We propose a selective dynamical decoupling scheme on a chain of permanently coupled qubits with XX-type interactions, which is capable of dynamically suppressing any coupling in the chain by applying sequences of local pulses to the individual qubits. We demonstrate that high-fidelity single- and two-qubit gates can be achieved by this procedure and that sequences of gates can be implemented by this pulse control alone. We discuss the applicability and physical limitations of our model specifically for strongly coupled superconducting flux qubits. Since dynamically modifying the couplings between flux qubits is challenging, they are a natural candidate for our approach.
We investigate the feasibility for the preservation of coherence and entanglement of one- and two-spin qubits coupled to an interacting quantum spin-1/2 chain within the dynamical decoupling (DD) scheme. The performance is examined by counting the number of computing pulses that can be applied periodically with periods of
T before qubits become decoherent, while an identical decoupling pulse sequence is applied within each cycle. By considering pulses with mixed directions and finite width controlled by magnetic fields, it is shown that pulse-width accumulation degrades the performance of sequences with larger numbers of pulses and that feasible magnetic fields in practice restrict consideration to sequences with few than 10 decoupling pulses within each cycle. Furthermore, within each cycle
T, exact nontrivial pulse sequences are found to suppress the qubit-bath coupling to
O(TN+1) progressively with the minimum number of pulses being 4, 7, and 12 for
N=1,2,3. These sequences, when applied to all qubits, are shown to preserve both the entanglement and coherence. Based on time-dependent density matrix renormalization, our numerical results show that for modest magnetic fields (10--40 T) available in laboratories, the overall performance is optimized when the number of pulses in each cycle is 4 or 7 with pulse directions alternating between
x and
z. Our results provide useful guides for the preservation of coherence and entanglement of spin qubits in the solid state.
We address the problem of decoupling the interactions in a spin network governed by a pair-interaction Hamiltonian. Combinatorial schemes for decoupling and for manipulating the couplings of Hamiltonians have been developed, which use selective pulses. In this paper, we consider an additional requirement on these pulse sequences: as few different control operations as possible should be used. This requirement is motivated by the fact that to find an optimal implementation of each individual selective pulse will be expensive since it requires to solve a pulse shaping problem. Hence, it is desirable to use as few different selective pulses as possible. As a first result, we show that for d-dimensional systems, where d⩾2, the ability to implement only two control operations is sufficient to turn off the time evolution. Next, we address the case of a bipartite system with local control and show that four different control operations are sufficient. Finally, turning to networks consisting of several d-dimensional nodes, we show that decoupling can be achieved if one is able to control a number of different control operations, which is logarithmic in the number of nodes. We give an explicit family of efficient decoupling schemes with logarithmic number of different pulses based on the classic Hamming codes. We also provide a table of the best known decoupling schemes for small networks of qubits.
Uhrig's dynamical decoupling pulse sequence has emerged as a universal and highly promising approach to decoherence suppression. So far, both the theoretical and experimental studies have examined single-qubit decoherence only. This work extends Uhrig's universal dynamical decoupling from one-qubit to two-qubit systems and even to general multilevel quantum systems. In particular, we show that by designing appropriate control Hamiltonians for a two-qubit or a multilevel system, Uhrig's pulse sequence can also preserve a generalized quantum coherence measure to the order of
1+O(TN+1) with only
N pulses. Our results lead to a very useful scheme for efficiently locking two-qubit entangled states. Future important applications of Uhrig's pulse sequence in preserving the quantum coherence of multilevel quantum systems can also be anticipated.
A field configuration utilizing local static fields and a few continuous-wave driving fields is constructed to achieve universal (but low-order) protection of two-qubit states. That is, two-qubit states can be protected against arbitrary system-environment coupling with control fields if their frequencies are sufficiently large as compared with the cutoff frequency of the environment. Equally important, we show that it is possible to construct driving fields to protect two-qubit entangling gates against decoherence, without assuming any particular form of system-environment coupling. Using a non-Markovian master equation, we further demonstrate the effectiveness of our continuous dynamical decoupling fields in protecting entanglement and the excellent performance of protected two-qubit gates in generating entanglement. The results are complementary to current studies of entanglement protection using universal dynamical decoupling pulse sequences.
In the field of quantum information, a major challenge is to protect and shield quantum systems from environmental influences, which cause dissipation and decoherence. One approach to address this problem is called dynamical decoupling, where we act on a quantum system with a series of fast and strong local control operations. If done correctly, the system's state gets rotated in discrete steps in its state space in such a way that the effects of the environment cancel up to a certain order. In the first part of this thesis, we will introduce the basics of dynamical decoupling and present a new approach for constructing dynamical decoupling schemes based on sequences of Weyl operators on networks of qudits. This approach goes beyond merely protecting a quantum system, as it is also capable of altering existing Hamiltonian interactions in ways suitable for quantum simulation purposes. We will also investigate how imperfect controls influence the effectiveness of dynamical decoupling and focus particularly on stochastic noise. In the second part of the thesis, we study concrete scenarios for the application of dynamical decoupling. First, we consider the task of quantum state transfer on a linear chain of qubits and use decoupling to protect the transfer from detrimental influences caused by a bend in the chain. We also look at how to design the specific interaction strengths required on the chain to make the state transfer work and extend this result to chains of qudits. Another chapter deals with decoupling the atomic centre-of-mass motion of a trapped atom or ion in a cavity interacting with a radiation field. Finally, we use decoupling to execute sequences of one- and two-qubit quantum gates on a chain of coupled qubits. Particular care is taken to ensure high fidelity operations in the presence of imperfect decoupling pulses.