arXiv subjects

Matthew Elliott

Publications and source records attributed to Matthew Elliott.

8 recordsLinked to original sources

arXiv2026

Mobile but Miserable: Social comparison networks and social mobility

Although social mobility is widely viewed as desirable, we document an 'inverse-U' shaped relationship with well-being: mobility is positively associated with well-being when low, but the association diminishes as mobility increases and eventually becomes negative. To explain this, we build a model in which agents are embedded in a social comparison network and suffer from falling behind their peers. The model highlights two channels that can cause welfare to be decreasing in mobility at high levels. First, when mobility is high, further increases widen already significant gaps between agents from similar parental backgrounds but of different abilities. Second, when mobility is high, high-ability agents are already relatively well off. So further increases in social mobility increase inequality. We find evidence supportive of both channels in US data. The model also predicts, and data supports, that social integration -- where relationships form more along ability than background lines -- allows societies to benefit from mobility for longer. We interpret this as social mobility being multidimensional with both economic and social dimensions that are complementary.

econ.TH↗

arXiv2023

Corporate Culture and Organizational Fragility

Complex organizations accomplish tasks through many steps of collaboration among workers. Corporate culture supports collaborations by establishing norms and reducing misunderstandings. Because a strong corporate culture relies on costly, voluntary investments by many workers, we model it as an organizational public good, subject to standard free-riding problems, which become severe in large organizations. Our main finding is that voluntary contributions to culture can nevertheless be sustained, because an organization's equilibrium productivity is endogenously highly sensitive to individual contributions. However, the completion of complex tasks is then necessarily fragile to small shocks that damage the organization's culture.

econ.TH↗

arXiv2021

A Network Approach to Public Goods: A Short Summary

Suppose agents can exert costly effort that creates nonrival, heterogeneous benefits for each other. At each possible outcome, a weighted, directed network describing marginal externalities is defined. We show that Pareto efficient outcomes are those at which the largest eigenvalue of the network is 1. An important set of efficient solutions, Lindahl outcomes, are characterized by contributions being proportional to agents' eigenvector centralities in the network. The outcomes we focus on are motivated by negotiations. We apply the results to identify who is essential for Pareto improvements, how to efficiently subdivide negotiations, and whom to optimally add to a team.

econ.TH↗

arXiv2020

Supply Network Formation and Fragility

We model the production of complex goods in a large supply network. Each firm sources several essential inputs through relationships with other firms. Individual supply relationships are at risk of idiosyncratic failure, which threatens to disrupt production. To protect against this, firms multisource inputs and strategically invest to make relationships stronger, trading off the cost of investment against the benefits of increased robustness. A supply network is called fragile if aggregate output is very sensitive to small aggregate shocks. We show that supply networks of intermediate productivity are fragile in equilibrium, even though this is always inefficient. The endogenous configuration of supply networks provides a new channel for the powerful amplification of shocks.

econ.TH↗

arXiv2017

Designing Kerr interactions using multiple superconducting qubit types in a single circuit

The engineering of Kerr interactions has great potential for quantum information processing applications in multipartite quantum systems and for investigation of many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this type of architecture could be of significant benefit for quantum technologies. Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconducting qubits with opposite anharmonicities to a single cavity enables the effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schr\"{o}dinger cat states for much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to the same pair of qubit devices. When one of the qubits is tunable in frequency, the strength of entangling interactions between the cavities can be varied on demand, forming the basis for logic operations on the two modes. Finally, we discuss the feasibility of producing an array of cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and a useful platform for quantum simulation in circuit quantum electrodynamics.

quant-ph↗

arXiv2016

Applications of the Fokker-Planck equation in circuit quantum electrodynamics

We study exact solutions of the steady state behaviour of several non-linear open quantum systems which can be applied to the field of circuit quantum electrodynamics. Using Fokker-Planck equations in the generalised P-representation we investigate the analytical solutions of two fundamental models. First, we solve for the steady-state response of a linear cavity that is coupled to an approximate transmon qubit and use this solution to study both the weak and strong driving regimes, using analytical expressions for the moments of both cavity and transmon fields, along with the Husimi Q-function for the transmon. Second, we revisit exact solutions of quantum Duffing oscillator which is driven both coherently and parametrically while also experiencing decoherence by the loss of single and pairs of photons. We use this solution to discuss both stabilisation of Schroedinger cat states and the generation of squeezed states in parametric amplifiers, in addition to studying the Q-functions of the different phases of the quantum system. The field of superconducting circuits, with its strong nonlinearities and couplings, has provided access to a new parameter regime in which returning to these exact quantum optics methods can provide valuable insights.

quant-ph↗

arXiv2015

Deterministic amplification of Schroedinger cat states in circuit quantum electrodynamics

We propose a dynamical scheme for deterministically amplifying photonic Schroedinger cat states based on a set of optimal state-transfers. The scheme can be implemented in strongly coupled qubit-cavity systems and is well suited to the capabilities of state of the art superconducting circuits. The ideal analytical scheme is compared with a full simulation of the open Jaynes-Cummings model with realistic device parameters. This amplification tool can be utilized for practical quantum information processing in non-classical continuous-variable states.

quant-ph↗

arXiv2015

Enhancement and state tomography of a squeezed vacuum with circuit quantum electrodynamics

We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and non-classical driving. We show that this scenario could be realised with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. In the presence of dissipation, we find that an effective Hartree-type decoupling with a Fokker-Planck equation yields a good approximation. We find that the stationary state is approximately a squeezed vacuum, which is enhanced by the $Q$-factor of the cavity but conserved by the interaction. The qubit non-linearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of realistic parameters, enables characterisation of itinerant squeezed fields.

quant-ph↗