Quantum Physics (quant-ph)

Abstract: Quantum computers are noisy at present in the absence of error correction and fault tolerance. Interim methods such as error suppression and mitigation find wide applicability. Another method, which is independent of other error suppression and mitigation, and can be applied in conjunction with them to further lower the noise in the system, is circuit cutting. In this paper, we propose a scheduler that finds the optimum schedule for the subcircuits obtained by circuit cutting on the available set of hardware to (i) maximize the overall fidelity, and (ii) ensure that the predefined maximum execution time for each hardware is not exceeded. The fidelity obtained by this method on various benchmark circuits is significantly better than that of the uncut circuit executed on the least noisy device. The average increase in the fidelity obtained by our method are respectively ~12.3% and ~21% for 10-qubit benchmark circuits without and with measurement error mitigation, even when each hardware was allowed the minimum possible execution time. This noise and time optimized distributed scheduler is an initial step towards providing the optimal performance in the current scenario where the users may have limited access to quantum hardware.

Abstract: Position error is treated as the leading obstacle that prevents Rydberg antiblockade gates from being experimentally realizable, because of the inevitable fluctuations in the relative motion between two atoms invalidating the antiblockade condition. In this work we report progress towards a high-tolerance antiblockade-based Rydberg SWAP gate enabled by the use of modified antiblockade condition combined with carefully-optimized laser pulses. Depending on the optimization of diverse pulse shapes our protocol shows that the time-spent in the double Rydberg state can be shortened by a factor of > 70%, which significantly reduces the position error. Moreover, we benchmark the robustness of the gate via taking account of the technical noises, such as the Doppler dephasing due to atomic thermal motion, the fluctuations in laser intensity and laser phase and the intensity inhomogeneity. As compared with other existing antiblockade-gate schemes the predicted gate fidelity is able to maintain at above 0.91 after a very conservative estimation of various experimental imperfections,ns, especially considered for realistic interaction deviation of $\delta$V /V $\approx$ 5.92% at T $\sim$ 20$\mu$K. Our work paves the way to the experimental demonstration of Rydberg antiblockade gates in the near future.

Abstract: A shortcut to adiabatic scheme is proposed for preparing a massive object in a macroscopic spatial superposition state. In this scheme we propose to employ counterdiabatic driving to maintain the system in the groundstate of its instantaneous Hamiltonian while the trap potential is tuned from a parabola to a double well. This, in turn, is performed by properly ramping a control parameter. We show that a few counterdiabatic drives are enough for most practical cases. A hybrid electromechanical setup in superconducting circuits is proposed for the implementation. The efficiency of our scheme is benchmarked by numerically solving the system dynamics in the presence of noises and imperfections. The results show that very high fidelity cat states with distinguishable spatial separations can be prepared with our protocol. Furthermore, the protocol is robust against noises and imperfections. We also discuss a method for verifying the final state via spectroscopy of a coupled circuit electrodynamical cavity mode.

Abstract: We study joint measurability of quantum observables in open systems governed by a master equation of Lindblad form. We briefly review the historical perspective of open systems and conceptual aspects of quantum measurements, focusing subsequently on describing emergent classicality under quantum decoherence. While decoherence in quantum states has been studied extensively in the past, the measurement side is much less understood - here we present and extend some recent results on this topic.

Abstract: The weak measurement (WM) and quantum measurement reversal (QMR) are crucial in protecting the collapse of quantum states. Recently, the idea of WM and QMR has been used to protect and enhance quantum correlations and universal quantum teleportation (UQT) protocol. Here, we study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using discrete Wigner functions (DWFs) with (without) WM and QMR. To take into account the effect of a noisy environment, we evolve the states via non-Markovian amplitude damping (AD) and random telegraph noise (RTN) quantum channels. To benchmark the performance of negative quantum states, we compare our results with the two-qubit maximally entangled Bell state. Interestingly, we observe that some of the negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.

Abstract: Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar\'e) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of $E(1,3)$-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of \emph{$E(1,3)$-invariant basic observables}, viz. the 4-momentum and the Pauli--Lubanski spin vectors of the systems. An analogous expression for \emph{$E(1,3)$-invariant elementary quantum mechanical systems} in terms of the \emph{basic quantum observables} in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the \emph{metric structure} of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum systems.

