Suppressing decoherence of quantum algorithms by jump codes

The stabilizing properties of one-error correcting jump codes are explored under realistic non-ideal conditions. For this purpose the quantum algorithm of the tent-map is decomposed into a universal set of Hamiltonian quantum gates which ensure perfect correction of spontaneous decay processes under ideal circumstances even if they occur during a gate operation. An entanglement gate is presented which is capable of entangling any two logical qubits of different one-error correcting code spaces. With the help of this gate simultaneous spontaneous decay processes affecting physical qubits of different code spaces can be corrected and decoherence can be suppressed significantly

Arbitrarily Accurate Dynamical Control in Open Quantum Systems

We show that open-loop dynamical control techniques may be used to synthesize unitary transformations in open quantum systems in such a way that decoherence is perturbatively compensated for to a desired (in principle arbitrarily high) level of accuracy, which depends only on the strength of the relevant errors and the achievable rate of control modulation. Our constructive and fully analytical solution employs concatenated dynamically corrected gates, and is applicable independently of detailed knowledge of the system-environment interactions and environment dynamics. Explicit implications for boosting quantum gate fidelities in realistic scenarios are addressed.Comment: 4 pages and 20 characters, 1 figure [improvements and fixes, PRL version

Dynamically Error-Corrected Gates for Universal Quantum Computation

Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary gates on an open quantum system without encoding or measurement overhead. Our results allow for a low-level error correction strategy solely based on Hamiltonian engineering using realistic bounded-strength controls and may substantially reduce implementation requirements for fault-tolerant quantum computing architectures.Comment: 5 pages, 3 figure

Automated Synthesis of Dynamically Corrected Quantum Gates

We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotations subject to realistic timing and pulse-shaping constraints are provided, which can deliver substantially improved gate fidelity for state-of-the-art experimental capabilities.Comment: 5 pages; further restructure and expansio

Fault-Tolerant Quantum Dynamical Decoupling

Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. Here we introduce a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors. This is important for coherent control of quantum systems such as quantum computers. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, we show that it is strictly advantageous to use concatenated, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault-tolerant and super-polynomially more efficient, at equal cost. We derive a condition on the pulse noise level below which concatenated is guaranteed to reduce decoherence.Comment: 5 pages, 4 color eps figures. v3: Minor changes. To appear in Phys. Rev. Let

Rigorous Bounds on the Performance of a Hybrid Dynamical-Decoupling Quantum-Computing Scheme

We study dynamical decoupling in a multiqubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the computation. We derive a rigorous error bound on the trace distance or fidelity between the desired computational state and the actual time-evolved state, for a system subject to coupling to a bounded-strength bath. The bound is expressed in terms of the operator norm of the effective Hamiltonian generating the evolution in the presence of decoupling and logic operations. We apply the bound to the case of periodic pulse sequences and find that in order to maintain a constant trace distance or fidelity, the number of cycles—at fixed pulse interval and width—should scale in inverse proportion to the square of the number of qubits. This sets a scalability limit on the protection of quantum computation using periodic dynamical decoupling