Quantum Physics (quant-ph)

Abstract: We conduct a systematic study of quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives, since they are widely-used components in quantum algorithms and also have attracted much experimental interest in recent years. Herein, we establish a circuit-polynomial correspondence to characterize the functionality of quantum circuits over the MCZR gate set with continuous parameters. An analytic method for exactly synthesizing such quantum circuit to implement any given diagonal unitary matrix with an optimal gate count is proposed, which also enables the circuit depth optimal for specific cases with pairs of complementary gates. Furthermore, we present a gate-exchange strategy together with a flexible iterative algorithm for effectively optimizing the depth of any MCZR circuit, which can also be applied to quantum circuits over any other commuting gate set. Besides the theoretical analysis, the practical performances of our circuit synthesis and optimization techniques are further evaluated by numerical experiments on two typical examples in quantum computing, including diagonal Hermitian operators and Quantum Approximate Optimization Algorithm (QAOA) circuits with tens of qubits, which can demonstrate a reduction in circuit depth by 33.40\% and 15.55\% on average over relevant prior works, respectively. Therefore, our methods and results provide a pathway for implementing quantum circuits and algorithms on recently developed devices.

Abstract: Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward approach based on pre-training parameterized quantum circuits, and show how they can be transformed into their conditional variant, making them usable as a subroutine in an AE algorithm. To identify a suitable circuit, we propose a genetic optimization approach that combines variable ansatzes and data encoding. We apply our algorithm to the problem of pricing financial derivatives. At the expense of a costly pre-training process, this results in a quantum circuit implementing the derivatives' payoff function more efficiently than previously existing quantum algorithms. In particular, we compare the performance for European vanilla and basket options.

Abstract: In this paper, we propose a generic quantum circuit resynthesis approach for compilation. We use an intermediate representation consisting of Paulistrings over {Z, I} and {X, I} called a ``mixed ZX-phase polynomial``. From this universal representation, we generate a completely new circuit such that all multi-qubit gates (CNOTs) are satisfying a given quantum architecture. Moreover, we attempt to minimize the amount of generated gates. The proposed algorithms generate fewer CNOTs than similar previous methods on different connectivity graphs ranging from 5-20 qubits. In most cases, the CNOT counts are also lower than Qiskit's. For large circuits, containing >= 100 Paulistrings, our proposed algorithms even generate fewer CNOTs than the TKET compiler. Additionally, we give insight into the trade-off between compilation time and final CNOT count.

Abstract: This paper provides an algebraic reconstruction of Einstein's own argument for the incompleteness of quantum mechanics -- the one that he thought did not make it into the EPR paper -- in order to clarify the assumptions that underlie an understanding of Einstein completeness as categoricity, the sense in which it is a type of descriptive completeness, and some of the various ways in which it has been more often misconstrued.

Abstract: Many-body localization (MBL) can occur when strong disorders prevent an interacting system from thermalization. To study the dynamics of such systems, it is typically necessary to perform an ensemble average over many different disorder configurations. Previous works have utilized an algorithm in which different disorder profiles are mapped into a quantum ancilla. By preparing the ancilla in a quantum superposition state, quantum parallelism can be harnessed to obtain the ensemble average in a single computation run. In this work, we modify this algorithm by performing a measurement on the ancilla. This enables the determination of conditional dynamics not only by the ensemble average but also by the quantum interference effect. Using a phenomenological analysis based on local integrals of motion, we demonstrate that this protocol can lead to an enhancement of the dephasing effect and a boost in the entanglement growth for systems in the deep MBL phase. We also present numerical simulations of the random XXZ model where this enhancement is also present in a smaller disorder strength, beyond the deep MBL regime.

