Quantum Physics (quant-ph)

Abstract: The Prisoner's Dilemma game (PDG) is one of the simple test-beds for the probabilistic nature of the human decision-making process. Behavioral experiments have been conducted on this game for decades and show a violation of the so-called \textit{sure thing principle}, a key principle in the rational theory of decision. Quantum probabilistic models can explain this violation as a second-order interference effect, which cannot be accounted for by classical probability theory. Here, we adopt the framework of generalized probabilistic theories and approach this explanation from the viewpoint of quantum information theory to identify the source of the interference. In particular, we reformulate one of the existing quantum probabilistic models using density matrix formalism and consider different amounts of classical and quantum uncertainties for one player's prediction about another player's action in PDG. This enables us to demonstrate that what makes possible the explanation of the violation is the presence of \textit{quantum coherence} in the player's initial prediction and its conversion to probabilities during the dynamics. Moreover, we discuss the role of other quantum information-theoretical quantities, such as quantum entanglement, in the decision-making process. Finally, we propose a three-choice extension of the PDG to compare the predictive powers of quantum probability theory and a more general probabilistic theory that includes it as a particular case and exhibits third-order interference.

Abstract: High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC for many-body state preparation.

Abstract: Quantifying coherence is an essential endeavor for both quantum mechanical foundations and quantum technologies. We present a bona fide measure of quantum coherence by utilizing the Tsallis relative operator $(\alpha, \beta)$-entropy. We first prove that the proposed coherence measure fulfills all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. We then study the ordering of the Tsallis relative operator $(\alpha, \beta)$-entropy of coherence, Tsallis relative $\alpha$-entropies of coherence, R\'{e}nyi $\alpha$-entropy of coherence and $l_{1}$ norm of coherence for both pure and mixed qubit states. This provides a new method for defining new coherence measure and entanglement measure, and also provides a new idea for further study of quantum coherence.

Abstract: Quantum adversarial machine learning is an emerging field that studies the vulnerability of quantum learning systems against adversarial perturbations and develops possible defense strategies. Quantum universal adversarial perturbations are small perturbations, which can make different input samples into adversarial examples that may deceive a given quantum classifier. This is a field that was rarely looked into but worthwhile investigating because universal perturbations might simplify malicious attacks to a large extent, causing unexpected devastation to quantum machine learning models. In this paper, we take a step forward and explore the quantum universal perturbations in the context of heterogeneous classification tasks. In particular, we find that quantum classifiers that achieve almost state-of-the-art accuracy on two different classification tasks can be both conclusively deceived by one carefully-crafted universal perturbation. This result is explicitly demonstrated with well-designed quantum continual learning models with elastic weight consolidation method to avoid catastrophic forgetting, as well as real-life heterogeneous datasets from hand-written digits and medical MRI images. Our results provide a simple and efficient way to generate universal perturbations on heterogeneous classification tasks and thus would provide valuable guidance for future quantum learning technologies.

Abstract: An alternative quantization rule, in which time becomes a self-adjoint operator and position is a parameter, is proposed in [E. O. Dias and F. Parisio, Phys. Rev. A 95, 032133 (2017)]. Thus, the authors derive a space-time-symmetric (STS) extension of quantum mechanics, wherein a new quantum state (intrinsic to the particle), $|{\phi}(x)\rangle$, is defined at each point in space. $|{\phi}(x)\rangle$ obeys a space-conditional (SC) Schr\"odinger equation that, in the time basis, predicts the arrival time of the particle at $x$. In this work, we provide an interpretation of both the eigenstates of the STS extension and the SC Schr\"odinger equation (analogous to the interpretation of the Schr\"odinger equation): Given an ``initial'' SC wave function, ${\pmb \phi}(t|x_0)$, the solution ${\pmb \phi}(t|x)$ is the probability amplitude for the particle to arrive at $t$, given that one moves the detector from $x_0$ to a new position $x$. Then, we compare states $|\psi(t)\rangle$ and $|{\phi}(x)\rangle$ (which describe statistical data collected at $t$ and $x$, respectively) and conclude that they should provide complementary information about the system. Finally, we solve the SC Schr\"odinger equation for an arbitrary space-dependent potential. We apply this solution to a potential barrier and compare it with a generalized Kijowski distribution.

