grid optimization problems, we demonstrate exponential classical optimizer runtime scaling even for small problem instances, and present initial findings that variational quantum algorithms such as QAOA and hybrid quantum annealing solvers may provide more favourable runtime scaling to obtain similar solution quality. These initial results suggest that quantum computing may be a key enabling technology in the future energy transition insofar that they may be able to solve business problems which are already challenging at small problem instance sizes., Comment: 12 pages. arXiv admin note: text overlap with arXiv:2309.05502

Analog quantum simulation allows for assessing static and dynamical properties of strongly correlated quantum systems to high precision. To perform simulations outside the reach of classical computers, accurate and reliable implementations of the anticipated Hamiltonians are required. To achieve those, characterization and benchmarking tools are a necessity. For digital quantum devices, randomized benchmarking can provide a benchmark on the average quality of the implementation of a gate set. In this work, we introduce a versatile framework for randomized analog benchmarking of bosonic and fermionic quantum devices implementing particle number preserving dynamics. The scheme makes use of the restricted operations which are native to analog simulators and other continuous variable systems. Importantly, like randomized benchmarking, it is robust against state preparation and measurement errors. We discuss the scheme's efficiency, derive theoretical performance guarantees and showcase the protocol with numerical examples., Comment: Main text 5 pages and 3 figures, references and supplementary material 16 pages and 5 figures

We propose an optimization method for rate-adaptive CV-QKD systems, improving the SKR by up to 15%. A single information reconciliation setup can generate secret keys up to a distance of 112 km. This enables a unified reconciliation system, thereby facilitating the commercialization of CV-QKD.

A quantum particle evolving by Schr\"odinger's equation in discrete space constitutes a continuous-time quantum walk on a graph of vertices and edges. When a vertex is marked by an oracle, the quantum walk effects a quantum search algorithm. Previous investigations of this quantum search algorithm on graphs with cliques have shown that the edges between the cliques can be weighted to enhance the movement of probability between the cliques to reach the marked vertex. In this paper, we explore the most restrictive form of this by analyzing search on a weighted barbell graph that consists of two cliques of the same size joined by a single weighted edge/bridge. This graph is generally irregular, so quantum walks governed by the graph Laplacian or by the adjacency matrix can differ. We show that the Laplacian quantum walk's behavior does not change, no matter the weight of the bridge, and so the single bridge is too restrictive to affect the walk. Similarly, the adjacency quantum walk's behavior is unchanged for most weights, but when the weight equals the size of a clique, the probability does collect at the clique containing the marked vertex, and utilizing a two-stage algorithm with different weights for each stage, the success probability is boosted from 0.5 to 0.996, independent of the size of the barbell graph., Comment: 16 pages, 10 figures

A central challenge in quantum machine learning is the design and training of parameterized quantum circuits (PQCs). Much like in deep learning, vanishing gradients pose significant obstacles to the trainability of PQCs, arising from various sources. One such source is the presence of non-local loss functions, which require the measurement of a large subset of qubits involved. To address this issue and facilitate parameter training for quantum applications using global loss functions, we propose Sequential Hamiltonian Assembly (SHA). SHA iteratively approximates the loss by assembling it from local components. To further demonstrate the feasibility of our approach, we extend our previous case study by introducing a new partitioning strategy, a new merger between QAOA and SHA, and an evaluation of SHA onto the Max-Cut optimization problem. Simulation results show that SHA outperforms conventional parameter training by 43.89% and the empirical state-of-the-art, Layer-VQE by 29.08% in the mean accuracy for Max-Cut. This paves the way for locality-aware learning techniques, mitigating vanishing gradients for a large class of practically relevant problems., Comment: This is an extended version of our previously published article arXiv:2312.05552, additionally providing a new partitioning strategy, a new merger between QAOA and SHA, and an evaluation of SHA in the Max-Cut optimization problem