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Superconductor Science and Technology

A Dayem loop qubit based on interfering superconducting nanowires

C. P. Sun, Alexey Bezryadin

Published Jul 29, 2026• 0 citations
Publisher

Abstract

Abstract We propose a qubit design based on two parallel superconducting nanowires (i.e. a ‘Dayem loop qubit’). The inclusion of two nanowires instead of one leads to the Little-Parks effect, which provides an option to control the qubit frequency in a wide range, which is possible because the vorticity remains fixed, since the rate of phase slips is exponentially low at low temperatures. Our key result is that even if each individual nanowire does not have a cubic nonlinearity in its current-phase relationship (CPR), quantum interference between two condensates, induced by a magnetic field, produces a cubic nonlinearity for the entire device. Our numerical simulations, supported by analytical solutions, show that such nonlinearity is sufficient to create functional transmon qubits based on pairs of thin homogeneous superconducting nanowires. We analyze both generic, i.e. cubic CPR, as well as more realistic microscopic CPR, having higher-order nonlinearities. For higher-order CPRs, we propose a simple power-law phenomenological approximation valid at very low temperatures, at which superconducting qubits normally operate.

DOI
10.1088/1361-6668/ae922c

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Abstract We propose a qubit design based on two parallel superconducting nanowires (i.e. a ‘Dayem loop qubit’). The inclusion of two nanowires instead of one leads to the Little-Parks effect, which provides an option to control the qubit frequency in a wide range, which is possible because the vorticity remains fixed, since the rate of phase slips is exponentially low at low temperatures. Our key result is that even if each individual nanowire does not have a cubic nonlinearity in its current-phase relationship (CPR), quantum interference between two condensates, induced by a magnetic field, produces a cubic nonlinearity for the entire device. Our numerical simulations, supported by analytical solutions, show that such nonlinearity is sufficient to create functional transmon qubits based on pairs of thin homogeneous superconducting nanowires. We analyze both generic, i.e. cubic CPR, as well as more realistic microscopic CPR, having higher-order nonlinearities. For higher-order CPRs, we propose a simple power-law phenomenological approximation valid at very low temperatures, at which superconducting qubits normally operate.
We propose a qubit design based on two parallel superconducting nanowires (i.e., a "Dayem loop qubit"). The inclusion of two nanowires instead of one leads to the Little-Parks effect, which provides an oscillator behavior for the qubit frequency as well as anharmonicity. Our key result is that even if the nanowires have an increasingly linear CPR at low supercurrents, the quantum interference between two condensates, induced by a magnetic field, leads to a restoration of cubic nonlinearity, which is predicted to be sufficient to create a functional transmon qubit based on thin superconducting wires. We consider both generic (cubic) current-phase relationships (CPR) as well as more realistic microscopic CPR, having higher-order nonlinearities. For higher-order CPRs, we propose a simple power-law phenomenological approximation valid at very low temperatures, at which superconducting qubits normally operate.
The topic of superconducting nanowires has recently been an interesting field of research which has included the study of the superconductor to insulator transition (SIT), the observation of macroscopic quantum behavior such as quantum phase slips (QPS), and the potential use of nanowires as qubits. Superconducting coplanar microwave waveguide resonators have also become a popular way of studying superconducting junctions and qubits, as they provide an extremely low noise environment. For example, superconducting two-dimensional Fabry-Perot resonators have been used by other groups to make non-demolition measurements of a qubit. The motivation of this thesis will be the merging of the fields of superconducting nanowires and the technique of using superconducting microwave resonators to study junctions by incorporating a nanowire into the resonator itself at a current anti-node. By doing this, the nonlinear effects of the nanowire can be studied which may find application in single photon detectors, mixers, and the readout of qubits. We also employ the technique of molecular templating to fabricate some of the thinnest superconducting nanowires ever studied (down to ~ 5 nm in diameter in some cases). In this thesis, we extend the understanding of the nonlinear properties of a nanowire- resonator system and investigate a new type of nonlinearity that involves a pulsing regime between the superconducting and normal phases of the nanowire. We develop a model, which describes the results quantitatively and by modeling the system, we are able to extract information regarding the relaxation time of the nanowire back into the superconducting