Abstract: The 1538 nm ${}^4$I$_{15/2}$ - ${}^4$I$_{13/2}$ transition of Er$^{3+}$ has an unusual hybrid electric-magnetic dipole character, and signatures of the hybrid moment can be expected in coherent transient measurements. Here, we investigate the effect of the hybrid moment in both sites of Er$^{3+}$:Y$_2$SiO$_5$ on Stark-modulated photon echo measurements, showing that it results in a reduction of visibility of the modulated signal as well as phase and polarization shifts. We interpret these effects using a simple optical Bloch equation model, showing that site 1 has a strongly mixed moment and site 2 is predominantly magnetic dipole. We discuss the implications of the hybrid moment for quantum information applications of quantum memories. We also use the echo measurements to extract the Stark shift of the optical transition along three orthogonal directions, finding values between 10.50 and 11.93 kHz/(V/cm) for site 1 and 1.61 and 15.35 kHz/(V/cm) for site 2. We observe a modification of the Zeeman shift by the electric field in both sites and discuss how this may be used to electrically control Er$^{3+}$ spin qubits.

Abstract: Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering algorithm, namely CHEM, that addresses the trade-off between circuit depth and accuracy. Based on variational quantum eigensolver and hardware-efficient ansatz, our method designs Clifford-based Hamiltonian transformation that (1) ensures a set of initial circuit parameters corresponding to the Hartree--Fock energy can be generated, (2) effectively maximizes the initial energy gradient with respect to circuit parameters, and (3) imposes negligible overhead for classical processing and does not require additional quantum resources. We demonstrate the efficacy of our approach using a quantum hardware emulator, achieving chemical accuracy for systems as large as 12 qubits with fewer than 30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers a promising avenue for practical quantum computational chemistry on near-term quantum devices.

Abstract: We study a quantum information engine (QIE) modeled by a multi-qubit working medium (WM) collectively coupled to a single thermal bath. We show that one can harness the collective effects to significantly enhance the performance of the QIE, as compared to equivalent engines lacking collective effects. We use one bit of information about the WM magnetization to extract work from the thermal bath. We analyze the work output, noise-to-signal ratio and thermodynamic uncertainty relation, and contrast these performance metrics of a collective QIE with that of an engine whose WM qubits are coupled independently to a thermal bath. We show that in the limit of high temperatures of the thermal bath, a collective QIE always outperforms its independent counterpart. In contrast to quantum heat engines, where collective enhancement in specific heat plays a direct role in improving the performance of the engines, here the collective advantage stems from higher occupation probabilities for the higher energy levels of the positive magnetization states, as compared to the independent case.

Abstract: We introduce a degree reduction method for symmetric polynomials on binary variables. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional method. The data shows that our method produces quadratic polynomial of less variables than the conventional method. The algorithm for our new degree reduction method is robust, and applies to any QUBO formulation for quantum annealing systems.

Abstract: Distributed quantum computing combines the computational power of multiple devices to overcome the limitations of individual devices. Circuit cutting techniques enable the distribution of quantum computations through classical communication. These techniques involve partitioning a quantum circuit into smaller subcircuits, each containing fewer qubits. The original circuit's outcome can be replicated by executing these subcircuits on separate devices and combining their results. However, the number of shots required to achieve a fixed result accuracy with circuit cutting grows exponentially with the number of cuts, posing significant costs. In contrast, quantum teleportation allows the distribution of quantum computations without an exponential increase in shots. Nevertheless, each teleportation procedure requires a pre-shared pair of maximally entangled qubits for transmitting a quantum state, and non-maximally entangled qubits cannot be used for this purpose. To address this, we propose a novel circuit cutting technique that leverages non-maximally entangled qubit pairs, effectively reducing the cost associated with circuit cutting. By considering the degree of entanglement in the pre-shared qubit pairs, our technique provides a continuum between existing circuit cutting methods and quantum teleportation, adjusting the cost of circuit cutting accordingly.

