Quantum Physics (quant-ph)

Abstract: Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local-global correspondence and discuss the relationships between the local-global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.

Abstract: In this paper, we investigate spin squeezing in a hybrid quantum system consisting of a Silicon-Vacancy (SiV) center ensemble coupled to a diamond acoustic waveguide via the strain interaction. Two sets of non-overlapping driving fields, each contains two time-dependent microwave fields, are applied to this hybrid system. By modulating these fields, the one-axis twist (OAT) interaction and two-axis two-spin (TATS) interaction can be independently realized. In the latter case the squeezing parameter scales to spin number as $\xi_R^2\sim1.61N^{-0.64}$ with the consideration of dissipation, which is very close to the Heisenberg limit. Furthermore, this hybrid system allows for the study of spin squeezing generated by the simultaneous presence of OAT and TATS interactions, which reveals sensitivity to the parity of the number of spins $N_{tot}$, whether it is even or odd. Our scheme enriches the approach for generating Heisenberg-limited spin squeezing in spin-phonon hybrid systems and offers the possibility for future applications in quantum information processing.

Abstract: In this paper, we develop a generic controlled alternate quantum walk model (called CQWM-P) by combining parity-dependent quantum walks with distinct arbitrary memory lengths and then construct a quantum-inspired hash function (called QHFM-P) based on this model. Numerical simulation shows that QHFM-P has near-ideal statistical performance and is on a par with the state-of-the-art hash functions based on discrete quantum walks in terms of sensitivity of hash value to message, diffusion and confusion properties, uniform distribution property, and collision resistance property. Stability test illustrates that the statistical properties of the proposed hash function are robust with respect to the coin parameters, and theoretical analysis indicates that QHFM-P has the same computational complexity as that of its peers.

Abstract: Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based error mitigation techniques. We also demonstrate that similar to results in fault tolerant quantum computing, code concatenation in fault-tolerant quantum error mitigation (FTQEM) can exponentially suppress the errors to arbitrary levels. We also provide analytical error thresholds for FTQEM with the repetition code. The post-selection rate in FTQEM can also be increased by correcting some of the outcomes. The benefits of FTQEM are demonstrated with numerical simulations and hardware demonstrations.

Abstract: Quantum computers promise a highly efficient approach to investigate quantum phase transitions, which describe abrupt changes between different ground states of many-body systems. At quantum critical points, the divergent correlation length and entanglement entropy render the ground state preparation difficult. In this work, we explore the imaginary-time evolution for probing the universal critical behavior as the universal information of the ground state can be extracted in the early-time relaxation process. We propose a systematic and scalable scheme to probe the universal behaviors via imaginary-time critical dynamics on quantum computers and demonstrate the validness of our approach by both numerical simulation and quantum hardware experiments. With the full form of the universal scaling function in terms of imaginary time, system size, and circuit depth, we successfully probe the universality by scaling analysis of the critical dynamics at an early time and with shallower quantum circuit depth. Equipped with quantum error mitigation, we also confirm the expected scaling behavior from experimental results on a superconducting quantum processor which stands as the first experimental demonstration on universal imaginary-time quantum critical dynamics.

Abstract: We investigate the behavior of relativistic electrons encountering a potential step through analogies with optical phenomena. By accounting for the conservation of Dirac current, we elucidate that the Goos-H\"anchen shift can be understood as a combination of two components: one arising from the current entering the transmission region and the other originating from the interference between the incident and reflected beams. This result has been proven to be consistent with findings obtained utilizing the stationary phase method. Moreover, we explore the transverse Imbert-Fedorov shift, by applying both current conservation and total angular momentum conservation, revealing intriguing parallel to the spin Hall effect. Beyond enriching our comprehension of fundamental quantum phenomena, our findings have potential applications for designing and characterizing devices using Dirac and topological materials.

Abstract: We utilize the theory of local amplitude transfers (LAT) to gain insights into quantum walks (QWs) and quantum annealing (QA) beyond the adiabatic theorem. By representing the eigenspace of the problem Hamiltonian as a hypercube graph, we demonstrate that probability amplitude traverses the search space through a series of local Rabi oscillations. We argue that the amplitude movement can be systematically guided towards the ground state using a time-dependent hopping rate based solely on the problem's energy spectrum. Building upon these insights, we extend the concept of multi-stage QW by introducing the guided quantum walk (GQW) as a bridge between QW-like and QA-like procedures. We assess the performance of the GQW on exact cover, traveling salesperson and garden optimization problems with 9 to 30 qubits. Our results provide evidence for the existence of optimal annealing schedules, beyond the requirement of adiabatic time evolutions. These schedules might be capable of solving large-scale combinatorial optimization problems within evolution times that scale linearly in the problem size.

