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arXiv:quant-ph/0402098 · Journal of Modern Optics

Overview of quantum error prevention and leakage elimination

Mark Byrd, Lian-Ao Wu, Daniel A. Lidar

Published Nov 1, 2004• 44 citations
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Abstract

Quantum error prevention strategies will be required to produce a scalable quantum computing device and are of central importance in this regard. Progress in this area has been quite rapid in the past few years. In order to provide an overview of the achievements in this area, we discuss the three major classes of error prevention strategies, the abilities of these methods and the shortcomings. We then discuss the combinations of these strategies which have recently been proposed in the literature. Finally, we present recent results in reducing errors on encoded subspaces using decoupling controls. We show how to generally remove mixing of an encoded subspace with external states (termed leakage errors) using decoupling controls. Such controls are known as ‘leakage elimination operations’ or ‘LEOs’.

DOI
10.1080/09500340408231803

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Quantum error prevention strategies will be required to produce a scalable quantum computing device and are of central importance in this regard. Progress in this area has been quite rapid in the past few years. In order to provide an overview of the achievements in this area, we discuss the three major classes of error prevention strategies, the abilities of these methods and the shortcomings. We then discuss the combinations of these strategies which have recently been proposed in the literature. Finally, we present recent results in reducing errors on encoded subspaces using decoupling controls. We show how to generally remove mixing of an encoded subspace with external states (termed leakage errors) using decoupling controls. Such controls are known as ‘leakage elimination operations’ or ‘LEOs’.
Decoherence-induced leakage errors can potentially damage physical or logical qubits embedded in a subspace of the entire Hilbert space by coupling them to other system levels. Here we report the first experimental implementation of Leakage Elimination Operators (LEOs) that aims to reduce this undermining. LEOs are a type of dynamical decoupling control that have been previously introduced to counteract leakage from a chosen subspace into the rest of a Hilbert space, and have been widely explored theoretically. Different from other error correction strategies, LEOs are compatible with any gate sequence in a code space, and thus, compatible with universal quantum computation. Using IBM's cloud quantum computer (QC), we design three potentially applicable examples of subspaces in two- and three-qubit Hilbert spaces and derive the explicit forms of the corresponding LEOs for these subspaces. For the first time, we experimentally demonstrate that these LEOs significantly suppress leakage. The results also show that the LEO time-scale condition can be satisfied with noise in the IBM's cloud QC and pave a way for quantum setups to get rid of leakage trouble.
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange-type interactions. This uses a decoherence-free subspace and an efficient set of dynamical decoupling operations. It also addresses the problem of controllability in solid-state quantum dot devices.
``Leakage'' errors are particularly serious errors which couple states within a code subspace to states outside of that subspace, thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for producing leakage elimination decoupling operations and examine the effects of the leakage eliminating operations on decoherence-free or noiseless subsystems which encode one logical, or protected qubit into three or four qubits. We find that by eliminating a large class of leakage errors, under some circumstances, we can create the conditions for a decoherence-free evolution. In other cases we identify a combined decoherence-free and quantum error correcting code which could eliminate errors in solid-state qubits with anisotropic exchange interaction Hamiltonians and enable universal quantum computing with only these interactions.
Proposals for scalable quantum computing devices suffer not only from decoherence due to their interaction with the environment, but also from severe engineering constraints. For example, our ability to implement quantum gates is determined, in part, by the experimentally available interactions with which quantum information may be processed. Here we review a practical solution to some of the major concerns, control and error prevention, addressing solid state proposals for quantum computing devices. Some noise is eliminated by encoding a logical qubit into two qubits, other noise is reduced by an efficient set of decoupling pulse sequences. The same encoding removes the need for single-qubit operations which pose a difficult design constraint. We also discuss several generalizations which follow from this work.
Decoherence-induced leakage errors can potentially damage physical or logical qubits by coupling them to other system levels. Here we report the first experimental implementation of Leakage Elimination Operators (LEOs) that aims to reduce this undermining, and that can be applied alongside universal quantum computing. Using IBM's cloud quantum computer, we have studied three potentially applicable examples of subspaces in two- and three-qubit Hilbert spaces and found that the LEOs significantly suppress leakage.
High-fidelity quantum operations require the system dynamics to be strictly confined to the computational subspace. In practice, however, control fields inevitably couple to leakage levels, giving rise to quantum state leakage that significantly reduces the fidelity of the operation. To address this challenge, we propose a general strategy for actively suppressing leakage errors by applying small, static offsets to tunable system parameters. This approach systematically mitigates leakage's detrimental impact on quantum control, without modifying the original control framework or incurring additional time overhead. By avoiding the need for extra suppression pulses or complex optimization procedures altogether, it offers a streamlined solution for leakage compensation while remaining fully compatible with subsequent optimal control techniques. Numerical validation conducted on superconducting quantum circuits demonstrates effective leakage suppression, enabling high-fidelity single-qubit gates, precise control of two-qubit interactions, and perfect state transfer in multi-level systems. Moreover, when integrated with optimal control techniques, our approach also allows for the cooperative suppression of both leakage errors and residual crosstalk. Therefore, this work provides a feasible technical pathway toward the low error thresholds required for fault-tolerant quantum computation.