Quantum Physics (quant-ph)

Abstract: We assess the use of variational quantum imaginary time evolution for solving partial differential equations. Our results demonstrate that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions compared to those with partial or linear entangling layers. To efficiently encode impulse functions, we propose a graphical mapping technique for quantum states that often requires only a single bit-flip of a parametric gate. As a proof of concept, we simulate colloidal deposition on a planar wall by solving the Smoluchowski equation including the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential energy. We find that over-parameterization is necessary to satisfy certain boundary conditions and that higher-order time-stepping can effectively reduce norm errors. Together, our work highlights the potential of variational quantum simulation for solving partial differential equations using near-term quantum devices.

Abstract: We extend the qubit-efficient encoding presented in [Tan et al., Quantum 5, 454 (2021)] and apply it to instances of the financial transaction settlement problem constructed from data provided by a regulated financial exchange. Our methods are directly applicable to any QUBO problem with linear inequality constraints. Our extension of previously proposed methods consists of a simplification in varying the number of qubits used to encode correlations as well as a new class of variational circuits which incorporate symmetries, thereby reducing sampling overhead, improving numerical stability and recovering the expression of the cost objective as a Hermitian observable. We also propose optimality-preserving methods to reduce variance in real-world data and substitute continuous slack variables. We benchmark our methods against standard QAOA for problems consisting of 16 transactions and obtain competitive results. Our newly proposed variational ansatz performs best overall. We demonstrate tackling problems with 128 transactions on real quantum hardware, exceeding previous results bounded by NISQ hardware by almost two orders of magnitude.

Abstract: The coherent control of the orbital state is crucial for color centers in diamonds for realizing extremely low-power manipulation. Here, we propose the neutrally charged nitrogen-vacancy center, NV$^0$, as an ideal system for orbital control through electric fields. We estimate electric susceptibility in the ground state of NV$^0$ to be comparable to that in the excited state of NV$^-$. Also, we demonstrate coherent control of the orbital states of NV$^0$. The required power for orbital control is three orders of magnitude smaller than that for spin control, highlighting the potential for interfacing a superconducting qubit operated in a dilution refrigerator.

Abstract: We analyse the stationary current of Bose particles across the Bose-Hubbard chain connected to a battery, focusing on the effect of inter-particle interactions. It is shown that the current magnitude drastically decreases as the strength of inter-particle interactions exceeds the critical value which marks the transition to quantum chaos in the Bose-Hubbard Hamiltonian. We found that this transition is well reflected in the non-equilibrium many-body density matrix of the system. Namely, the level-spacing distribution for eigenvalues of the density matrix changes from Poisson to Wigner-Dyson distributions. With the further increase of the interaction strength, the Wigner-Dyson spectrum statistics changes back to the Poisson statistics which now marks fermionization of the bosonic particles. With respect to the stationary current, this leads to the counter-intuitive dependence of the current magnitude on the particle number.

Abstract: The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layerwise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions.

Abstract: Various techniques have been used in recent years for verifying quantum computers, that is, for determining whether a quantum computer/system satisfies a given formal specification of correctness. Barrier certificates are a recent novel concept developed for verifying properties of dynamical systems. In this article, we investigate the usage of barrier certificates as a means for verifying behaviours of quantum systems. To do this, we extend the notion of barrier certificates from real to complex variables. We then develop a computational technique based on linear programming to automatically generate polynomial barrier certificates with complex variables taking real values. Finally, we apply our technique to several simple quantum systems to demonstrate their usage.

Abstract: In this paper, the application of quantum simulations and quantum machine learning to solve low-energy nuclear physics problems is explored. The use of quantum computing to deal with nuclear physics problems is, in general, in its infancy and, in particular, the use of quantum machine learning in the realm of nuclear physics at low energy is almost nonexistent. We present here three specific examples where the use of quantum computing and quantum machine learning provides, or could provide in the future, a possible computational advantage: i) the determination of the phase/shape in schematic nuclear models, ii) the calculation of the ground state energy of a nuclear shell model-type Hamiltonian and iii) the identification of particles or the determination of trajectories in nuclear physics experiments.

Abstract: Digital-Analog Quantum Computation (DAQC) has recently been proposed as an alternative to the standard paradigm of digital quantum computation. DAQC creates entanglement through a continuous or analog evolution of the whole device, rather than by applying two-qubit gates. This manuscript describes an in-depth analysis of DAQC by extending its implementation to arbitrary connectivities and by performing the first systematic study of its scaling properties. We specify the analysis for three examples of quantum algorithms, showing that except for a few specific cases, DAQC is in fact disadvantageous with respect to the digital case.

