Quantum Physics (quant-ph)

Abstract: Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable matrix functions in these techniques is difficult for large-scale quantum systems: there is no analytical result other than trivial cases as far as we know and we often suffer also from numerical instability. We propose recursive QET or QSVT (r-QET or r-QSVT), in which we can execute complicated matrix functions by recursively organizing block-encoding by low-degree QET or QSVT. Owing to the simplicity of recursive relations, it works only with a few parameters with exactly determining the parameters, while its iteration results in complicated matrix functions. In particular, by exploiting the recursive relation of Newton iteration, we construct the matrix sign function, which can be applied for eigenstate filtering for example, in a tractable way. We show that an analytically-obtained parameter set composed of only $8$ different values is sufficient for executing QET of the matrix sign function with an arbitrarily small error $\varepsilon$. Our protocol will serve as an alternative protocol for constructing QET or QSVT for some useful matrix functions without numerical instability.

Abstract: We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. Starting from the microscopic description of the latter in terms of two tunneling BCS models in the strong-coupling quasi-spin formulation, we derive the Hamiltonian governing the quantum behavior of the circuit in the limit of a large number $N$ of quasi-spins. Our approach relies on the identification of suitable quantum fluctuations, i.e. of collective quasi-spin operators, which account for the presence of fluctuation operators in the superconducting phase that retain a quantum character in spite of the large-$N$ limit. We show indeed that these collective quantum fluctuations generate the Heisenberg algebra on the circle and that their dynamics reproduces the one of the quantized charge-qubit, without the need of a phenomenological ``third quantization'' of a semiclassically inspired model. As a byproduct of our derivation, we explicitly obtain the temperature dependence of the junction critical Josephson current in the strong coupling regime, a result which is not directly accessible using standard approximation techniques.

Abstract: The barren plateau phenomenon is one of the main obstacles to implementing variational quantum algorithms in the current generation of quantum processors. Here, we introduce a method capable of avoiding the barren plateau phenomenon in the variational determination of the geometric measure of entanglement for a large number of qubits. The method is based on measuring compatible two-qubit local functions whose optimization allows for achieving a well-suited initial condition, from which a global function can be further optimized without encountering a barren plateau. We analytically demonstrate that the local functions can be efficiently estimated and optimized. Numerical simulations up to 18-qubit GHZ and W states demonstrate that the method converges to the exact value. In particular, the method allows for escaping from barren plateaus induced by hardware noise or global functions defined on high-dimensional systems. Numerical simulations with noise are in agreement with experiments carried out on IBM's quantum processors for 7 qubits.

Abstract: In this paper, we study static bistability and mechanical cooling of a dissipative optomechanical cavity filled with a Kerr medium. The system exhibits optical bistability for a wide input-power range with the power threshold being greatly reduced, in contrast to the case of purely dissipative coupling. At the bistable regime, the membrane can be effectively cooled down to a few millikelvin from the room temperature under the unresolved sideband condition, where the effective mechanical temperature is a nonmonotonic function of intracavity intensity and reaches its minimum near the turning point of the upper stable branch. When the system is in the cryogenics environment, the effective mechanical temperature at the bistable regime shows a similar feature as in the room temperature case, but the optimal cooling appears at the monostable regime and approaches the mechanical ground state. Our results are of interest for further understanding bistable optomechanical systems, which have many applications in nonclassical state preparations and quantum information processing.

Abstract: We propose and analyze a method for improving quantum chemical energy calculations on a quantum computer impaired by decoherence and shot noise. The error mitigation approach relies on the fact that the one- and two-particle reduced density matrices (1- and 2-RDM) of a chemical system need to obey so-called N-representability constraints. We post-process the result of an RDM measurement by projecting it into the subspace where certain N-representability conditions are fulfilled. Furthermore, we utilize that such constraints also hold in the hole and particle-hole sector and perform projections in these sectors as well. We expand earlier work by conducting a careful analysis of the method's performance in the context of quantum computing. Specifically, we consider typical decoherence channels (dephasing, damping, and depolarizing noise) as well as shot noise due to a finite number of projective measurements. We provide analytical considerations and examine numerically three example systems, \ch{H2}, \ch{LiH}, and \ch{BeH2}. From these investigations, we derive our own practical yet effective method to best employ the various projection options. Our results show the approach to significantly lower energy errors and measurement variances of (simulated) quantum computations.

