Quantum Physics (quant-ph)

Abstract: Linear-feedback shift register (LFSR) based pseudo-random number generator (PRNG) has applications in a plethora of fields. The issue of being linear is generally circumvented by introducing non-linearities as per the required applications, with some being adhoc but fulfilling the purpose while others with a theoretical proof. The goal of this study is to develop a sufficiently ``random" resource for Quantum Key Distribution (QKD) applications with a low computational cost. However, as a byproduct, we have also studied the effect of introducing minimum non-linearity with experimental verification. Starting from the numerical implementation to generate a random sequence, we have implemented a XOR of two LFSR sequences on a low-cost FPGA evaluation board with one of the direct use cases in QKD protocols. Such rigorously tested random numbers could also be used like artificial neural networks or testing of circuits for integrated chips and directly for encryption for wireless technologies.

Abstract: The Rydberg dipole-blockade has emerged as the standard mechanism to induce entanglement between neutral atom qubits. In these protocols, laser fields that couple qubit states to Rydberg states are modulated to implement entangling gates. Here we present an alternative protocol to implement entangling gates via Rydberg dressing and a microwave-field-driven spin-flip blockade. We consider the specific example of qubits encoded in the clock states states of cesium. An auxiliary hyperfine state is optically dressed so that it acquires partial Rydberg character. It thus acts as a proxy Rydberg state, with a nonlinear light-shift that plays the role of blockade strength. A microwave-frequency field coupling a qubit state to this dressed auxiliary state can be modulated to implement entangling gates. Logic gate protocols designed for the optical regime can be imported to this microwave regime, for which experimental control methods are more robust. We show that unlike the strong dipole-blockade regime usually employed in Rydberg experiments, going to a moderate-spin-flip-blockade regime results in faster gates and smaller Rydberg decay. We study various regimes of operations that can yield high-fidelity two-qubit entangling gates and characterize their analytical behavior. In addition to the inherent robustness of microwave control, we can design these gates to be more robust to thermal fluctuations in atomic motion as well to laser amplitude, and other noise sources such as stray background fields.

Abstract: Out of the general thought, a quantum system can be prepared into a target eigenstate through repeated measurements on a coupled ancillary qubit rather than direct transitions in the Hamiltonian. In this work, we find that the positive operator-valued measures (POVMs) on the system, which is induced by the projective measurement on the qubit, can filter out the unwanted states except the target one. We discuss the measurement-based purification of entanglement in which maximally entangled states (Bell states and GHZ states) can be distilled from the maximally mixed states, and demonstrate the significant acceleration of a stimulated Raman adiabatic passage (STIRAP). Our scheme is not limited to the nondegenerate systems and allows arbitrary eigenstate generation. It offers a promising way to a generic state-preparation algorithm, enriching the functionalities of general quantum measurement.

Abstract: Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an in-depth investigation using the methodologies of sampling coordinates of observables and convex functions to refine the uncertainty relations in both the product form of two observables and summation form of multiple observables.

Abstract: For the study of quantum dynamics the use of Wigner's phase space representation can be rewarding. It describes the state by Wigner's real-valued distribution W and its dynamics by a vector field in phase space, the Wigner current J . Basically, only the Wigner representation can be used for this type of visual study of quantum dynamics so conveniently and directly. What does it teach us about the most fundamental ingredient of quantum dynamics, the quantum jump between energy levels? Quite a lot, as it turns out.

Abstract: We address the swapping of various quantum correlation measures including: Bell-nonlocality, EPR-steering, usefulness for teleportation, entanglement, quantum obesity, as well as the effect that local filtering operations have on the swapping of such correlations. In the first part of this work we address the raw swapping protocol (i. e. without local filtering) and our findings are as follows. First, using the Bloch representation of quantum states, we show that all of the above properties of a general quantum state can fully be preserved whenever the state is swapped together with arbitrary combinations of Bell states and Bell measurements. This generalises a result shown for the concurrence of states in the X-form. Second, we derive an explicit formula for the quantum obesity of the final post-swapping state in terms of the obesity of general input states and measurements, and therefore establishing the limit at which obesity can be swapped. In the second part we address the effect of local filtering operations on the swapping of quantum correlations. Specifically, we explore whether experimentalists should implement local filters before or after the swapping protocol takes place, so in order to maximize the final amount of correlations. In this regard, we first show that these two scenarios are equivalent for the family of Bell-diagonal states, for all of the above-mentioned quantum correlations. We then prove that applying local filters first can be more efficient when considering the strictly larger family of almost Bell-diagonal states, with the quantum obesity as the test property. Finally, we provide numerical evidence for this latter phenomenon (local filtering first is more efficient) holding true for general two-qubit states in the X-form, for all of the above-mentioned quantum correlations.

