Quantum Physics (quant-ph)

Abstract: If the potential energy in a nearest neighbor tight binding model is flipped, we show that the time evolution of the wavefunction probability is conserved as long as the initial conditions only occupy even lattice sites or odd lattice sites and are real up to a global phase. This means that positive potentials trap particles just as well as negative potentials. Generalizations of this potential inversion theorem are discussed, and it is found that wavefunction probability evolution is conserved for these initial conditions for any transformation which flips the sign of all odd-distance hopping terms or all even-distance hopping terms. This predicts that electron pairs time evolve like positronium and therefore form bound states. We show a mapping of any lattice spin model onto a lattice hopping model and discuss general symmetries of these spin models using the potential inversion theorem.

Abstract: We study the monogamy of arbitrary quantum entanglement measures $E$ for tripartite quantum systems. Both sufficient and necessary conditions for $E$ to be monogamous in terms of the $\alpha$th power of $E$ are explicitly derived. It is shown that such monogamy of a entanglement measure $E$ only depends on the boundedness of the solution set of certain equations. Moreover, the monogamy conditions have been also obtained with respect to certain subsets of quantum states for a given quantum correlation. Detailed examples are given to illustrate our results.

Abstract: The prospect of quantum computing with a potential exponential speed-up compared to classical computing identifies it as a promising method in the search for alternative future High Energy Physics (HEP) simulation approaches. HEP simulations, such as employed at the Large Hadron Collider at CERN, are extraordinarily complex and require an immense amount of computing resources in hardware and time. For some HEP simulations, classical machine learning models have already been successfully developed and tested, resulting in several orders of magnitude speed-up. In this research, we proceed to the next step and explore whether quantum computing can provide sufficient accuracy, and further improvements, suggesting it as an exciting direction of future investigations. With a small prototype model, we demonstrate a full quantum Generative Adversarial Network (GAN) model for generating downsized eight-pixel calorimeter shower images. The advantage over previous quantum models is that the model generates real individual images containing pixel energy values instead of simple probability distributions averaged over a test sample. To complete the picture, the results of the full quantum GAN model are compared to hybrid quantum-classical models using a classical discriminator neural network.

Abstract: Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP-hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. Two main paradigms for quantum hardware are then discussed: quantum annealing and gate-based quantum computing. While quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation (QAO) algorithm and the quantum alternating operator ansatz (QAOA) framework, are discussed in detail. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.

Abstract: G\"oran Lindblad in 1983 published a monograph on non-equilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We high-light two aspects. The first is the idea that while all unitaries can be allowed in principle, different theories result from limiting which unitary evolutions are realized in the real world. The second is that Lindblad's proposal for thermodynamic entropy (as opposed to information-theoretic entropy) foreshadows much more recent investigations into optimal quantum transport which is a current research focus in several fields.

Abstract: Lawrence et al. have presented an argument purporting to show that ``relative facts do not exist'' and, consequently, ``Relational Quantum Mechanics is incompatible with quantum mechanics''. The argument is based on a GHZ-like contradiction between constraints satisfied by measurement outcomes in an extended Wigner's friend scenario. Here we present a strengthened version of the argument, and show why, contrary to the claim by Lawrence et al., these arguments do not contradict the consistency of a theory of relative facts. Rather, considering this argument helps clarify how one should not think about a theory of relative facts, like RQM.

Abstract: Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid non-variational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental-friendly. Since our algorithm is non-variational, it is also free from the "barren plateaus" problem. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator.

Abstract: We show strong positive spatial correlations in the qubits of a D-Wave 2000Q quantum annealing chip that are connected to qubits outside their own unit cell. By simulating the dynamics of spin networks, we then show that correlation between nodes is affected by a number of factors. The different connectivity of qubits within the network means that information transfer is not straightforward even when all the qubit-qubit couplings have equal weighting. The similarity between connected nodes is further changed when the couplings' strength is scaled according to the physical length of the connections (here to simulate dipole-dipole interactions). This highlights the importance of understanding the architectural features and potentially unprogrammed interactions/connections that can divert the performance of a quantum system away from the idealised model of identical qubits and couplings across the chip.

Abstract: Quantum entanglement has been identified as a crucial concept underlying many intriguing phenomena in condensed matter systems such as topological phases or many-body localization. Recently, instead of considering mere quantifiers of entanglement like entanglement entropy, the study of entanglement structure in terms of the entanglement spectrum has shifted into the focus leading to new insights into fractional quantum Hall states and topological insulators, among others. What remains a challenge is the experimental detection of such fine-grained properties of quantum systems. The development of protocols for detecting features of the entanglement spectrum in cold atom systems, which are one of the leading platforms for quantum simulation, is thus highly desirable and will open up new avenues for experimentally exploring quantum many-body physics. Here we present a method to bound the width of the entanglement spectrum, or entanglement dimension, of cold atoms in lattice geometries, requiring only measurements in two experimentally accessible bases and utilizing ballistic time-of-flight (ToF) expansion. Building on previous proposals for entanglement certification for photon pairs, we first consider entanglement between two atoms of different atomic species and later generalize to higher numbers of atoms per species and multispecies configurations showing multipartite high-dimensional entanglement. Through numerical simulations we show that our method is robust against typical experimental noise effects and thus will enable high-dimensional entanglement certification in systems of up to 8 atoms using currently available experimental techniques.