Abstract: For a linear non-Hermitian system, I demonstrate that a Hamiltonian can be constructed such that the non-Hermitian equations can be expressed exactly in the form of Hamilton's canonical equations. This is first shown for discrete systems and then extended to continuous systems. With this Hamiltonian formulation, I am able to identify a conserved charge by applying Noether's theorem and recognize adiabatic invariants. When applied to Hermitian systems, all the results reduce to the familiar ones associated with the Schr\"odinger equation.

Abstract: Superconducting quantum circuits are a natural platform for quantum simulations of a wide variety of important lattice models describing topological phenomena, spanning condensed matter and high-energy physics. One such model is the bosonic analogue of the well-known fermionic Kitaev chain, a 1D tight-binding model with both nearest-neighbor hopping and pairing terms. Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of striking features associated with non-Hermitian systems, including chiral transport and a dramatic sensitivity to boundary conditions known as the non-Hermitian skin effect. Here, using a multimode superconducting parametric cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The lattice sites are mapped to frequency modes of the cavity, and the $\textit{in situ}$ tunable complex hopping and pairing terms are created by parametric pumping at the mode-difference and mode-sum frequencies, respectively. We experimentally demonstrate important precursors of nontrivial topology and the non-Hermitian skin effect in the bosonic Kitaev chain, including chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. Our experiment is an important first step towards exploring genuine many-body non-Hermitian quantum dynamics.

Abstract: Steering resources, central for quantum advantages in one-sided device-independent quantum information tasks, can be enhanced via local filters. Recently, reversible steering conversion under local filters has been fully characterised. Here, we solve the problem in the irreversible scenario, which leads to a complete understanding of stochastic steering distillation. This result also provides an operational interpretation of the max-relative entropy as the optimal filter success probability. We further show that all steering measures can be used to quantify measurement incompatibility in certain stochastic steering distillation scenarios. Finally, for a broad class of steering robustness measures, we show that their maximally achievable values in stochastic steering distillation are always upper bounded by different types of incompatibility robustness measures. Hence, measurement incompatibility sets the fundamental limitations for stochastic steering distillation.

Abstract: In this paper we study the dynamics of an ensemble of nitrogen-vacancy centers in diamond when its photoluminescence is detected by means of a widefield imaging system. We develop a seven-level model and use it to simulate the widefield detection of nitrogen-vacancy centers Rabi oscillations. The simulation results are compared with experimental measurements showing a good agreement. In particular, we use the model to explain the asymmetric shape of the detected Rabi oscillations due to an incomplete repolarization of the nitrogen-vacancy center during the pulse sequence implemented for the detection of Rabi oscillations.

Abstract: Keldysh field theory, based on adiabatic assumptions, serves as an widely used framework for addressing nonequilibrium many-body systems. Nonetheless, the validity of such adiabatic assumptions when addressing interacting Gibbs states remains a topic of contention. We use the knowledge of work statistics developed in nonequilibrium thermodynamics to study this problem. Consequently, we deduce a universal theorem delineating the characteristics of evolutions that transition an initial Gibbs state to another. Based on this theorem, we analytically ascertain that adiabatic evolutions fail to transition a non-interacting Gibbs state to its interacting counterpart. However, this adiabatic approach remains a superior approximation relative to its non-adiabatic counterpart. Numerics verifying our theory and predictions are also provided. Furthermore, our findings render insights into the preparation of Gibbs states within the domain of quantum computation.

Abstract: Eisenbud-Wigner-Smith delay and the Larmor time give different estimates for the duration of a quantum scattering event. The difference is most pronounced in the case where de-Broglie wavelength is large compared to the size of the scatterer. We use the methods of quantum measurement theory to analyse both approaches, and to decide which one of them, if any, describes the duration a particle spends in the region which contains the scattering potential. The cases of transmission, reflection and three-dimensional elastic scattering are discussed in some detail.