Abstract: The topological state of matter is a potential resource to realize long-term fault-tolerant quantum computers beyond the near-term noisy intermediate-scale quantum devices. To achieve the realization, we need a deep understanding of topological behaviors in real quantum computers. However, quantum-circuit algorithms to analyze topological properties have still been insufficient. Here we propose three quantum-circuit algorithms, (i) to find the ground state in the selected parity subspace, (ii) to determine the many-body topological invariant, and (iii) to visualize the zero-energy edge mode. To demonstrate these algorithms, we adopt the interacting Kitaev chain as a typical model of many-body topological superconductors in one dimension. The algorithms are applicable to not only one-dimensional topological superconductors but other topological states including higher-dimensional systems.

Abstract: The Duan-Lukin-Cirac-Zoller (DLCZ) scheme is a potential method to establish remote entanglements and realize large-scale quantum networks. Here we propose a DLCZ-like scheme based on the noiseless photon echo in rare-earth ion-doped crystals. Correlated photon pairs with a controllable delay can be created by the direct optical rephasing. Theoretical analysis indicates that the protocol is efficient in the low-optical-depth regime. This protocol could be feasibly implemented to establish long-lived quantum correlations between a photon and a spin-wave excitation in rare-earth ion-doped crystals.

Abstract: Interfacing the different building blocks of a future large scale quantum network will demand efficient and noiseless frequency conversion of quantum light. Nitrogen-vacancy (NV) centers in diamond are a leading candidate to form the nodes of such a network. However, the performance of a suitable converter remains a bottleneck, with existing demonstrations severely limited by parasitic noise arising at the target telecom wavelength. Here, we demonstrate a new platform for efficient low-noise quantum frequency conversion based on a monolithic bulk ppKTP cavity and show its suitability for the conversion of 637 nm single photons from NV centers in diamond to telecommunication wavelengths. By resonantly enhancing the power of an off-the-shelf pump laser, we achieve an internal conversion efficiency of $(72.3\pm 0.4)\%$ while generating only $(110\pm 4) \mbox{ kHz/nm}$ noise at the target wavelength without the need for any active stabilization. This constitutes a 5-fold improvement in noise over existing state-of-the-art single-step converters at this wavelengths. We verify the almost ideal preservation of non-classical correlations by converting photons from a spontaneous parametric down-conversion source and moreover show the preservation of time-energy entanglement via Franson interferometry.

Abstract: The matrix rank and its positive versions are robust for small approximations, i.e. they do not decrease under small perturbations. In contrast, the multipartite tensor rank can collapse for arbitrarily small errors, i.e. there may be a gap between rank and border rank, leading to instabilities in the optimization over sets with fixed tensor rank. Can multipartite positive ranks also collapse for small perturbations? In this work, we prove that multipartite positive and invariant tensor decompositions exhibit gaps between rank and border rank, including tensor rank purifications and cyclic separable decompositions. We also prove a correspondence between positive decompositions and membership in certain sets of multipartite probability distributions, and leverage the gaps between rank and border rank to prove that these correlation sets are not closed. It follows that testing membership of probability distributions arising from resources like translational invariant Matrix Product States is impossible in finite time. Overall, this work sheds light on the instability of ranks and the unique behavior of bipartite systems.

Abstract: Strong long-distance spin-spin coupling is desperately demanded for solid-state quantum information processing, but it is still challenged. Here, we propose a hybrid quantum system, consisting of a coplanar waveguide (CPW) resonator weakly coupled to a single nitrogen-vacancy spin in diamond and a yttrium-iron-garnet (YIG) nanosphere holding Kerr magnons, to realize strong long-distance spin-spin coupling. With a strong driving field on magnons, the Kerr effect can squeeze magnons, and thus exponentially enhance the coupling between the CPW resonator and the sequeezed magnons, which produces two cavity-magnon polaritons, i.e., the high-frequency polariton (HP) and low-frequency polariton (LP). When the enhanced cavity-magnon coupling approaches to the critical value, the spin is fully decoupled from the HP, while the coupling between the spin and the LP is significantly improved. In the dispersive regime, a strong spin-spin coupling is achieved with accessible parameters, and the coupling distance can be up to $\sim$cm. Our proposal provides a promising way to manipulate remote solid spins and perform quantum information processing in weakly coupled hybrid systems.