Abstract: Connectivity is a fundamental structural property of matroids, and has been studied algorithmically over 50 years. In 1974, Cunningham proposed a deterministic algorithm consuming $O(n^{2})$ queries to the independence oracle to determine whether a matroid is connected. Since then, no algorithm, not even a random one, has worked better. To the best of our knowledge, the classical query complexity lower bound and the quantum complexity for this problem have not been considered. Thus, in this paper we are devoted to addressing these issues, and our contributions are threefold as follows: (i) First, we prove that the randomized query complexity of determining whether a matroid is connected is $\Omega(n^2)$ and thus the algorithm proposed by Cunningham is optimal in classical computing. (ii) Second, we present a quantum algorithm with $O(n^{3/2})$ queries, which exhibits provable quantum speedups over classical ones. (iii) Third, we prove that any quantum algorithm requires $\Omega(n)$ queries, which indicates that quantum algorithms can achieve at most a quadratic speedup over classical ones. Therefore, we have a relatively comprehensive understanding of the potential of quantum computing in determining the connectedness of matroids.\

Abstract: Quantum photonic processors are emerging as promising platforms to prove preliminary evidence of quantum computational advantage towards the realization of universal quantum computers. In the context of non-universal noisy intermediate quantum devices, photonic-based sampling machines solving the Gaussian Boson Sampling problem currently play a central role in the experimental demonstration of a quantum computational advantage. In particular, the recently developed photonic machine Borealis, a large-scale instance of a programmable Gaussian Boson Sampling device encoded in the temporal modes of single photons, is available online for external users. In this work, we test the performances of Borealis as a sampling machine and its possible use cases in graph theory. We focused on the validation problem of the sampling process in the presence of experimental noise, such as photon losses, that could undermine the hardness of simulating the experiment. To this end, we used a recent protocol that exploits the connection between Guassian Boson Sampling and graphs perfect match counting. Such an approach to validation also provides connections with the open question on the effective advantage in using noisy Gaussian Boson Sampling devices for graphs similarity and isomorphism problems.

Abstract: Quantum incompatibility is referred as the phenomenon that some quantum measurements cannot be performed simultaneously, and is also used in various quantum information tasks. However, it is still a challenge to certify whether a given set of multiple high-dimensional measurements respects a specific structure of incompatibility. To address this problem, we propose a modified quantum state discrimination protocol that decomposes complex compatibility structures into pair-wise ones and employs noise robustness to witness incompatibility structures. Our method is capable of detecting genuine $n$-wise incompatibility and some specific general compatibility structures, as demonstrated by our experimental verification of incompatibility structures of $4$ mutually unbiased bases in a qutrit system. The experimental results show that our approach is a direct and intuitive tool to witness incompatibility structures in high-dimensional multi-measurement scenarios.

Abstract: Quantum state transfer by propagating wave packets of electromagnetic radiation requires tunable couplings between the sending and receiving quantum systems and the propagation channel or waveguide. The highest fidelity of state transfer in experimental demonstrations so far has been in superconducting circuits. Here, the tunability always comes together with nonlinear interactions, arising from the same Josephson junctions that enable the tunability. The resulting non-linear dynamics correlates the photon number and spatio-temporal degrees of freedom and leads to a multi-mode output state, for any multi-photon state. In this work, we study as a generic example the release of complex quantum states from a superconducting resonator, employing a flux tunable coupler to engineer and control the release process. We quantify the multi-mode character of the output state and discuss how to optimize the fidelity of a quantum state transfer process with this in mind.

Abstract: In an amended version of non-Hermitian interaction picture we propose to work with the states $\psi(t)$ in a dyadic representation. The control of evolution via two conjugate Schr\"{o}diner equations then renders the usual necessity of the construction of the time-dependent inner-product-metric operator $\Theta(t)$ redundant. The primary information about dynamics is assumed carried by a non-Hamiltonian observable (say, $R(t)$). A specific realization of phase transitions is then rendered possible via the Kato's exceptional-point (EP) degeneracy of the eigenvalues of $R(t)$ at the EP time $t=t^{(EP)}$. For illustration a cosmological model is proposed mimicking the unitary-evolution birth of the Universe from an initial quantum Big Bang singularity.

Abstract: In this paper, we adopt \c{hi}-type states to design a novel circular semiquantum private comparison (SQPC) protocol which can determine the equality of private inputs from two semiquantum users within one round implementation under the help of a semi-honest third party (TP) who possesses complete quantum capabilities. Here, it is assumed that the semi-honest TP has the abilities to launch all possible attacks to steal useful information about two semiquantum users' private inputs but cannot conspire with anyone else. The travelling particles go from TP to Alice, Alice to Bob and back from Bob to TP. The security analysis turns out the proposed SQPC protocol can resist both the outside attacks and the inside attacks. The proposed SQPC protocol has no demand for unitary operations. Compared with some existing SQPC protocols of equality with quantum entangled states, the proposed SQPC protocol has some advantages more or less:(1)it requires no pre-shared key among different participants; (2)it doesn't need quantum entanglement swapping; and(3)it employs no delay lines.