Abstract: Semi-quantum private comparison (SQPC) enables two classical users with limited quantum capabilities to compare confidential information using a semi-honest third party (TP) with full quantum power. However, entanglement swapping, as an important property of quantum mechanics in previously proposed SQPC protocols is usually neglected. In this paper, we propose a novel SQPC protocol based on the entanglement swapping of Bell states, where two classical users do not require additional implementation of the semi-quantum key distribution protocol to ensure the security of their private data. Security analysis shows that our protocol is resilient to both external and internal attacks. To verify the feasibility and correctness of the proposed SQPC protocol, we design and simulate the corresponding quantum circuits using IBM Qiskit. Finally, we compare and discuss the proposed protocol with previous similar work. The results reveal that our protocol maintains high qubit efficiency, even when entanglement swapping is employed. Consequently, our proposed protocol may have broader applicability in semi-quantum environments.

Abstract: A proper quantum memory is argued to consist in a quantum channel which cannot be simulated with a measurement followed by classical information storage and a final state preparation, i.e. an entanglement breaking (EB) channel. The verification of quantum memories (non-EB channels) is a task in which an honest user wants to test the quantum memory of an untrusted, remote provider. This task is inherently suited for the class of protocols with trusted quantum inputs, sometimes called measurement-device-independent (MDI) protocols. Here, we study the MDI certification of non-EB channels in continuous variable (CV) systems. We provide a simple witness based on adversarial metrology, and describe an experimentally friendly protocol that can be used to verify all non Gaussian incompatibility breaking quantum memories. Our results can be tested with current technology and can be applied to test other devices resulting in non-EB channels, such as CV quantum transducers and transmission lines.

Abstract: In the field of quantum information science and technology, the representation and visualization of quantum states and processes are essential for both research and education. In this context, a focus especially lies on ensembles of few qubits. While powerful representations exist for single-qubit illustrations, such as the infamous Bloch sphere, similar visualizations to intuitively understand quantum correlations or few-body entanglement are scarce. Here, we present the dimensional circle notation as a representation of such ensembles, adapting the so-called circle notation of qubits. The $n$-particle system is represented in an $n$-dimensional space, and the mathematical conditions for separability lead to symmetry conditions of the quantum state visualized. This notation promises significant potential for conveying nontrivial quantum properties and processes such as entanglement, measurements and unitary operations in few-qubit systems to a broader audience, and it could enhance understanding of these concepts beyond education as a bridge between intuitive quantum insight and formal mathematical descriptions.

Abstract: The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum states via the density matrix and its purification. The unique gauge-invariant QGT of mixed states is derived, whose real part is the Bures metric and its imaginary part is the Uhlmann form. In contrast to the imaginary part of the pure-state QGT that is proportional to the Berry curvature, the Uhlmann form vanishes identically for ordinary physical processes. Moreover, there exists a Pythagorean-like equation that links different local distances, reflecting the underlying fibration. The Bures metric reduces to the Fubini-Study metric as temperature approaches zero if the eigenvalues of the density matrix do not change during the process, establishing a correspondence between the distances of pure and mixed states. To complete the comprehensive view of the geometry and QGT of mixed states, we present two examples contrasting different aspects of their local geometries.

Abstract: We study collisions of ultracold CaF molecules in strong static electric fields. Such fields allow the creation of long-range barriers in the interaction potential, which prevent the molecules reaching the short-range region where inelastic and other loss processes are likely to occur. We carry out coupled-channel calculations of rate coefficients for elastic scattering and loss. We develop an efficient procedure for including energetically well-separated rotor functions in the basis set via a Van Vleck transformation. We show that shielding is particularly efficient for CaF and allows the rate of 2-body loss processes to be reduced by a factor of $10^7$ or more at a field of 23 kV/cm. The loss rates remain low over a substantial range of fields. Electron and nuclear spins cause strong additional loss in some small ranges of field, but have little effect elsewhere. The results pave the way for evaporative cooling of CaF towards quantum degeneracy.

Abstract: This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity $\mathcal{O}(n^3)$ in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical representation in terms of leaves, axils, and twins. It captures both, the connection structure of a graph and the $2$-body marginal properties of the associated graph state. We relate the foliage partition to the size of LC-orbits and use it to bound the number of LC-automorphisms of graphs. We also show the invariance of the foliage partition when generalized to weighted graphs and qudit graph states.

Abstract: The efficient probing of spectral features of quantum many-body systems is important for characterising and understanding the structure and dynamics of quantum materials. In this work, we establish a framework for probing the excitation spectrum of quantum many-body systems with quantum simulators. Our approach effectively realises a spectral detector by processing the dynamics of observables with time intervals drawn from a defined probability distribution, which only requires native time evolution governed by the Hamiltonian without any ancilla. The critical element of our method is the engineered emergence of frequency resonance such that the excitation spectrum can be probed. We show that the time complexity for transition energy estimation has a logarithmic dependence on simulation accuracy, and discuss the noise e robustness of our spectroscopic method. We present simulation results for the spectral features of typical quantum systems, including quantum spins, fermions and bosons. We experimentally demonstrate how spectroscopic features of spin lattice models can be probed with IBM quantum devices.