Abstract: Based on the two-qubit Jaynes-Cummings model - a common cavity quantum electrodynamics model, and extending to modification of the three-qubit Tavis-Cummings model, we investigate the quantum correlation between light and matter in bipartite quantum systems. By resolving the quantum master equation, we are able to derive the dissipative dynamics in open systems. To gauge the degree of quantum entanglement in the two-qubit system, von Neumann entropy and concurrence are introduced. Quantum discord, which can properly measure the quantum correlation in both closed and open systems, is also introduced. In addition, consideration is given to the impacts of initial entanglement and dissipation strength on quantum discord. Finally we discussed two different cases of nuclei motion: quantum and classical.

Abstract: The building blocks of quantum algorithms and software are quantum gates, with the appropriate combination of quantum gates leading to a desired quantum circuit. Deep expert knowledge is necessary to discover effective combinations of quantum gates to achieve a desired quantum algorithm for solving a specific task. This is especially challenging for quantum machine learning and signal processing. For example, it is not trivial to design a quantum Fourier transform from scratch. This work proposes a quantum architecture search algorithm which is based on a Monte Carlo graph search and measures of importance sampling. It is applicable to the optimization of gate order, both for discrete gates, as well as gates containing continuous variables. Several numerical experiments demonstrate the applicability of the proposed method for the automatic discovery of quantum circuits.

Abstract: Remote clock synchronization is crucial for many classical and quantum network applications. Current state-of-the-art remote clock synchronization techniques achieve femtosecond-scale clock stability utilizing frequency combs, which are supplementary to quantum-networking hardware. Demonstrating an alternative, we synchronize two remote clocks across our freespace testbed using a method called two-way quantum time transfer (QTT). In one second we reach picosecond-scale timing precision under very lossy and noisy channel conditions representative of daytime space-Earth links with commercial off-the-shelf quantum-photon sources and detection equipment. This work demonstrates how QTT is potentially relevant for daytime space-Earth quantum networking and/or providing high-precision secure timing in GPS-denied environments.

Abstract: Topological data analysis (TDA) has emerged as a powerful tool for extracting meaningful insights from complex data. TDA enhances the analysis of objects by embedding them into a simplicial complex and extracting useful global properties such as the Betti numbers, i.e. the number of multidimensional holes, which can be used to define kernel methods that are easily integrated with existing machine-learning algorithms. These kernel methods have found broad applications, as they rely on powerful mathematical frameworks which provide theoretical guarantees on their performance. However, the computation of higher-dimensional Betti numbers can be prohibitively expensive on classical hardware, while quantum algorithms can approximate them in polynomial time in the instance size. In this work, we propose a quantum approach to defining topological kernels, which is based on constructing Betti curves, i.e. topological fingerprint of filtrations with increasing order. We exhibit a working prototype of our approach implemented on a noiseless simulator and show its robustness by means of some empirical results suggesting that topological approaches may offer an advantage in quantum machine learning.

Abstract: Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying entanglement structure, on a lattice or more generally a (hyper)graph, with virtual entangled pairs or multipartite entangled states associated to (hyper)edges. Changing this underlying entanglement structure into another can lead to both theoretical and computational benefits. We study a natural resource theory which generalizes the notion of bond dimension to entanglement structures using multipartite entanglement. It is a direct extension of resource theories of tensors studied in the context of multipartite entanglement and algebraic complexity theory, allowing for the application of the sophisticated methods developed in these fields to tensor networks. The resource theory of tensor networks concerns both the local entanglement structure of a quantum many-body state and the (algebraic) complexity of tensor network contractions using this entanglement structure. We show that there are transformations between entanglement structures which go beyond edge-by-edge conversions, highlighting efficiency gains of our resource theory that mirror those obtained in the search for better matrix multiplication algorithms. We also provide obstructions to the existence of such transformations by extending a variety of methods originally developed in algebraic complexity theory for obtaining complexity lower bounds.