Abstract: Remote state preparation enables one to prepare and manipulate quantum state non-locally. As an essential quantum resource, optical cat state is usually prepared locally by subtracting photons from a squeezed vacuum state. For remote quantum information processing, it is essential to prepare and manipulate optical cat states remotely based on Gaussian entanglement, which remains a challenge. Here, we present experimental preparation of optical cat states based on a remotely distributed two-mode Gaussian entangled state in a lossy channel. By performing photon subtraction and homodyne projective measurement at Alice's station, an optical cat state is prepared remotely at Bob's station. Furthermore, the prepared cat state is rotated by changing Alice's measurement basis of homodyne detection, which demonstrates the remote manipulation of it. By distributing two modes of the two-mode Gaussian entangled state in lossy channels, we demonstrate that the remotely prepared cat state can tolerate much more loss in Alice's channel than that in Bob's channel. We also show that cat states with amplitudes larger than 2 can be prepared by increasing the squeezing level and subtracting photon numbers. Our results make a crucial step toward remote hybrid quantum information processing involving discrete- and continuous-variable techniques.

Abstract: We propose an efficient nonlinear readout scheme for entangled non-Gaussian spin states (ENGSs) based on the intrinsic quasi-cyclic dynamics of interacting spin-1/2 systems. We focus on two well-known spin models of twist-and-turn (TNT) and two-axis-counter-twisting (TACT), where ENGS can be generated by spin dynamics starting from unstable fixed points. In the TNT model, non-Gaussian probe state evolves directly back to the vicinity of initial state during the subsequent time-forward evolution for path recombining, accompanied by quantum magnification of encoded signal and refocusing of the associated quantum noise. Based on low-order moment measurement, we find the optimal metrological gain nearly saturates the quantum Cramer-Rao bound (QCRB) and follows the Heisenberg scaling. For the TACT case, the QCRB can also be nearly approached when the state converges to either of the two unstable fixed points, respectively corresponding to the initial state or its orthogonal coherent state. The latter case goes beyond previous studies where tracing back to or crossing the initial states is mostly considered. The present protocol does not require time-reversal as in typical nonlinear interferometries, and it also avoids complicated measurement of nonlinear observables or full probability distributions. The operational approach we discuss presents a practical way for realizing high-precision and detection-noise-robust quantum metrology with ENGS.

Abstract: We propose a general scheme to generate entanglement encoded in the photon number basis, via a sequential resonant two-photon excitation of a three-level system. We apply it to the specific case of a quantum dot three-level system, which can emit a photon pair through a biexciton-exciton cascade. The state generated in our scheme constitutes a tool for secure communication, as the multipartite correlations present in the produced state may provide an enhanced rate of secret communication with respect to a perfect GHZ state.

Abstract: Is quantum localization preserved under the effect of interactions that make a system non-integrable and completely chaotic? This work attempts to answer this question through a detailed study of the momentum-coupled, two-body linear kicked rotor model. It was recently shown that dynamical many-body localization exists in an integrable model of spatially interacting linear kicked rotors. Later, such localized phases in a non-integrable model -- coupled relativistic kicked rotors -- were also shown to exist. However, the presence of dynamical localization remains an open question in an interacting system that is far from the integrable limit and hence is completely chaotic. In this work, we show that chaos can be induced in the integrable linear kicked rotor model through interactions between the momenta of rotors. An approximate estimate of its Lyapunov exponent is obtained. Further, the quantum dynamics of this chaotic model, upon variation of kicking and interaction strengths, is shown to exhibit a variety of phases -- classically induced localization, dynamical localization, subdiffusive and diffusive phases. We also discuss this perspective from entanglement production in this system. By defining an effective Hilbert space dimension, the entanglement growth rate can be understood using appropriate random matrix averages.

