Continuously decoupling single-qubit operations from a perturbing thermal bath of scalar bosons

Abstract

We investigate the use of continuously-applied external fields to maximize the fidelity of quantum logic operations performed on a decohering qubit. Assuming a known error operator and an environment represented by a scalar boson field at a finite temperature, we show how decoherence during logical operations can be efficiently reduced by applying a superposition of two external vector fields: one rotating orthogonally to the direction of the other, which remains static. The required field directions, frequency of rotation and amplitudes to decouple noise dynamically are determined by the coupling constants and the desired logical operation. We illustrate these findings numerically for a Hadamard quantum gate and an environment with ohmic spectral density.A quantum computer, when finally built, will be more efficient than current classical computers to solve certain kinds of problems [1]. The theory of quantum information processing generally takes advantage of the inherent parallelism exhibited by unitary operations on quantumstate superpositions. The terms of these linear combinations are tensor products of quantum bits, or "qubits" [2], which, linearly superposed, result in states with the desired properties of entanglement and interference [3]. In principle, the choice of an appropriate external field would guarantee a correct dynamics for the system, selected among those exhibiting unitary symmetry. However, during the actual quantum evolution of the system, since it cannot be completely separated from its environment, the unitary symmetry breaks down. The consequent decay of the quantum state purity is a manifestation of the ubiquitous phenomenon of decoherence [4].There are at least three major classes of strategic devices proposed to counteract the deleterious and unavoidable effects of decoherence: quantum error correcting codes [5], decoherence-free subspaces and subsystems [6], and dynamical decoupling [7,8,9,10]. Because the first two of these strategies require more than one physical qubit to protect each logical qubit, dynamical decoupling is the simplest of the three, since it requires, in principle, only controllable external fields to directly protect each physical qubit. Even without precise knowledge of the error structure and strengths, the pulsed dynamicaldecoupling scheme is effective, but usually employ an articulate time sequence of external-field pulses which, for experimental implementations, requires sophisticated control procedures. Moreover, the pulses have to be so short as to start and finish well within the environmental correlation time interval, so the field intensities involved must be high. Initial attempts to use continuously- * Electronic address: felipe@ifsc.usp.br applied fields instead of pulses have appeared recently [11] and these preliminary analyses show that, although pulses are not necessary for protecting against the effects of particular error structures assumed known, employing fast control cycles is inevitable. From the practical point of view of experimental rea...

Protecting theSWAPoperation from general and residual errors by continuous dynamical decoupling

“…This scheme, known as continuous dynamical decoupling (CDD), has attracted a lot of attention in recent years [26][27][28][29][30][31][32][33][34][35]. The CDD procedure is more experimentally friendly than pulsed procedures and it also sets a natural stage for the implementation of two-qubit quantum gates [36][37][38].…”

Decoherence control: Universal protection of two-qubit states and two-qubit gates using continuous driving fields

“…Our procedure is analogous to Ref. [46,47], but for most general systemenvironment coupling in two-qubit systems. The extension here is worthwhile because in actual realizations of two-qubit gates, it is unavoidable that the two-qubit interaction Hamiltonian will suffer from fluctuations, on top of local noise terms seen by each individual qubit.…”

“…Indeed, continuous DD schemes to protect a single qubit have attracted considerable interest [44][45][46][47]. Among the known features of single-qubit continuous DD, most relevant here is the fact that continuous control fields may be constructed to protect a quantum state and implement a gate at the same time, without the use of any overhead [46,47] (thus forming a type of DCG [41,42]). However, it is imperative, considering the complexity of two-qubit decoherence, that such Hamiltonians be constructed for twoqubit gates as well.…”

“…For example, there is no longer any concern about pulse timings or pulse-sequence engineering, and the higher driving frequencies that we can achieve with continuous fields are naturally expected to eliminate higher frequency noise sources [44]. Indeed, continuous DD schemes to protect a single qubit have attracted considerable interest [44][45][46][47]. Among the known features of single-qubit continuous DD, most relevant here is the fact that continuous control fields may be constructed to protect a quantum state and implement a gate at the same time, without the use of any overhead [46,47] (thus forming a type of DCG [41,42]).…”

Proposal for High-Fidelity Quantum Simulation Using a Hybrid Dressed State

“…quantum error correction [13,14], decoherence free subspace [15][16][17][18][19][20][21], and dynamical decoupling [22][23][24][25][26][27][28][29][30][31], have been developed for the suppression or avoidance of quantum decoherence. Each of these methods are best suited for specific scenarios.…”