Quantum Physics (quant-ph)

Abstract: We revisit the Perelomov SU(1,1) displaced coherent states states as possible quantum states of light. We disclose interesting statistical aspects of these states in relation with photon counting and squeezing. In the non-displaced case we discuss the efficiency of the photodetector as inversely proportional to the parameter k of the discrete series of unitary irreducible representations of SU(1,1). In the displaced case, we study the counting and squeezing properties of the states in terms of k and the number of photons in the original displaced state. We finally examine the quantization of a classical radiation field which is based on these families of coherent states. The procedure yields displacement operators which might allow to prepare such states in the way proposed by Glauber for the standard coherent states.

Abstract: We investigate the thermodynamics of a a hybrid quantum device consisting of two qubits collectively interacting with a quantum rotor and coupled dissipatively to two equilibrium reservoirs at different temperatures. By modelling the dynamics and the steady state of the system using the local and global master equations, we identify the functioning of the device as either a thermal engine, refrigerator or accelerator. In addition, we also look into the device's capacity to operate as a heat rectifier, and optimise both the rectification coefficient and the heat flow simultaneously. Drawing an analogy to heat rectification and since we are interested in the conversion of energy into the rotor's kinetic energy, we introduce the concept of angular momentum rectification which may be employed for controlling work extraction through an external load.

Abstract: In this paper, we study the geometric phase (GP) of two-mode entangled squeezed-coherent states (ESCSs), undergoing a unitary cyclic evolution. It is revealed that by increasing the squeezing parameter of the first or the second mode of a balanced ESCS, the GP compresses in an elliptical manner along the axis of the coherence parameter of the corresponding mode. While in the case of unbalanced ESCS, the GP compresses in a hyperbolic manner by increasing the squeezing parameters of either mode. By generalizing to higher constituting-state dimensions, it is found that the GPs of both balanced and unbalanced ESCSs, increase for a specific value of the coherence parameter. Based on these findings, using the interferometry approach, we suggest a theoretical scheme for the physical generation of the balanced ESCS.

Abstract: In this study, we analyze the phase synchronization of multiple quantum oscillators using a phase reduction method. In the previous study [arXiv:2208.12006], we proposed a Lie-algebraic phase reduction that reduces the dynamics of quantum limit-cycle oscillation to the phase variable. Furthermore, we reported that the back-action of continuous measurement induces clustering among the quantum oscillators. To analyze synchronization of multiple quantum oscillators without being biased by this back-action, we employ the heterodyne detection scheme, which averages out the back-action of continuous measurement over all possible observables. We demonstrate that common Hermitian noise induces synchronization between two quantum oscillators, which is a signature of the noise-induced synchronization, and that the number of possible clusters in the phase space is restricted by the number of bosonic levels. By applying the mean-field approximation, we analyze synchronization of quantum oscillators in the presence of global coupling. We can derive the noisy Kuramoto model from quantum van der Pol oscillators and adapt a generalized Ott-Antonsen ansatz to it, in the presence of global coupling in the heterodyne detection scheme.

Abstract: In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on a resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Computations, represented as measurement patterns, may be rewritten to optimise resource use and for other purposes. Such rewrites need to preserve the existence of flow to ensure the new pattern can still be implemented deterministically. The majority of existing work in this area has focused on rewrites that reduce the number of qubits, yet it can be beneficial to increase the number of qubits for certain kinds of optimisation, as well as for obfuscation. In this work, we introduce several ZX-calculus rewrite rules that increase the number of qubits and preserve the existence of Pauli flow. These rules can be used to transform any measurement pattern into a pattern containing only (general or Pauli) measurements within the XY-plane. We also give the first flow-preserving rewrite rule that allows measurement angles to be changed arbitrarily, and use this to prove that the `neighbour unfusion' rule of Staudacher et al. preserves the existence of Pauli flow. This implies it may be possible to reduce the runtime of their two-qubit-gate optimisation procedure by removing the need to regularly run the costly gflow-finding algorithm.

Abstract: Classical polarimetry is a rich and well established discipline within classical optics with many applications in different branches of science. Ever-growing interest in utilizing quantum resources in order to make highly sensitive measurements, prompted the researchers to describe polarized light in a quantum mechanical framework and build a quantum theory of polarimetry within this framework. In this work, inspired by the polarimetric studies in biological tissues, we study the ultimate limit of rotation angle estimation with a known rotation axis in a quantum polarimetric process, which consists of three quantum channels. The rotation angle to be estimated is induced by the retarder channel on the Stokes vector of the probe state. However, the diattenuator and depolarizer channels act on the probe state, which effectively can be thought of as a noise process. Finally the quantum Fisher information (QFI) is calculated and the effect of these noise channels and their ordering is studied on the estimation error of the rotation angle.