Abstract: Here we present a new protocol for controlled quantum key agreement and another protocol for key agreement with a specific focus on the security analysis. Specifically, detailed security proof is provided against impersonated fraudulent attack and collective attacks and it is established that the proposed protocols are not only secure, but they also satisfy other desired properties of such schemes (i.e., fairness and correctness). Further, the proposed schemes are critically compared with a set of schemes for quantum key agreement and an existing scheme for controlled quantum key agreement (Tang et al.'s protocol) in terms of efficiency and the required quantum resources. Especially, it is observed that in contrast to the existing schemes, the present scheme does not require quantum memory. In addition, the protocol for controlled quantum key agreement proposed here is found to require quantum resources (Bell state and single photon state) that are easier to produce and maintain compared to the quantum resources (GHZ states) required by the only known existing protocol for the same purpose, i.e., Tang et al.'s protocol.

Abstract: We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert Space followed by an imposition of - what effectively amounts to - a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach-Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlargers the Hilbert Space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.

Abstract: Continuous U(1) gauge symmetry, which guarantees the conservation of the total excitations in linear bosonic systems, will be broken when it comes to the strong-coupling regime where the rotation wave approximation (RWA) fails. Here we develop analytic solutions for multi-mode bosonic systems with XX-type couplings beyond RWA, and proposed a novel scheme to implement high-fidelity quantum state transfer (QST) and entanglement preparation (EP) with high speed. The scheme can be realized with designated coupling strength and pulse duration with which the excitation number keeps unchanged regardless of the breakdown of the global U(1) symmetry. In the QST tasks, we consider several typical quantum states and demonstrate that this method is robust against thermal noise and imperfections of experimental sequence. In the EP tasks, the scheme is successfully implemented for the preparation of Bell states and W-type states, within a shortest preparation time.

Abstract: In this work we present a novel strategy to evaluate multi-variable integrals with quantum circuits. The procedure first encodes the integration variables into a parametric circuit. The obtained circuit is then derived with respect to the integration variables using the parameter shift rule technique. The observable representing the derivative is then used as the predictor of the target integrand function following a quantum machine learning approach. The integral is then estimated using the fundamental theorem of integral calculus by evaluating the original circuit. Embedding data according to a reuploading strategy, multi-dimensional variables can be easily encoded into the circuit's gates and then individually taken as targets while deriving the circuit. These techniques can be exploited to partially integrate a function or to quickly compute parametric integrands within the training hyperspace.

Abstract: We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability distribution vectors (PDVs) in terms of majorization relation. While the utmost lower bound coincides with $(1/N,...,1/N)$ for any two orthogonal bases, the majorization certainty relation for $M\geqslant3$ is shown to be nontrivial. The universal majorization bounds for three mutually complementary observables and a more general set of observables in dimension-2 are achieved. It is found that one cannot prepare a quantum state with PDVs of incompatible observables spreading out arbitrarily. Moreover, we obtain a complementary relation for the quantum coherence as well, which characterizes a trade-off relation of quantum coherence with different bases.

Abstract: A recent theoretical proposal for teleamplification requires preparation of Fock states, programmable interferometers, and photon-number resolving detectors to herald the teleamplification of an input state. These enable teleportation and heralded noiseless linear amplification of a photonic state up to an arbitrarily large energy cutoff. We report on adapting this proposal for Borealis and demonstrating teleamplification of squeezed-vacuum states with variable amplification factors. The results match the theoretical predictions and exhibit features of amplification in the teleported mode. This demonstration motivates the continued development of photonic quantum computing hardware for noiseless linear amplification's applications across quantum communication, sensing, and error correction.

Abstract: Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source ($547{\pm}2$ Hz) from a solid-state quantum emitter and a stable polarisation-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to $\mathcal{F}=0.7278{\pm}0.0106$. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.