state. We also study double nanowire-resonator systems where two closely spaced parallel nanowires interrupt the resonator center conductor and form a loop where vortex tunneling processes can occur. Using a double nanowire-resonator we are able to observe the Little-Parks effect at low temperatures (where the resistance of the wires is immeasurably low) and are able to confirm the multivalued nature of the current phase relationship (CPR) in nanowires. Additionally, we observe an anomalous transmission regime where the periodic pulsing is replaced by stochastic amplitude fluctuations. In addition to microwave measurements on nanowires, we also study the normal state in resistively shunted nanowires with dc measurements where the inclusion of a shunt resistor is observed to change the nature of the normal state from the Joule heated state to a state that preserves phase coherence. Finally, the statistics on switching current events in graphene proximity junctions are analyzed and compared to the well known results for Josephson junctions. Only thermal activation (and no macroscopic quantum tunneling) is observed in graphene proximity superconducting junctions down to temperatures of ~ 300 mK.
Abstract Macroscopic phase coherence in superconductors enables quantum interference and phase manipulation at realistic device length scales. Numerous superconducting electronic devices are based on the modulation of the supercurrent in superconducting loops. While the overall behavior of symmetric superconducting loops has been studied, the effects of asymmetries in such devices remain under-explored and poorly understood. Here we report on an experimental and theoretical study of the flux modulation of the persistent current in a doubly connected asymmetric aluminum nanowire loop. A model considering the length and electronic cross-section asymmetries in the loop provides a quantitative account of the observations. Comparison with experiments give essential parameters such as persistent and critical currents as well as the amount of asymmetry which can provide feedback into the design of superconducting quantum devices.
The critical temperature in a superconducting ring changes periodically with the magnetic flux threading it, giving rise to the well-known Little-Parks magnetoresistance oscillations. Periodic changes of the critical current in a superconducting quantum interference device (SQUID), consisting of two Josephson junctions in a ring, lead to a different type of magnetoresistance oscillations utilized in detecting extremely small changes in magnetic fields. Here we demonstrate current-induced switching between Little-Parks and SQUID magnetoresistance oscillations in a superconducting nano-ring without Josephson junctions. Our measurements in Nb nano-rings show that as the bias current increases, the parabolic Little-Parks magnetoresistance oscillations become sinusoidal and eventually transform into oscillations typical of a SQUID. We associate this phenomenon with the flux-induced non-uniformity of the order parameter along a superconducting nano-ring, arising from the superconducting leads ('arms') attached to it. Current enhanced phase slip rates at the points with minimal order parameter create effective Josephson junctions in the ring, switching it into a SQUID.
In thin superconducting wires, phase-slip by thermal activation near the critical temperature is a well-known effect. It has recently become clear that phase-slip by quantum tunnelling through the energy barrier can also have a significant rate at low temperatures. In this paper, it is suggested that quantum phase-slip can be used to realize a superconducting quantum bit without Josephson junctions. A loop containing very thin nanofabricated wire is biased with an externally applied magnetic flux of half a flux quantum, resulting in two states with opposite circulating current and equal energy. Quantum phase-slip should provide coherent coupling between these two macroscopic states. Numbers are given for a wire of amorphous niobium-silicon that can be fabricated with advanced electron beam lithography.
Superconducting qubits are widely used in quantum computing research and industry. We describe a superconducting kinetic inductance qubit (and introduce the term Kineticon to describe it) operating at W-band frequencies with a nonlinear nanowire section that provides the anharmonicity required for two distinct quantum energy states. Operating the qubits at higher frequencies may relax the dilution refrigerator temperature requirements for these devices and paves the path for multiplexing a large number of qubits. Millimeter-wave operation requires superconductors with relatively high Tc, which implies high gap frequency, 2Δ/h, beyond which photons break Cooper pairs. For example, NbTiN with Tc= 15 K has a gap frequency near 1.4 THz, which is much higher than that of aluminum (90 GHz), allowing for operation throughout the millimeter-wave band. Here we describe a design and simulation of a W-band Kineticon qubit embedded in a 3-D cavity. We perform classical electromagnetic calculations of the resulting field distributions.