Simulated coherent electron shuttling in silicon quantum dots

Abstract

Shuttling of single electrons in gate-defined silicon quantum dots is numerically simulated. A minimal gate geometry without explicit tunnel barrier gates is introduced, and used to define a chain of accumulation mode quantum dots, each controlled by a single gate voltage. One-dimensional potentials are derived from a three-dimensional electrostatic model, and used to construct an effective Hamiltonian for efficient simulation. Control pulse sequences are designed by maintaining a fixed adiabaticity, so that different shuttling conditions can be systematically compared. We first use these tools to optimize the device geometry for maximum transport velocity, considering only orbital states and neglecting valley and spin degrees of freedom. Taking realistic geometrical constraints into account, charge shuttling speeds up to ∼ 300 m/s preserve adiabaticity. Coherent spin transport is simulated by including spin-orbit and valley terms in an effective Hamiltonian, shuttling one member of a singlet pair and tracking the entanglement fidelity. With realistic device and material parameters, shuttle speeds in the range 10 − 100 m/s with high spin entanglement fidelities are obtained when the tunneling energy exceeds the Zeeman energy. High fidelity also requires the inter-dot valley phase difference to be below a threshold determined by the ratio of tunneling and Zeeman energies, so that spin-valley-orbit mixing is weak. In this regime, we find that the primary source of infidelity is a coherent spin rotation that is correctable, in principle. The results pertain to proposals for large-scale spin qubit processors in isotopically purified silicon that rely on coherent shuttling of spins to rapidly distribute quantum information between computational nodes.

The spider-web array--a sparse spin qubit array

“…1. From recent modeling of a shuttling protocol similar to the one used here [43], we estimate that with a 50 nm gate pitch we can achieve t sh ≈ 50 ns, maintaining >99.9% fidelity. State-of-the-art quantum dot qubit systems, with operation mechanisms similar to the ones proposed here, have demonstrated Rabi frequencies and exchange couplings ∼10 MHz [5,8,44], which correspond in our system to t 1q , t sw ≈ 25 ns.…”

Multicore Quantum Computing

“…The velocity of the detuning sweep must be sufficiently slow to minimize diabatic transitions to excited valley-orbit states, while slow enough to ensure charge noise does not induce transitions near avoided crossings. Such restrictions are dependent on device design and the degree of pulse optimisation, though speeds on the order of 1 nanosecond per tunneling event are considered feasible [52][53][54]. With a dot-to-dot spacing of 50-100 nm, the distance of a few microns can be traversed in tens to hundreds of nanoseconds, comparable to single-and two-qubit gate times in silicon quantum dot processors [55].…”

“…Previous theoretical treatments have given substantial attention to the ability of a single shuttling event to preserve an arbitrary input state's fidelity [52,[60][61][62][63]. However, a shuttling channel does not need to be able to shuttle arbitrary states to constitute a useful resource.…”

“…If the quality of the shuttled state is measured on the basis of fidelity, population loss into higher-energy states will degrade the quality of our Bell pairs unless recovered through appropriate calibrations [52,62], i.e., such a unitary evolution does not inherently destroy information but does rather introduce a coherent error. Although the coherent error introduced by the unitary evolution under our Hamiltonian in Eq.…”

Measurement of tunnel coupling in a Si double quantum dot based on charge sensing

“…It allows single-qubit operations on a charge qubit, and exchange gates for spin qubits [19][20][21][22][23][24][25]. Interdot shuttling is also crucial for information transfer on chip [26][27][28][29][30][31][32][33]. With spin and spin-charge hybrid qubits having been demonstrated as hopeful candidates for foundational building blocks of future quantum processors [34][35][36][37][38][39][40], accurately characterizing tunnel coupling between quantum dots is an imperative task in characterizing these qubits.…”