Abstract: Quantum thermodynamic quantities, normally formulated with the assumption of weak system-bath coupling (SBC), can often be contested in physical circumstances with strong SBC. This work presents an alternative treatment that enables us to use standard concepts based on weak SBC to tackle with quantum thermodynamics with strong SBC. Specifically, via a physics-motivated mapping between strong and weak SBC, we show that it is possible to identify thermodynamic quantities with arbitrary SBC, including work and heat that shed light on the first law of thermodynamics with strong SBC. Quantum fluctuation theorems, such as the Tasaki-Crooks relation and the Jarzynski equality are also shown to be extendable to strong SBC cases. Our theoretical results are further illustrated with a working example.

Abstract: We employ an $n$-replica Keldysh field theory to investigate the effects of measurements and decoherence on long distance behaviors of quantum critical states. We classify different measurements and decoherence based on their timescales and symmetry properties, and demonstrate that they can be described by $n$-replica Keldysh field theories with distinct physical and replica symmetries. Low energy effective theories for various scenarios are then derived using the symmetry and fundamental consistency conditions of the Keldysh formalism. We apply this framework to study the critical Ising model in both one and two spatial dimensions. In one dimension, we demonstrate that (1) measurements over a finite period of time along the transverse spin direction do not modify the asymptotic scaling of correlation functions and entanglement entropy, whereas (2) measurements along the longitudinal spin direction lead to an area law entangled phase. We also show that (3) decoherence noises over a finite time can be mapped to specific boundary conditions of a critical Ashkin-Teller model, and the entanglement characteristics of the resulting mixed state can be determined. For measurements and decoherence over an extensive time, we demonstrate that (4) the von Neumann entanglement entropy of a large subsystem can exhibit a (sub-)dominant logarithmic scaling in the stationary state for weak measurement (decoherence) performed in a basis that is symmetric under the Ising symmetry, but (5) reduces to an area law for measurements and decoherence in the longitudinal direction. Our results demonstrate that the Keldysh formalism is a useful tool for systematically studying the effects of measurements and decoherence on long-wavelength physics.

Abstract: Quantum coherence is the basic concept of superposition of quantum states and plays an important role in quantum metrology. We show how a pair of uniformly accelerated observers with a local two-mode Gaussian quantum state affects the Gaussian quantum coherence. We find that the quantum coherence decreases with increasing acceleration, which is due to the Unruh effect that destroys the quantum resource. Essentially, the variation of quantum coherence is caused by the modes mismatch between the input and output mode. Through 2000 randomly generated states, we demonstrate that such mismatch is dominated by the acceleration effect and mildly affected by the waveform parameters. Moreover, the squeezing parameter acted as a suppressor of the reduced coherence, but it tended to be invalid in the high squeezing. In addition, the squeezing parameter can act as a suppressor of the reduced coherence, but the effect of the squeezing parameter tends to be ineffective under high squeezing conditions.

Abstract: The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.

Abstract: Quantum Error-Correcting Codes (QECCs) are vital for ensuring the reliability of quantum computing and quantum communication systems. Among QECCs, stabilizer codes, particularly graph codes, have attracted considerable attention due to their unique properties and potential applications. Concatenated codes, whichcombine multiple layers of quantum codes, offer a powerful technique for achieving high levels of error correction with a relatively low resource overhead. In this paper, we examine the concatenation of graph codes using the powerful and versatile graphical language of ZX-calculus. We establish a correspondence between the encoding map and ZX-diagrams, and provide a simple proof of the equivalence between encoding maps in the Pauli X basis and the graphic operation "generalized local complementation" (GLC) as previously demonstrated in [J. Math. Phys. 52, 022201]. Our analysis reveals that the resulting concatenated code remains a graph code only when the encoding qubits of the same inner code are not directly connected. When they are directly connected, additional Clifford operations are necessary to transform the concatenated code into a graphcode, thus generalizing the results in [J. Math. Phys. 52, 022201]. We further explore concatenated graph codesin different bases, including the examination of holographic codes as concatenated graph codes. Our findings showcase the potential of ZX-calculus in advancing the field of quantum error correction.