Abstract: Recent work has identified cosmic ray events as an error source limiting the lifetime of quantum data. These errors are correlated and affect a large number of qubits, leading to the loss of data across a quantum chip. Previous works attempting to address the problem in hardware or by building distributed systems still have limitations. We approach the problem from a different perspective, developing a new hybrid hardware-software-based strategy based on the 2-D surface code, assuming the parallel development of a hardware strategy that limits the phonon propagation radius. We propose to flee the area: move the logical qubits far enough away from the strike's epicenter to maintain our logical information. Specifically, we: (1) establish the minimum hardware requirements needed for our approach; (2) propose a mapping for moving logical qubits; and (3) evaluate the possible choice of the code distance. Our analysis considers two possible cosmic ray events: those far from both ``holes'' in the surface code and those near or overlapping a hole. We show that the probability that the logical qubit will be destroyed can be reduced from 100% to the range 4% to 15% depending on the time required to move the logical qubit.

Abstract: Controlled quantum teleportation (CQT) can be considered as a variant of quantum teleportation in which three parties are involved where one party acts as the controller. The usability of the CQT scheme depends on two types of fidelities viz. conditioned fidelity and non-conditioned fidelity. The difference between these fidelities may be termed as power of the controller and it plays a vital role in the CQT scheme. Thus, our aim is to estimate the power of the controller in such a way so that its estimated value can be obtained in an experiment. To achieve our goal, we have constructed a witness operator and have shown that its expected value may be used in the estimation of the lower bound of the power of the controller. Furthermore, we have shown that it is possible to make the standard W state useful in the CQT scheme if one of its qubits either passes through the amplitude damping channel or the phase damping channel. We have also shown that the phase damping channel performs better than the amplitude damping channel in the sense of generating more power of the controller in the CQT scheme.

Abstract: Photon counting simulations are crucial for designing and optimizing quantum photonic devices. The naive way to simulate time-integrated measurements of light requires integrating multi-variable correlations. This causes simulation times to increase exponentially with the correlation order, or number of detected photons. In this work, I present a method to simulate time-integrated quantities from the time dynamics of quantum emitters without multi-variable integration. The approach uses an effective master equation defined by a zero-photon generator -- a generator of time dynamics conditioned on the absence of detected light. The zero-photon conditional dynamics depends on an efficiency parameter for each detector. These parameters can take complex values to define a set of virtual detector configurations that can be exploited to reconstruct integrated quantities using an inverse Z-transform such as a discrete Fourier transform. The method can accelerate the simulation of single-photon sources and entangled photonic resource states for measurement-based quantum computing while accounting for physical imperfections of realistic devices. It also provides a general framework to simulate interactions between stationary qubits mediated by measurements of flying qubits, which has applications to model noise for distributed quantum computing and quantum communication protocols.

Abstract: The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this mapping makes the transition from the classical to the quantum regimes very clear, because the thermal Wigner function tends to the Boltzmann distribution in the high temperature limit. We approximate this quantum phase space representation of the canonical density operator for general temperatures in terms of classical trajectories, which are obtained through a Wick rotation of the semiclassical approximation for the Weyl propagator. A numerical scheme which allows us to apply the approximation for a broad class of systems is also developed. The approximation is assessed by testing it against systems with one and two degrees of freedom, which shows that, for a considerable range of parameters, the thermodynamic averages are well reproduced.

Abstract: Superconducting nanowire single-photon detectors (SNSPDs) have been widely used to study the discrete nature of quantum states in form of photon-counting experiments. We show that SNSPDs can also be used to study continuous variables of quantum states by performing homodyne detection. By measuring the interference of a continuous wave local oscillator with the vacuum state using two SNSPDs, we show that the variance of the difference in count rates is linearly proportional to the intensity of the local oscillator over almost five orders of magnitude. The resulting shot-noise clearance of $(46.0\pm1.1)~\mathrm{dB}$ is the highest reported clearance for a balanced optical homodyne detector, demonstrating their potential for measuring highly squeezed states in the continuous-wave regime. Using the same data, we also analyse the discrete photon statistics of the local oscillator. This shows that a single detector can be used to characterize quantum states in terms of both discrete and continuous variables.

