We investigate the impact of different connectivities on the decoherence time in quantum systems under quasistatic Heisenberg noise. We considered three types of elementary units, including node, stick and triangle and connect them into ring, chain, and tree configurations. We find that rings exhibit greater stability compared with chains, contrary to the expectation that higher average connectivity leads to decreased stability. Additionally, the stick configuration is more stable than the triangle configuration. We also observe similar trends in entanglement entropy and return probability, indicating their potential use in characterizing decoherence time. Our findings provide insights into the interplay between connectivity and stability in quantum systems, with implications for the design of robust quantum technologies and quantum error correction strategies.
We investigate the impact of different connectivities on the decoherence time in quantum systems under quasistatic Heisenberg noise. We considered three types of elementary units, including node, stick and triangle and connect them into ring, chain, and tree configurations. We find that rings exhibit greater stability compared with chains, contrary to the expectation that higher average connectivity leads to decreased stability. Additionally, the stick configuration is more stable than the triangle configuration. We also observe similar trends in entanglement entropy and return probability, indicating their potential use in characterizing decoherence time. Our findings provide insights into the interplay between connectivity and stability in quantum systems, with implications for the design of robust quantum technologies and quantum error correction strategies.
We determine the interqubit crosstalk- and charge-noise-induced decoherence time T2∗ for a system of L exchange-coupled electronic spin qubits in arrays of size L=3--14 for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}=|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\cdots}\ensuremath{\rangle}$. We show that a power law behavior, ${T}_{2}^{*}\ensuremath{\propto}{L}^{\ensuremath{-}\ensuremath{\gamma}}$, is a good fit to the results for the chain and ring geometries as a function of the number of qubits and provide numerical results for the exponent $\ensuremath{\gamma}$. We find that T2∗ depends crucially on the multiqubit geometry of the system. We also calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring T2∗. A key finding is that T2∗ decreases with increasing L. We also demonstrate that these results may be understood in terms of perturbation theory and its breakdown.
Charge noise remains the primary obstacle to the development of quantum information technologies with semiconductor spin qubits. We use an exact analytical calculation to determine the effects of quasistatic charge noise on a ring of three equally spaced exchange-coupled quantum dots. We calculate the disorder-averaged return probability from a specific initial state and use it to determine the coherence time T2∗ and show that it depends on only the disorder strength and not the mean interaction strength. We also use a perturbative approach to investigate other arrangements of three or four qubits, finding that the return probability contains multiple oscillation frequencies. These oscillations decay in a Gaussian manner, determined by differences in energy levels of the Hamiltonian. We give quantitative values for gate times resulting in several target fidelities. We find that the decoherence time decreases with an increasing number of qubits. Our work provides useful analytical insight into the charge noise dynamics of coupled spin qubits.
We theoretically consider the temporal dynamics of two coupled spin qubits (e.g., semiconductor quantum dots) driven by the interqubit spin-spin coupling. The presence of environmental noise (e.g., charge traps, nuclear spins, random magnetic impurities) is accounted for by including random magnetic field and random interqubit coupling terms in the Hamiltonian. Both Heisenberg coupling and Ising coupling between the spin qubits are considered, corresponding respectively to exchange and capacitive gates as appropriate for single spin and singlet-triplet semiconductor qubit systems, respectively. Both exchange (Heisenberg) and capacitive (Ising) coupling situations can be solved numerically exactly even in the presence of noise, leading to the key findings that (i) the steady-state return probability to the initial state remains close to unity in the presence of strong noise for many, but not all, starting spin configurations, and (ii) the return probability as a function of time is oscillatory with a characteristic noise-controlled decay toward the steady-state value. We also provide results for the magnetization dynamics of the coupled two-qubit system. Our predicted dynamics can be directly tested in the already existing semiconductor spin qubit setups providing insight into their coherent interaction dynamics. Retention of the initial state spin memory even in the presence of strong environmental noise has important implications for quantum computation using spin qubits.
We consider the decoherence of a quantum system S coupled to a quantum environment E. For states chosen uniformly at random from the unit hypersphere in the Hilbert space of the closed system S+E we derive a scaling relationship for the sum of the off-diagonal elements of the reduced density matrix of S as a function of the size DE of the Hilbert space of E. This sum decreases as 1/DE as long as ${D}_{E}\ensuremath{\gg}1$. We test this scaling prediction by performing large-scale simulations which solve the time-dependent Schr\"odinger equation for a ring of spin-1/2 particles, four of them belonging to S and the others to E, and for this ring with small world bonds added in E and/or between S and E. The spin-1/2 particles experience nearest-neighbor interactions that are identical for the interactions within S and random for the interactions within E and between S and E, or that are all identical. Provided that the time evolution drives the whole system from the initial state toward a scaling state, a state which has similar properties as states belonging to the class of quantum states for which we derived the scaling relationship, the scaling prediction holds. We examine various interaction parameters and initial states for our model system to find whether or not the time evolution reaches the class of states that have the scaling property. For the homogeneous ring we find that the evolution for select initial states does not reach these scaling states. This conclusion is not modified if we add some homogeneous random connections. For a ring we find that some randomness in the interaction parameters is required so that most initial configurations are driven toward the scaling state. Furthermore, if the amount of randomness is small the time required to reach the scaling states may be very large. For the case of all random interactions in E the ring is driven toward the scaling state. Adding small world bonds between S and E with random interaction strengths may decrease the time required to reach the scaling state or may prevent the scaling state from being reached. For the latter case we show that increasing the complexity of the environment by adding extra connections within the environment suffices to observe the predicted scaling behavior.
Abstract Understanding how decoherence disrupts quantum walks is vital for developing robust quantum technologies, as environmental interactions often degrade quantum properties or induce transitions to classical random walks. We investigate the stability of continuous-time quantum walks across different network topologies subjected to three distinct decoherence mechanisms: energy-based intrinsic decoherence, node-based Haken–Strobl noise, and edge-based quantum stochastic walk. By defining stability as the preservation of quantum properties, we find that densely connected networks, such as the complete network, and hub dominated networks, such as scale-free and star topologies, are stable under Haken–Strobl noise but become uniquely vulnerable under quantum stochastic walk. However, these same networks exhibit lower coherence in the noiseless regime due to their inherent localization, highlighting a fundamental trade-off between localization and coherence. Furthermore, the centrality of the initialization node has a pronounced impact on relaxation time, underscoring the critical role of local topological features in quantum dynamics.
Understanding how intrinsic decoherence affects the interplay between geometry, dynamics, and entanglement in quantum systems is a central challenge in quantum information science. In this work, we develop a unified framework that explores this interplay for a pair of interacting spins governed by an XXZ-type Heisenberg model under an external magnetic field and intrinsic decoherence. We quantify entanglement using the concurrence measure and examine its evolution under decoherence, revealing that intrinsic noise rapidly suppresses entanglement as it increases. We then analyze the Hilbert-Schmidt and Bures distances between quantum states and show how both the degree of entanglement and the noise rate modulate these distances and their associated quantum speeds. Importantly, we demonstrate that the Hilbert-Schmidt speed is more responsive to entanglement and coherence loss than the Bures speed, making it a powerful tool for probing the geometry of quantum dynamics. Moreover, we solve the quantum brachistochrone problem in the presence of intrinsic decoherence, identifying the minimal evolution time and the corresponding optimal entangled states. Finally, we explore the geometric phase accumulated during the system's evolution. Our results show that decoherence hinders geometric phase accumulation, while entanglement counteracts this effect, enhancing phase stability.