Abstract: We present a method to simulate the dynamics of large driven-dissipative many-body open quantum systems using a variational encoding of the Wigner or Husimi-Q quasi-probability distributions. The method relies on Monte-Carlo sampling to maintain a polynomial computational complexity while allowing for several quantities to be estimated efficiently. As a first application, we present a proof of principle investigation into the physics of the driven-dissipative Bose-Hubbard model with weak nonlinearity, providing evidence for the high efficiency of the phase space variational approach.

Abstract: Quantum systems with dynamical symmetries have conserved quantities which are preserved under coherent controls. Therefore such systems can not be completely controlled by means of only coherent control. In particular, for such systems maximal transition probability between some pair of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximal attainable transition probability. Simplest example of such situation occurs in a three-level quantum system with dynamical symmetry, for which maximal probability of transition between the ground and the intermediate state by only coherent control is $1/2$, and by coherent control assisted by incoherent control implemented by non-selective measurement of the ground state is about $0.687$, as was previously analytically computed. In this work we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). This used in this work measurement-driven control is different both from quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points and second order traps. For comparison, we study the transition probability between the ground and highest excited state, as well as the case when both these transition probabilities are assisted by incoherent control implemented by measurement of the intermediate state.

Abstract: Quantum collision models normally consist of a system interacting with a set of ancillary units representing the environment. While these ancillary systems are usually assumed to be either two level systems (TLS) or harmonic oscillators, in this work we move further and represent each ancillary system as a structured system, i.e., a system made out of two or more subsystems. We show how this scenario modifies the kind of master equation that one can obtain for the evolution of the open systems. Moreover, we are able to consider a situation where the ancilla state is thermal yet has some coherence. This allows the generation of coherence in the steady state of the open system and, thanks to the simplicity of the collision model, this allows us to better understand the thermodynamic cost of creating coherence in a system. Specifically, we show that letting the system interact with the coherent degrees of freedom requires a work cost, leading to the natural fulfillment of the first and second law of thermodynamics without the necessity of {\it ad hoc} formulations.

Abstract: Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for application of quantum phase estimation algorithms, in particular for large systems. In this note, we take up some simple examples of (classical) coupled oscillators and show how the algorithm works by using qubitization methods based on a sparse structure of the matrix. We explicitly construct block-encoding oracles along the way, propose a way to prepare initial states, and briefly touch on a more generic oracle construction for systems with repetitive structure. As a demonstration, we also give rough estimates of the necessary number of physical qubits and actual runtime it takes when carried out on a fault-tolerant quantum computer.

Abstract: We provide a general framework to compute the von Neumann entanglement entropy of a subsystem of a quantum system subject to stochastic resetting to its initial state with rate $r$. Using this framework we compute exactly the entanglement entropy of a single spin in a two-spin system. This system consists of a pair of ferromagnetically coupled spins in the presence of a transverse magnetic field and subjected to stochastic resetting to the $\mid \downarrow\downarrow \rangle$ state with rate $r$. We show that resetting drives the system to a non-equilibrium steady state where the von Neumann entropy exhibits rich behaviour as a function of the resetting rate and the interaction strength. In particular, even in the noninteracting limit, a small amount of resetting drives the system to a maximally entangled state. We also calculate analytically the temporal growth of the von Neumann entropy. Our results show that quantum resetting provides a simple and effective mechanism to enhance entanglement between two parts of a quantum system.

Abstract: We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal persistent topological features of the underlying data set. This is achieved via the computation of homological invariants that can be visualized as a persistence barcode encoding all relevant topological information. In this work, we apply this technique to study multipartite quantum systems by interpreting the individual systems as vertices of a simplicial complex. To construct a persistence complex from a given multipartite quantum state, we use a generalization of the bipartite mutual information called the deformed total correlation. Computing the persistence barcodes of this complex yields a visualization or `topological fingerprint' of the multipartite entanglement in the quantum state. The barcodes can also be used to compute a topological summary called the integrated Euler characteristic of a persistence complex. We show that in our case this integrated Euler characteristic is equal to the deformed interaction information, another multipartite version of mutual information. When choosing the linear entropy as the underlying entropy, this deformed interaction information coincides with the $n$-tangle, a well-known entanglement measure. The persistence barcodes thus provide more fine-grained information about the entanglement structure than its topological summary, the $n$-tangle, alone, which we illustrate with examples of pairs of states with identical $n$-tangle but different barcodes. Furthermore, a variant of persistent homology computed relative to a fixed subset yields an interesting connection to strong subadditivity and entropy inequalities. We also comment on a possible generalization of our approach to arbitrary resource theories.