Abstract: Quantum oscillators with nonlinear driving and dissipative terms have gained significant attention due to their ability to stabilize cat-states for universal quantum computation. Recently, superconducting circuits have been employed to realize such long-lived qubits stored in coherent states. We present a generalization of these oscillators, which are not limited to coherent states, in the presence of different nonlinearities in driving and dissipation, exploring different degrees. Specifically, we present an extensive analysis of the asymptotic dynamical features and of the storage of squeezed states. We demonstrate that coherent superpositions of squeezed states are achievable in the presence of a strong symmetry, thereby allowing for the storage of squeezed cat-states. In the weak symmetry regime, accounting for linear dissipation, we investigate the potential application of these nonlinear driven-dissipative resonators for quantum computing and quantum associative memory and analyze the impact of squeezing on their performance.

Abstract: Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.

Abstract: The set of correlations between measurement outcomes observed by separated parties in a Bell test is of vital importance in Device-Independent (DI) information processing. However, characterising this set of quantum correlations is a hard problem, with a number of open questions. Here, we present families of quantum Bell inequalities that approximate this set in Bell scenarios with an arbitrary number of players, settings and outcomes, and study their applications to device-independent information processing. Firstly, it is known that quantum correlations on the non-signaling boundary are of crucial importance in the task of DI randomness extraction from weak sources. In the Bell scenario of two players with two $k$-outcome measurements, we derive inequalities that show a separation of the quantum boundary from classes of non-local faces of the non-signaling polytope of dimension $\leq 4k-4$, extending previous results from nonlocality distillation and the collapse of communication complexity. Secondly, in the scenario of two players with $m$ binary measurements, we consider a non-trivial portion of the quantum boundary that generalizes the boundary that for $m=2$ discovered by Tsirelson-Landau-Masanes. We prove that all points on this generalized boundary serve to self-test the two-qubit singlet and the corresponding $m$ measurements. In this scenario, we also derive a low-dimensional region of the quantum boundary that coincides with the boundary of the set of classical correlations. Finally, we conclude our investigation of the quantum boundary by answering the open quantum whether there exists a bipartite $(3,3)$-inputs, $(2,3)$-outputs pseudo-telepathy game in the negative.

Abstract: In the near-term noisy intermediate-scale quantum (NISQ) era, high noise will significantly reduce the fidelity of quantum computing. Besides, the noise on quantum devices is not stable. This leads to a challenging problem: At run-time, is there a way to efficiently achieve a consistent high-fidelity quantum system on unstable devices? To study this problem, we take quantum learning (a.k.a., variational quantum algorithm) as a vehicle, such as combinatorial optimization and machine learning. A straightforward approach is to optimize a Circuit with a parameter-shift approach on the target quantum device before using it; however, the optimization has an extremely high time cost, which is not practical at run-time. To address the pressing issue, in this paper, we proposed a novel quantum pulse-based noise adaptation framework, namely QuPAD. In the proposed framework, first, we identify that the CNOT gate is the fidelity bottleneck of the conventional VQC, and we employ a more robust parameterized multi-quit gate (i.e., Rzx gate) to replace the CNOT gate. Second, by benchmarking the Rzx gate with different parameters, we build a fitting function for each coupling qubit pair, such that the deviation between the theoretic output of the Rzx gate and its on-device output under a given pulse amplitude and duration can be efficiently predicted. On top of this, an evolutionary algorithm is devised to identify the pulse amplitude and duration of each Rzx gate (i.e., calibration) and find the quantum circuits with high fidelity. Experiments show that the runtime on quantum devices of QuPAD with 8-10 qubits is less than 15 minutes, which is up to 270x faster than the parameter-shift approach. In addition, compared to the vanilla VQC as a baseline, QuPAD can achieve 59.33% accuracy gain on a classification task, and average 66.34% closer to ground state energy for molecular simulation.

Abstract: We employ the recently developed technique of null bootstrap to obtain the energy eigenvalues and the ladder operators of the sextic anharmonic oscillator up to second order in the coupling. We confirm our results by deriving the same from traditional perturbation theory. We further extend the analysis to non-Hermitian PT symmetric Hamiltonians, focusing on the shifted harmonic oscillator and the cubic theory.