Abstract: Considering non-Hermitian systems implemented by utilizing enlarged quantum systems, we determine the fundamental limits for the sensitivity of non-Hermitian sensors from the perspective of quantum information. We prove that non-Hermitian sensors do not outperform their Hermitian counterparts (directly couples to the parameter) in the performance of sensitivity, due to the invariance of the quantum information about the parameter. By scrutinizing two concrete non-Hermitian sensing proposals, which are implemented using full quantum systems, we demonstrate that the sensitivity of these sensors is in agreement with our predictions. Our theory offers a comprehensive and model-independent framework for understanding the fundamental limits of non-Hermitian quantum sensors and builds the bridge over the gap between non-Hermitian physics and quantum metrology.

Abstract: We propose a method for solving the hidden subgroup problem in nilpotent groups. The main idea is iteratively transforming the hidden subgroup to its images in the quotient groups by the members of a central series, eventually to its image in the commutative quotient of the original group; and then using an abelian hidden subgroup algorithm to determine this image. Knowing this image allows one to descend to a proper subgroup unless the hidden subgroup is the full group. The transformation relies on finding zero sum subsequences of sufficiently large sequences of vectors over finite prime fields. We present a new deterministic polynomial time algorithm for the latter problem in the case when the size of the field is constant. The consequence is a polynomial time exact quantum algorithm for the hidden subgroup problem in nilpotent groups having constant nilpotency class and whose order only have prime factors also bounded by a constant.

Abstract: TThe welded tree problem is a black-box problem to find the exit of the welded tree with $\Theta(2^n)$ vertices starting from the given entrance, for which there are quantum algorithms with exponential speedups over the best classical algorithm. The original quantum algorithm is based on continuous time quantum walks (CTQW), and it has never been clear whether there are efficient algorithms based on discrete time quantum walks (DTQW) until recently the multidimensional quantum walk framework was proposed (Jeffery and Zur, STOC'2023). In this paper, we propose a rather concise algorithm based purely on the simplest coined quantum walks, which is simply to iterate the naturally defined coined quantum walk operator for a predetermined time $T \in O(n \log n)$ and then measure to obtain the exit name with $\Omega(\frac{1}{n})$ probability. The algorithm can be further promoted to be error-free and with $O(n^{1.5} \log n)$ query complexity. The numerical simulation strongly implies that the actual complexity of our algorithm is $O(n^{4/3})$. The significance of our results may be seen as follows. (i) Our algorithm is rather concise compared with the one in (Jeffery and Zur, STOC'2023), which not only changes the stereotype that the exiting DTQW frameworks before the multidimensional one can achieve at most a quadratic speedup over the best classical algorithm, but also re-displays the power of the simplest framework of quantum walks. (ii) Our algorithm can be made error-free theoretically, whereas all the existing methods cannot. Thus, it is one of the few examples of an exponential separation between the error-free (exact) quantum and the randomized query complexities, which perhaps also change people's idea that quantum mechanics is inherently probabilistic and thus deterministic quantum algorithms with exponential speedups for the problem are out of the question.

Abstract: We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are the transmission distance between quantum channels and the entropic channel divergence. We investigate their mathematical properties and discuss their physical meaning. Additionally, we establish a chain rule for the entropic channel divergence, which implies the amortization collapse, a relevant result with potential applications in the field of discrimination of quantum channels and converse bounds. Finally, we analyze the distinguishability between two given Pauli channels and study exemplary Hamiltonian dynamics under decoherence.

Abstract: We compare the performance of a quantum local algorithm to a similar classical counterpart on a well-established combinatorial optimization problem LocalMaxCut. We show that a popular quantum algorithm first discovered by Farhi, Goldstone, and Gutmannn [1] called the quantum optimization approximation algorithm (QAOA) has a computational advantage over comparable local classical techniques on degree-3 graphs. These results hint that even small-scale quantum computation, which is relevant to the current state-of the art quantum hardware, could have significant advantages over comparably simple classical computation.

Abstract: We describe the generation of entangling gates on superconductor-semiconductor hybrid qubits by ac voltage modulation of the Josephson energy. Our numerical simulations demonstrate that the unitary error can be below $10^{-5}$ in a variety of 75-ns-long two-qubit gates (CZ, $i$SWAP, and $\sqrt{i\mathrm{SWAP}}$) implemented using parametric resonance. We analyze the conditional ZZ phase and demonstrate that the CZ gate needs no further phase correction steps, while the ZZ phase error in SWAP-type gates can be compensated by choosing pulse parameters. With decoherence considered, we estimate that qubit relaxation time needs to exceed $70\mu\mathrm{s}$ to achieve the 99.9% fidelity threshold.