Abstract: Gaussian correlations emerge in a large class of many-body quantum systems quenched out of equilibrium, as demonstrated in recent experiments on coupled one-dimensional superfluids [Schweigler et al., Nature Physics 17, 559 (2021)]. Here, we present a mechanism by which an initial state of a Rydberg atom array can retain persistent non-Gaussian correlations following a global quench. This mechanism is based on an effective kinetic blockade rooted in the ground state symmetry of the system, which prevents thermalizing dynamics under the quench Hamiltonian. We propose how to observe this effect with Rydberg atom experiments and we demonstrate its resilience against several types of experimental errors. These long-lived non-Gaussian states may have practical applications as quantum memories or stable resources for quantum-information protocols due to the protected non-Gaussianity away from equilibrium.

Abstract: The single-channel Jost function is calculated with the computational R-matrix on a Lagrange-Jacobi mesh, in order to study its behaviour at complex wavenumbers. Three potentials derived from supersymmetric transformations are used to test the accuracy of the method. Each of these potentials, with s-wave or p-wave bound, resonance or virtual states, has a simple analytical expression for the Jost function, which is compared with the calculated Jost function. Siegert states and Siegert pseudostates are determined by finding the zeros of the calculated Jost function. Poles of the exact Jost function are not present in the calculated Jost function due to the truncation of the potential in the R-matrix method. Instead, Siegert pseudostates arise in the vicinity of the missing poles.

Abstract: We introduce a new structure, the critical multi-cubic lattice. Notably the critical multi-cubic lattice is the first true generalization of the cubic lattice to higher dimensional spaces. We then introduce the notion of a homomorphism in the category of critical multi-cubic lattices, compute its automorphism group, and construct a Hilbert space over which we represent the group. With this unitary representation, we re-derive the generalized Pauli matrices common in quantum computation while also defining an algebraic framework for an infinite system of qudits. We also briefly explore the critical multi-cubic lattice as a novel implication algebra serving as a logical framework for qudit gates.

Abstract: Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production which is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.

Abstract: We show that the position of the exceptional points (EPs) in the parameter space of a chiral molecule coupled to the photoionization continuum by a three-color field is enantiosensitive. Using a minimal model of a three-level system driven by a three-color field to form a cyclic loop transition, we investigate the enantiosensitivity of the EPs with respect to the system parameters and exploit the asymmetric switch mechanism associated with the encirclement of an EP in parameter space in an enantio-selective way. Our work paves the way for future applications of enantiosensitive EPs in chiral systems.

Abstract: Quantum tunneling is the phenomenon that makes superconducting circuits "quantum". Recently, there has been a renewed interest in using quantum tunneling in phase space of a Kerr parametric oscillator as a resource for quantum information processing. Here, we report a direct observation of quantum interference induced by such tunneling in a planar superconducting circuit. We experimentally elucidate all essential properties of this quantum interference, such as mapping from Fock states to cat states, a temporal oscillation induced by the pump detuning, as well as its characteristic Rabi oscillations and Ramsey fringes. Finally, we perform gate operations as manipulations of the observed quantum interference. Our findings lay the groundwork for further studies on quantum properties of Kerr parametric oscillators and their use in quantum information technologies.

Abstract: Quantum computers are gaining attention for their ability to solve certain problems faster than classical computers, and one example is the quantum expectation estimation algorithm that accelerates the widely-used Monte Carlo method in fields such as finance. A previous study has shown that quantum generative adversarial networks(qGANs), a quantum circuit version of generative adversarial networks(GANs), can generate the probability distribution necessary for the quantum expectation estimation algorithm in shallow quantum circuits. However, a previous study has also suggested that the convergence speed and accuracy of the generated distribution can vary greatly depending on the initial distribution of qGANs' generator. In particular, the effectiveness of using a normal distribution as the initial distribution has been claimed, but it requires a deep quantum circuit, which may lose the advantage of qGANs. Therefore, in this study, we propose a novel method for generating an initial distribution that improves the learning efficiency of qGANs. Our method uses the classical process of label replacement to generate various probability distributions in shallow quantum circuits. We demonstrate that our proposed method can generate the log-normal distribution, which is pivotal in financial engineering, as well as the triangular distribution and the bimodal distribution, more efficiently than current methods. Additionally, we show that the initial distribution proposed in our research is related to the problem of determining the initial weights for qGANs.