Abstract: The Wigner function formalism serves as a crucial tool for simulating continuous-variable and odd-prime dimensional quantum circuits, as well as assessing their classical hardness. However, applying such a formalism to qubit systems is limited due to the negativity in the Wigner function induced by Clifford operations. In this work, we introduce a novel classical simulation method for non-adaptive Clifford circuits based on the framed Wigner function, an extended form of the qubit Wigner function characterized by a binary-valued frame function. Our approach allows for updating phase space points under Clifford circuits without inducing negativity in the Wigner function by switching to a suitable frame when applying each Clifford gate. By leveraging this technique, we establish a sufficient condition for efficient classical simulation of Clifford circuits even with non-stabilizer inputs, where direct application of the Gottesmann-Knill tableau method is not feasible. We further develop a graph-theoretical approach to identify classically simulatable marginal outcomes of Clifford circuits and explore the number of simulatable qubits of log-depth circuits. We also present the Born probability estimation scheme using the framed Wigner function and discuss its precision. Our approach opens new avenues for quasi-probability simulation of quantum circuits, thereby expanding the boundary of classically simulatable circuits.

Abstract: Quantum computers possess the potential to process data using a remarkably reduced number of qubits compared to conventional bits, as per theoretical foundations. However, recent experiments have indicated that the practical feasibility of retrieving an image from its quantum encoded version is currently limited to very small image sizes. Despite this constraint, variational quantum machine learning algorithms can still be employed in the current noisy intermediate scale quantum (NISQ) era. An example is a hybrid quantum machine learning approach for edge detection. In our study, we present an application of quantum transfer learning for detecting cracks in gray value images. We compare the performance and training time of PennyLane's standard qubits with IBM's qasm\_simulator and real backends, offering insights into their execution efficiency.

Abstract: In this study, we present a revision of the Quantum Optimal Control Theory (QOCT) originally proposed by Rabitz et al (Phys. Rev. A 37, 49504964 (1988)), which has broad applications in physical and chemical physics. First, we identify the QOCT equations as the Euler-Lagrange equations of the functional associated to the control scheme. In this framework we prove that the extremal functions found by Rabitz are not continuous, as it was claimed in previous works. Indeed, we show that the costate is discontinuous and vanishes after the measurement time. In contrast, we demonstrate that the driving field is continuous. We also identify a new set of continuous solutions to the QOCT. Overall, our work provides a significant contribution to the QOCT theory, promoting a better understanding of the mathematical solutions and offering potential new directions for optimal control strategies.

Abstract: Entangled states are an important resource for quantum information processing and for the fundamental understanding of quantum physics. An intriguing open question would be whether entanglement can improve the performance of quantum heat engines in particular. One of the promising platforms to address this question is to use entangled atoms as a non-thermal bath for cavity photons, where the cavity mirror serves as a piston of the engine. Here we theoretically investigate a photonic quantum engine operating under an effective reservoir consisting of quantum-correlated pairs of atoms. We find that maximally entangled Bell states alone do not help extract useful work from the reservoir unless some extra populations in the excited states or ground states are taken into account. Furthermore, high efficiency and work output are shown for the non-maximally entangled superradiant state, while negligible for the subradiant state due to lack of emitted photons inside the cavity. Our results provide insights in the role of quantum-correlated atoms in a photonic engine and present new opportunities in designing a better quantum heat engine.

Abstract: Photonic and bosonic systems subject to incoherent, wide-bandwidth driving cannot typically reach stable finite-density phases using only non-dissipative Hamiltonian nonlinearities; one instead needs nonlinear losses, or a finite pump bandwidth. We describe here a very general mechanism for circumventing this common limit, whereby Hamiltonian interactions can cut-off heating from a Markovian pump, by effectively breaking a symmetry of the unstable, linearized dynamics. We analyze two concrete examples of this mechanism. The first is a new kind of $\mathcal{PT}$ laser, where Hermitian Hamiltonian interactions can move the dynamics between the $\mathcal{PT}$ broken and unbroken phases and thus induce stability. The second uses onsite Kerr or Hubbard type interactions to break the chiral symmetry in a topological photonic lattice, inducing exotic phenomena from topological lasing to the stabilization of Fock states in a topologically protected edge mode.

Abstract: Energy extraction from quantum batteries by means of completely positive trace-preserving (CPTP) maps is quite well-studied in the literature. It naturally leads to the concept of CPTP-local passive states, which identify bipartite states from which no energy can be squeezed out by applying any CPTP map to a particular subsystem. Here we show that energy can be extracted efficiently from CPTP-local passive states employing non-completely positive trace-preserving (NCPTP) but still physically realizable maps on the same part of the shared battery on which operation of CPTP maps were useless. Thus, we realize that energy extraction from CPTP-local passive states using an unknown map can be utilized as a witness for detection of the NCPTP nature of that map. Further, we show that the maximum extractable energy using local CPTP maps on one party can be strictly less than that using local NCPTP maps on the same party. Finally, we provide a necessary condition for an arbitrary bipartite state to be unable to supply any energy using NCPTP operations on one party with respect to an arbitrary but fixed Hamiltonian.