Abstract: A quantum internet holds promise for accomplishing distributed quantum sensing and large-scale quantum computer networks, as well as quantum communication among arbitrary clients all over the globe. The main building block is efficient distribution of entanglement, entangled bits (ebits), across quantum networks. This could be achieved by aggregating quantum repeater protocols. However, the existing protocol is not practical as it requires point-to-point entanglement generation, the first step of the protocol, not only to suppress the error, depending on the whole size of the networks, but also to be run more than necessary. Here we present a practical recipe on how to aggregate quantum networks in order to present ebits to clients with minimum cost. This is combined with a conception of concatenation to enable arbitrary clients to have arbitrary long-distance communication with fixed error across quantum networks, regardless of the overall size. Our recipe forms the basis of designing a quantum internet protocol to control a self-organizing large-scale quantum network.

Abstract: Active states, from which work can be extracted by time-dependent perturbations, are an important resource for quantum thermodynamics in the absence of heat baths. Here we characterize this resource, establishing a resource theory that captures the operational scenario where an experimenter manipulates a quantum system by means of energy-preserving operations and resets to non-active states. Our resource theory comes with simple conditions for state convertibility and an experimentally accessible resource quantifier that determines the maximum advantage of active states in the task of producing approximations of the maximally coherent state by means of energy-preserving quantum operations.

Abstract: Quantum computing can be used to speed up the simulation time (more precisely, the number of queries of the algorithm) for physical systems; one such promising approach is the Hamiltonian simulation (HS) algorithm. Recently, it was proven that the quantum singular value transformation (QSVT) achieves the minimum simulation time for HS. An important subroutine of the QSVT-based HS algorithm is the amplitude amplification operation, which can be realized via the oblivious amplitude amplification or the fixed-point amplitude amplification in the QSVT framework. In this work, we execute a detailed analysis of the error and number of queries of the QSVT-based HS and show that the oblivious method is better than the fixed-point one in the sense of simulation time for a given error tolerance. Based on this finding, we apply the QSVT-based HS to the one-dimensional linearized Vlasov-Poisson equation and demonstrate that the linear Landau damping can be successfully simulated.

Abstract: We carry out the first investigation of the properties of spherical Wigner negativity over unitary orbits of mixed spin states, and completely characterize, in all finite dimensions, the set of absolutely Wigner-positive (AWP) states. Employing the Birkhoff-von Neumann theorem on doubly stochastic matrices, we describe this characterization via a set of linear eigenvalue constraints, which together define a polytope in the simplex of mixed spin-j states centred on the maximally mixed state. Such constraints naturally arise from the underlying structure of the SU(2)-covariant Wigner function. In each dimension, a Hilbert-Schmidt ball representing a tight, purity-based AWP sufficiency criterion is exactly determined, while another ball representing AWP necessity is conjectured. Comparisons are made to absolute symmetric state separability and spherical Glauber-Sudarshan positivity, with additional details given for low spin quantum numbers.

Abstract: Let us consider a situation where two information brokers, whose currency is, of course, information, need to reciprocally exchange information. The two brokers, being somewhat distrustful, would like a third, mutually trusted, entity to be involved in the exchange process so as to guarantee the successful completion of the transaction, and also verify that it indeed took place. Can this be done in such a way that both brokers receive their information simultaneously and securely, and without the trusted intermediary ending up knowing the exchanged information? This work presents and rigorously analyzes a new quantum entanglement-based protocol that provides a solution to the above problem. The proposed protocol is aptly named entanglement-based reciprocal simultaneous information exchange protocol. Its security is ultimately based on the assumption of the existence of a third trusted party. Although, the reciprocal information flow is between our two information brokers, the third entity plays a crucial role in mediating this process, being a guarantor and a verifier. The phenomenon of quantum entanglement is the cornerstone of this protocol, as it makes possible its implementation even when all entities are spatially separated, and ensuring that, upon completion, the trusted third party remains oblivious of the actual information that was exchanged.

