Modulated longitudinal gates on encoded spin qubits via curvature couplings to a superconducting cavity

Abstract

Understanding how and to what magnitude solid-state qubits couple to metallic wires is crucial to the design of quantum systems such as quantum computers. Here, we investigate the coupling between a multi-level system, or qudit, and a superconducting (SC) resonator's electromagnetic field, focusing on the interaction involving both the transition and diagonal dipole moments of the qudit. Specifically, we explore the effective dynamical (time-dependent) longitudinal coupling that arises when a solid-state qudit is adiabatically modulated at small gate frequencies and amplitudes, in addition to a static dispersive interaction with the SC resonator. For the first time, we derive Hamiltonians describing the longitudinal multi-level interactions in a general dispersive regime, encompassing both dynamical longitudinal and dispersive interactions. These Hamiltonians smoothly transition between their adiabatic values, where the couplings of the n-th level are proportional to the level's energy curvature concerning a qudit gate voltage, and the substantially larger dispersive values, which occur due to a resonant form factor.We provide several examples illustrating the transition from adiabatic to dispersive coupling in different qubit systems, including the charge (1e DQD) qubit, the transmon, the double quantum dot singlet-triplet qubit, and the triple quantum dot exchange-only qubit. In some of these qubits, higher energy levels play a critical role, particularly when their qubit's dipole moment is minimal or zero. For an experimentally relevant scenario involving a spin-charge qubit with magnetic field gradient coupled capacitively to a SC resonator, we showcase the potential of these interactions. They enable close-to-quantum-limited quantum non-demolition (QND) measurements and remote geometric phase gates, demonstrating their practical utility in quantum information processing.

Opinion: Democratizing Spin Qubits

“…3) Explore alternative readout and coupling approaches via classical and quantum cavities: transverse versus longitudinal coupling versus modulated longitudinal coupling [48][49][50][51]71].…”

“…7 One more thing: coupling spins to a superconducting cavity We've already discussed using superconducting resonators for readout, we can go further by exploring spin-qubit entangling protocols [71,80] via superconducting cavity or transmission lines. By putting the cavity on the gate-chip, see Figure 9, we can optimize for high Q.…”

Tunable hole spin-photon interaction based on g-matrix modulation

“…Light acts on two-level systems either transversally or longitudinally, that is by changing or preserving the level occupations, respectively. These actions trigger different dynamics; transverse coupling underpins highfidelity readout [15] and control operations [16][17][18][19][20][21], while longitudinal coupling has recently emerged as a valuable resource for fast quantum non-demolition measurements [22][23][24][25][26][27] and entangling gates [23,[28][29][30][31][32][33][34][35][36][37][38][39]]. Yet, controlling the relative strength of longitudinal and transverse couplings requires specific circuit design [22][23][24][25][26][27], driving protocols [40] or additional elements such as micro-magnets [41].…”

Fully tunable longitudinal spin-photon interactions in Si and Ge quantum dots

“…While challenging to engineer in superconducting circuits [48,49], large longitudinal interactions emerge naturally in hole spin qubits, where, in contrast to alternative theoretical proposals [51][52][53][54][55][56] and recent experiments [52], they do not require multiple quantum dots, nor parametric driving. We show that longitudinal interactions in hole dots are fully tunable and can be modulated by oscillating electric fields, enabling significantly faster qubit readout protocols [57,58] and two-qubit gates [59,60].…”

“…Also, T g is significantly shortened at large ω r because J ∝ ω 3 r . In contrast to alternative proposals [56,59,60], our approach does not require an ac modulation of γ γ γ. Here, we consider a square pulse of time T g , and we neglect the turning on time τ on , as well as non-RWA corrections.…”