Abstract: Variational quantum algorithms have been advocated as promising candidates to solve combinatorial optimization problems on near-term quantum computers. Their methodology involves transforming the optimization problem into a quadratic unconstrained binary optimization (QUBO) problem. While this transformation offers flexibility and a ready-to-implement circuit involving only two-qubit gates, it has been shown to be less than optimal in the number of employed qubits and circuit depth, especially for polynomial optimization. On the other hand, strategies based on higher-order binary optimization (HOBO) could save qubits, but they would introduce additional circuit layers, given the presence of higher-than-two-qubit gates. In this paper, we study HOBO problems and propose new approaches to encode their Hamiltonian into a ready-to-implement circuit involving only two-qubit gates. Our methodology relies on formulating the circuit design as a combinatorial optimization problem, in which we seek to minimize circuit depth. We also propose handy simplifications and heuristics that can solve the circuit design problem in polynomial time. We evaluate our approaches by comparing them with the state of the art, showcasing clear gains in terms of circuit depth.

Abstract: We study how to optimally realize the Yang-Baxter gates on quantum computers. We consider two types of Yang-Baxter gates. One is from the study of the topological entanglement. The other is from the quantum integrable circuit. We present the optimal realizations of Yang-Baxter gates with the minimal number of CNOT or $R_{zz}$ gates. We also study the pulse realizations of Yang-Baxter gates. We test and compare the different realizations on IBM quantum computers. We find that the pulse realizations of Yang-Baxter gates always have higher gate fidelity compared to the optimal CNOT or $R_{zz}$ realizations. Based on the above optimal realizations, we demonstrate the simulation of Yang-Baxter equation on quantum computers. Our results provide a guideline for further experimental study based on the Yang-Baxter gate.

Abstract: The dynamics of open quantum systems is formulated in a minimally extended state space comprising the degrees of freedom of a system of interest and a finite set of non-unitary, pure-state reservoir modes. This formal structure, derived from the Feynman-Vernon path integral for the reduced density, is shown to lead to an exact time-local evolution equation in a mixed Liouville-Fock space. The crucial ingredient is a mathematically consistent decomposition of the reservoir auto-correlation in terms of harmonic modes with complex-valued frequencies and amplitudes, which are obtained from any given spectral noise power of the physical reservoir. This formulation provides a universal framework to obtain a family of equivalent representations which are directly related to new and established schemes for efficient numerical simulations. By restricting some of the complex-valued mode parameters and performing linear transformations, we make connections to previous approaches, whose auxiliary degrees of freedom are thus revealed as restricted versions of the minimally extended state space presented here. From a practical perspective, the new framework offers a computational tool which combines numerical efficiency and accuracy with long time stability and broad applicability over the whole temperature range and also for strongly structured reservoir mode densities. It can thus deliver high precision data with modest computational resources and simulation times for actual quantum technological devices.

Abstract: Quantum computing is an emerging paradigm that has shown great promise in accelerating large-scale scientific, optimization, and machine-learning workloads. With most quantum computing solutions being offered over the cloud, it has become imperative to protect confidential and proprietary quantum code from being accessed by untrusted and/or adversarial agents. In response to this challenge, we propose SPYCE, which is the first known solution to obfuscate quantum code and output to prevent the leaking of any confidential information over the cloud. SPYCE implements a lightweight, scalable, and effective solution based on the unique principles of quantum computing to achieve this task.

Abstract: We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a quantum system, endowing it with a Riemannian metric structure, and investigate its deep link with the entanglement of the states of this space. As a measure we adopt the \emph{entanglement distance} $E$ preliminary proposed in Ref. \cite{PhysRevA.101.042129}. Our analysis shows that entanglement has a geometric interpretation: $E(|\psi\rangle$ is the minimum value of the sum of the squared distances between $\psi\rangle$ and its conjugate states, namely the states ${\bf v}^\mu \cdot {\bm \sigma}^\mu |\psi\rangle$, where ${\bf v}^\mu$ are unit vectors and $\mu$ runs on the number of parties. Within the proposed geometric approach, we derive a general method to determine when two states are not the same state up to the action of local unitary operators. Furthermore, we prove that the entanglement distance, along with its convex roof expansion to mixed states, fulfils the three conditions required for an entanglement measure: that is {\it i)} $E(|\psi\rangle) =0$ iff $|\psi\rangle$ is fully separable; {\it ii)} $E$ is invariant under local unitary transformation; {\it iii)} $E$ doesn't increase under local operation and classical communications. Two different proofs are provided for this latter property. We also show that in the case of two qubits pure states, the entanglement distance for a state $|\psi\rangle$ coincides with two times the square of the concurrence of this state. Finally, we apply the proposed geometric approach to the study of the entanglement magnitude and the equivalence classes properties, of three families of states linked to the Greenberger-Horne-Zeilinger states, the Briegel Raussendorf states and the W states.