Abstract: The quantum no-broadcasting theorem has an analogue in modal quantum theory (MQT), a toy model based on finite fields. The failure of broadcasting in MQT is related to the failure of distributivity of the lattice of subspaces of the state space.

Abstract: Reinforcement learning is a growing field in AI with a lot of potential. Intelligent behavior is learned automatically through trial and error in interaction with the environment. However, this learning process is often costly. Using variational quantum circuits as function approximators can reduce this cost. In order to implement this, we propose the quantum natural policy gradient (QNPG) algorithm -- a second-order gradient-based routine that takes advantage of an efficient approximation of the quantum Fisher information matrix. We experimentally demonstrate that QNPG outperforms first-order based training on Contextual Bandits environments regarding convergence speed and stability and thereby reduces the sample complexity. Furthermore, we provide evidence for the practical feasibility of our approach by training on a 12-qubit hardware device.

Abstract: Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrix-product-states (MPS) calculations. Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

Abstract: We demonstrate strong dispersive coupling between a fluxonium superconducting qubit and a 690 megahertz mechanical oscillator, extending the reach of circuit quantum acousto-dynamics (cQAD) experiments into a new range of frequencies. We have engineered a qubit-phonon coupling rate of $g\approx2\pi\times14~\text{MHz}$, and achieved a dispersive interaction that exceeds the decoherence rates of both systems while the qubit and mechanics are highly nonresonant ($\Delta/g\gtrsim10$). Leveraging this strong coupling, we perform phonon number-resolved measurements of the mechanical resonator and investigate its dissipation and dephasing properties. Our results demonstrate the potential for fluxonium-based hybrid quantum systems, and a path for developing new quantum sensing and information processing schemes with phonons at frequencies below 700 MHz to significantly expand the toolbox of cQAD.

Abstract: We demonstrate strong coupling of gigahertz-frequency nanomechanical resonators to a frequency-tunable superconducting microwave resonator via a galvanically bonded flip-chip method. By tuning the microwave resonator with an external magnetic field, we observe a series of hybridized microwave-mechanical modes and report coupling strengths of $\sim {15}~\text{MHz}$ at cryogenic temperatures. The demonstrated multi-chip approach provides flexible rapid characterization and simplified fabrication, and could potentially enable coupling between a variety of quantum systems. Our work represents a step towards a plug-and-play architecture for building more complex hybrid quantum systems.

Abstract: Taking accurate measurements of the temperature of quantum systems is a challenging task. The mathematical peculiarities of quantum information make it virtually impossible to measure with infinite precision. In the present letter, we introduce a generalize thermal state, which is conditioned on the pointer states of the available measurement apparatus. We show that this conditional thermal state outperforms the Gibbs state in quantum thermometry. The origin for the enhanced precision can be sought in its asymmetry quantified by the Wigner-Yanase-Dyson skew information. This additional resource is further clarified in a fully resource-theoretic analysis, and we show that there is a Gibbs-preserving map to convert a target state into the conditional thermal state. Finally, we relate the quantum J-divergence between the conditional thermal state and the same target state to quantum heat.

Abstract: In this work, we present a new method, based on Feynman-like diagrams, for computing the effective Hamiltonian of driven nonlinear oscillators. The pictorial structure associated with each diagram corresponds directly to a Hamiltonian term, the prefactor of which involves a simple counting of topologically equivalent diagrams. We also leverage the algorithmic simplicity of our scheme in a readily available computer program that generates the effective Hamiltonian to arbitrary order. At the heart of our diagrammatic method is a novel canonical perturbation expansion developed in phase space to capture the quantum nonlinear dynamics. A merit of this expansion is that it reduces to classical harmonic balance in the limit of $\hbar\rightarrow0$. Our method establishes the foundation of the dynamic control of quantum systems with the precision needed for future quantum machines. We demonstrate its value by treating five examples from the field of superconducting circuits. These examples involve an experimental proposal for the Hamiltonian stabilization of a three-legged Schr\"odinger cat, modeling of energy renormalization phenomena in superconducting circuits experiments, a comprehensive characterization of multiphoton resonances in a driven transmon, a proposal for an novel inductively shunted transmon circuit, and a characterization of classical ultra-subharmonic bifurcation in driven oscillators. Lastly, we benchmark the performance of our method by comparing it with experimental data and exact Floquet numerical diagonalization.