Abstract: In this contribution to the memorial issue of G\"oran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.

Abstract: Smooth Csisz\'ar $f$-divergences can be expressed as integrals over so-called hockey stick divergences. This motivates a natural quantum generalization in terms of quantum Hockey stick divergences, which we explore here. Using this recipe, the Kullback-Leibler divergence generalises to the Umegaki relative entropy, in the integral form recently found by Frenkel. We find that the R\'enyi divergences defined via our new quantum $f$-divergences are not additive in general, but that their regularisations surprisingly yield the Petz R\'enyi divergence for $\alpha < 1$ and the sandwiched R\'enyi divergence for $\alpha > 1$, unifying these two important families of quantum R\'enyi divergences. Moreover, we find that the contraction coefficients for the new quantum $f$ divergences collapse for all $f$ that are operator convex, mimicking the classical behaviour and resolving some long-standing conjectures by Lesniewski and Ruskai. We derive various inequalities, including new reverse Pinsker inequalites with applications in differential privacy and also explore various other applications of the new divergences.

Abstract: Security of quantum key distribution (QKD) protocols relies solely on quantum physics laws, namely, on the impossibility to distinguish between non-orthogonal quantum states with absolute certainty. Due to this, a potential eavesdropper cannot extract full information from the states stored in their quantum memory after an attack despite knowing all the information disclosed during classical post-processing stages of QKD. Here, we introduce the idea of encrypting classical communication related to error-correction in order to decrease the amount of information available to the eavesdropper and hence improve the performance of quantum key distribution protocols. We analyze the applicability of the method in the context of additional assumptions concerning the eavesdropper's quantum memory coherence time and discuss the similarity of our proposition and the quantum data locking (QDL) technique.

Abstract: We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a one-shot quantum covering lemma in terms of smooth min-entropies by leveraging decoupling techniques from quantum Shannon theory. This covering result is shown to be equivalent to a coding theorem for rate distortion under a posterior (reverse) channel distortion criterion [Atif, Sohail, Pradhan, arXiv:2302.00625]. Both one-shot results directly yield corollaries about the i.i.d. asymptotics, in terms of the coherent information of the channel. The power of our quantum covering lemma is demonstrated by two additional applications: first, we formulate a quantum channel resolvability problem, and provide one-shot as well as asymptotic upper and lower bounds. Secondly, we provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels, in particular separating for the first time the simultaneous identification capacity from the unrestricted one, proving a long-standing conjecture of the last author.

Abstract: Photon loss is the fundamental issue toward the development of quantum communication. We present a proposal to mitigate photon loss even at large distances and hence to create a global-scale quantum communication architecture. In this proposal, photons are sent directly through space, using a chain of co-moving low-earth orbit satellites. This satellite chain would bend the photons to move along the earth's curvature and control photon loss due to diffraction by effectively behaving like a set of lenses on an optical table. Numerical modeling of photon propagation through these "satellite lenses" shows that diffraction loss in entanglement distribution can be almost eliminated even at global distances of 20,000 km while considering beam truncation at each satellite and the effect of different errors. In the absence of diffraction loss, the effect of other losses (especially reflection loss) becomes important and they are investigated in detail. The total loss is estimated to be less than 30 dB at 20,000 km if other losses are constrained to 2% at each satellite, with 120 km satellite separation and 60 cm diameter satellite telescopes eliminating diffraction loss. Such low-loss satellite-based optical-relay protocol would enable robust, multi-mode global quantum communication and wouldn't require either quantum memories or repeater protocol. The protocol can also be the least lossy in almost all distance ranges available (200 - 20,000 km). Recent advances in space technologies may soon enable affordable launch facilities for such a satellite-relay network. We further introduce the "qubit transmission" protocol which has a plethora of advantages with both the photon source and the detector remaining on the ground. A specific lens setup was designed for the "qubit transmission" protocol which performed well in simulation that included atmospheric turbulence in the satellite uplink.