Temporal interferometry: A mechanism for controlling qubit transitions during twisted rapid passage with possible application to quantum computing

Abstract

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle φ(t) at the same time that it is inverted. For polynomial twist: φ(t) ∼ Bt n . We show that for n ≥ 3, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength B, which can be used to control the time-separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wavefunction. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.

Indirect methods to control population distribution in a large spin system

“…Also, Landau-Zener-Stückelberg interferometry, based on periodic passage of an avoided level crossing responsible for the LZ transition, has been found to be a useful tool for studying properties of atomic and superconducting qubit systems [36], including perfect population transfer and implementation quantum gates for quantum control and quantum computing [37][38][39].…”

High-fidelity quantum state preparation using neighboring optimal control

“…where |ψ 0, f is a good approximation to the Bell state |β 01 . In this subsection we use a form of non-adiabatic rapid passage known as twisted rapid passage (TRP) [4,5] to provide the nominal control F 0 (t). The reader will find a summary of TRP essentials in Appendix A.…”

“…A TRP essentials and the dimensionless Hamiltonian H 0 det (τ) (i) TRP Essentials: To introduce twisted rapid passage (TRP) [4,5] we consider a single-qubit interacting with an external field F(t) via the Zeeman interaction H(t) = −σ · F(t), where the σ i are the Pauli matrices (i = x, y, z). TRP is a generalization of adiabatic rapid passage (ARP).…”

“…In Section 2 we formulate the NOC problem and determine the Euler-Lagrange equations whose solution determines the optimal control F * (t) and the resulting optimal quantum state |ψ * . In Section 3 (4) we illustrate the general approach by using it to prepare a high-fidelity approximation to the two qubit Bell state |β 01 = (1/ √ 2) [ |01 + |10 ] with error probability ε ∼ 10 −6 (10 −5 ), assuming ideal (non-ideal) control. The high-fidelity of the final state provides proof-of-principle for the performance gains possible using NOC, even in the presence of imperfect control.…”

Zhu-Nakamura theory and the superparabolic level-glancing models

“…The relevance of this model, besides its relative simplicity, comes from the fact that the transitions are localized in the vicinity of the crossings so the above-mentioned behavior of the energy levels and the coupling often form a good approximation to describe the dynamics of many real physical systems. This and other level-crossing models have been widely applied over the years, for example, to the studies of atomic and molecular collisions [1,2], laser-atom interactions [8], and quantum information processing [9] and in attempts to understand the dynamics of quantum phase transitions [10,11].…”