Abstract: A simple proof is given that the upper and lower speed limits derived in Phys. Rev. A67 (2003), 052109, coincide. Only the most elementary analytical tools are used.

Abstract: We discuss the idea of extracting energy stochastically from a quantum battery, which is based on performing a projective measurement on an auxiliary system. The battery is initially connected to the auxiliary system and allowed to evolve unitarily. After some time, we execute a measurement on the auxiliary system and choose a particular outcome. The auxiliary is then traced out of the system, and the relevant state of the battery is the final state. We consider the product of the energy difference between the initial and final states with the probability of getting the measurement outcome that reduces to that final state. We define the maximum value of this quantity as the stochastically extractable energy. Restricting ourselves to a particular uncountable set of states, we find that stochastically extractable energy is always higher than the maximum energy that can be extracted from the battery by applying unitary operations, even if the initial auxiliary-battery state is a product. We show that a non-zero entanglement present initially between the battery and the auxiliary can induce an even higher amount of stochastic energy extraction than that for product initial states. Further, the set of states for which stochastically extractable energy is zero is determined for all product initial states and found to only consist of a single state, viz., the ground state.

Abstract: In this work we identify coherent electron-vibron interactions between near-resonant and non-resonant electronic levels that contribute beyond standard optomechanical models for off-resonant or resonance SERS. By developing an open-system quantum model using first molecular interaction principles, we show how the Raman interference of both resonant and non-resonant contributions can provide several orders of magnitude modifications of the SERS peaks with respect to former optomechanical models and over the fluorescence backgrounds. Our results demonstrate Raman enhancements and suppressions of coherent nature that significantly impact the standard estimations of the optomechanical contribution from SERS spectra.

Abstract: The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of an exponential scaling in terms of number of qubits. To circumvent this, quantum states can be represented as matrix product states (MPS), a product of tensors separated by so-called bond dimensions. Limiting bond dimensions growth approximates the state, but also limits its ability to represent entanglement. Methods based on this representation have been the most popular tool at simulating large quantum systems. But how to trust resulting approximate quantum states for such intractable systems sizes ? I propose here a method for inferring the fidelity of an approximate quantum state without direct comparison to its exact counterpart, and use it to design an ``entanglement-aware'' (EA) algorithm for both pure and mixed states. As opposed to state of the art methods which limit bond dimensions up to an arbitrary maximum value, this algorithm receives as input a fidelity, and adapts dynamically its bond dimensions to both local entanglement and noise such that the final quantum state fidelity at least reaches the input fidelity. I show that this algorithm far surpasses standard fixed bond dimension truncation schemes. In particular, a noiseless random circuit of 300 qubits and depth 75 simulated using MPS methods takes one week of computation time, while EA-MPS only needs 2 hours to reach similar quantum state fidelity.

Abstract: In this paper, we show that quantum feedback control may be applied to generate desired states for atomic and photonic systems based on a semi-infinite waveguide coupled with multiple two-level atoms. In this set-up, an initially excited atom can emit one photon into the waveguide, which can be reflected by the terminal mirror or other atoms to establish different feedback loops via the coherent interactions between the atom and photon. When there are at most two excitations in the waveguide quantum electrodynamics (waveguide QED) system, the evolution of quantum states can be interpreted using random graph theory. While this process is influenced by the environment, and we clarify that the environment-induced dynamics can be eliminated by measurement-based feedback control or coherent drives. Thus, in the open system atom-waveguide interactions, measurement-based feedback can modulate the final steady quantum state, while simultaneously, the homodyne detection noise in the measurement process can induce oscillations, which is treated by the coherent feedback designs.

Abstract: The quantum Fisher information (QFI) is a fundamental quantity in quantum physics and is central to the field of quantum metrology. It certifies quantum states that have useful multipartite entanglement for enhanced metrological tasks. Thus far, only lower bounds with finite distance to the QFI have been measured on quantum devices. Here, we present the experimental measurement of a series of polynomial lower bounds that converge to the QFI, done on a quantum processor. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust against drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement and the Heisenberg limit attained by our prepared state. Then, we prepare the ground state of the transverse field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by increasing the circuit depth.