Abstract: The generic behavior of purely dissipative open quantum many-body systems with local dissipation processes can be investigated using random matrix theory, revealing a hierarchy of decay timescales of observables organized by their complexity as shown in [Wang et al., $\href{https://link.aps.org/doi/10.1103/PhysRevLett.124.100604}{Phys. Rev. Lett. \textbf{124}, 100604 (2020)}]$. This hierarchy is reflected in distinct eigenvalue clusters of the Lindbladian. Here, we analyze how this spectrum evolves when unitary dynamics is present, both for the case of strongly and weakly dissipative dynamics. In the strongly dissipative case, the unitary dynamics can be treated perturbatively and it turns out that the locality of the Hamiltonian determines how susceptible the spectrum is to such a perturbation. For the physically most relevant case of (dissipative) two-body interactions, we find that the correction in the first order of the perturbation vanishes, leading to the relative robustness of the spectral features. For weak dissipation, the spectrum flows into clusters with well-separated eigenmodes, which we identify to be the local symmetries of the Hamiltonian.

Abstract: In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure that, under a given feedback control law, ensures convergence to the minimum energy eigenstate of a given energy function. By including quantum non-demolition (QND) measurements in the loop, convergence to a pure state can be ensured from an arbitrary mixed initial state. Based on existing results on strict control Lyapunov functions, we formulate a semidefinite optimization problem, whose solution defines a non-unique control Hamiltonian, which is sufficient to ensure almost sure convergence to the minimum energy eigenstate under the given feedback law and the action of QND measurements. A numerical example is provided to showcase the proposed methodology.

Abstract: Phase is a basic ingredient for quantum states since quantum mechanics uses complex numbers to describe quantum states. In this letter, we introduce a rigorous framework to quantify the phase of quantum states. To do so, we regard phase as a quantum resource, and specify the free states and free operations. We determine the conditions a phase measure should satisfy and provide some phase measures. We also propose the notion of intrinsic phase for quantum states.

Abstract: The scalability of quantum networking will benefit from quantum and classical communications coexisting in shared fibers, the main challenge being spontaneous Raman scattering noise. We investigate the coexistence of multi-channel O-band quantum and C-band classical communications. We characterize multiple narrowband entangled photon pair channels across 1282 nm-1318 nm co-propagating over 48 km installed standard fiber with record C-band power (>18 dBm) and demonstrate that some quantum-classical wavelength combinations significantly outperform others. We analyze the Raman noise spectrum, optimal wavelength engineering, multi-photon pair emission in entangled photon-classical coexistence, and evaluate the implications for future quantum applications.

Abstract: We investigate die-level and wafer-scale uniformity of Dolan-bridge and bridgeless Manhattan Josephson junctions, using multiple substrates with and without through-silicon vias (TSVs). Dolan junctions fabricated on planar substrates have the highest yield and lowest room-temperature conductance spread, equivalent to ~100 MHz in transmon frequency. In TSV-integrated substrates, Dolan junctions suffer most in both yield and disorder, making Manhattan junctions preferable. Manhattan junctions show pronounced conductance decrease from wafer centre to edge, which we qualitatively capture using a geometric model of spatially-dependent resist shadowing during junction electrode evaporation. Analysis of actual junction overlap areas using scanning electron micrographs supports the model, and further points to a remnant spatial dependence possibly due to contact resistance.

Abstract: The Jensen-Shannon divergence has been successfully applied as a segmentation tool for symbolic sequences, that is to separate the sequence into subsequences with the same symbolic content. In this work, we propose a method, based on the the Jensen-Shannon divergence, for segmentation of what we call \textit{quantum generated sequences}, which consist in symbolic sequences generated from measuring a quantum system. For one-qubit and two-qubit systems, we show that the proposed method is adequate for segmentation.

Abstract: Nonperturbative expressions for the Zou-Wang-Mandel interference patterns and normalized first-order coherence function are derived by bringing the canonical formalism of continuous-variable (CV) Gaussian states to bear on the mode-structure of the experiment. Generalizations to two-mode squeezing networks or $\mathcal{H}$-graph states with more than four modes directly follow from the general method used to analyze the minimal example.