Abstract From available data, 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. Then, by simulating the dynamics of three different spin networks and two different initial conditions, 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. Connected nodes behave even more dissimilarly 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 From available data, 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. Then, by simulating the dynamics of three different spin networks and two different initial conditions, 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. Connected nodes behave even more dissimilarly 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.
An important challenge in superconducting quantum computing is the need to physically couple many devices using quasi-two-dimensional fabrication processes. Recent advances in the design and fabrication of quantum annealing processors have enabled an increase in pairwise connectivity among thousands of qubits. One benefit of this is the ability to minor-embed optimization problems using fewer physical qubits for each logical spin. Here we demonstrate the benefit of this progress in the problem of minimizing the energy of three-dimensional spin glasses. Comparing the previous generation D-Wave 2000Q system to the new Advantage system, we observe improved scaling of solution time and improved consistency over multiple graph embeddings.
Graph structure of quantum spin networks plays an essential role in applying quantum annealing (QA). The Ising model is the typical choice to describe the interactions between the spins in the networks. Here, we explore the interplay of different interaction types between the spins and the structure of the underlying network on the performance of QA. Specifically, we consider the Heisenberg XY and antisymmetric anisotropic exchange interaction models, in addition to the usual Ising Model, in graph structures ranging from linear chains to complete graphs with different connectivities. We find that the QA performance of the Ising model shows less variation with the change of graph structure among different interaction types. The Heisenberg XY model suffers from significant performance losses with increasing connections beyond linear chains, which we attribute to increasing entropy built-up. Anisotropic exchange interactions turn out to be an impractical choice for complete graphs due to the diminishing energy gap during annealing. Furthermore, we investigate the effect of inhomogeneous couplings and reveal a trade-off between coupling strength and performance, especially significant for the case of the anisotropic exchange model.
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.
The distribution of entanglement between the nodes of a quantum network plays a fundamental role in quantum information applications. In this work, we investigate the dynamics of a network of qubits where each edge corresponds to an independent two-qubit interaction. By applying tools from percolation theory, we study how entanglement dynamically spreads across the network. We show that the interplay between unitary evolution and spatially correlated disorder leads to a non-standard percolation phenomenology, significantly richer than uniform bond percolation and featuring hysteresis. A two-colour correlated bond percolation model, whose phase diagram is determined via numerical simulations and a mean-field theory, fully elucidates the physics behind this phenomenon.
Abstract Quantum annealing is a type of analog computation that aims to use quantum mechanical fluctuations in search of optimal solutions of QUBO (quadratic unconstrained binary optimization) or, equivalently, Ising problems. Since NP-hard problems can in general be mapped to Ising and QUBO formulations, the quantum annealing paradigm has the potential to help solve various NP-hard problems. Current quantum annealers, such as those manufactured by D-Wave Systems, Inc. have various practical limitations including the size (number of qubits) of the problem that can be solved, the qubit connectivity, and error due to the environment or system calibration, which can reduce the quality of the solutions. Typically, for an arbitrary problem instance, the corresponding QUBO (or Ising) structure will not natively embed onto the available qubit architecture on the quantum chip. Thus, in these cases, a minor embedding of the problem structure onto the device is necessary. However, minor embeddings on these devices do not always make use of the full sparse chip hardware graph, and a large portion of the available qubits stay unused during quantum annealing. In this work, we embed a disjoint random QUBO on the unused parts of the chip alongside the QUBO to be solved, which acts as an indicator of the solution quality of the device over time. Using experiments on three different D-Wave quantum annealers, we demonstrate that (i) long term trends in solution quality exist on the D-Wave device, and (ii) the unused qubits can be used to measure the current level of noise of the quantum system.
In this thesis, we study the operation of existing quantum annealers by simulating the real-time dynamics of two coupled flux qubits based on SQUIDs (superconducting quantum interference devices) during quantum annealing processes. We investigate two aspects. First, we study the influence of the higher energy levels which are neglected when deriving the qubit Hamiltonian from the superconducting circuit model including the tunable coupler. Second, we investigate the influence of an environment on the qubit system during quantum annealing. For the latter, we examine two different models for the environment, a generic spin bath and non-interacting two-level systems. For simulating the dynamics, we use the Suzuki-Trotter product-formula algorithm to solve the time-dependent Schrödinger equation numerically. We find that the higher energy levels as well as the presence of the tunable coupler have little influence on the performance of the quantum annealing process for most of the investigated problem instances, suggesting that the two-level approximation works very well. However, we find that for a particular class of instances, the results of the SQUID model and the qubit model show certain deviations. Additionally, we perform experiments on the D-Wave 2000Q quantum annealer. Our study of the two models for the environment suggests that the model of non-interacting two-level systems is better suited to describe the data obtained from the real device than the generic spin bath model.