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Applied Physics Letters

Decoherence suppression combining quantum uncollapsing and dynamical decoupling

Kai Xu, Xiayu Linpeng, Z. L. Wang

Published Jun 30, 2014• 2 citations
Publisher

Abstract

We demonstrate a protocol, that combines quantum uncollapsing and dynamical decoupling, to protect the quantum state stored in a qubit against decoherence errors. The protocol can simultaneously suppress the two kinds of decoherence processes: the energy relaxation and the low-frequency noise induced dephasing. We present the analytical derivation and numerical simulations in detail. We also provide a preliminary experimental test in superconducting phase qubits, using the process fidelity to calibrate the performance of the protocol. Our results suggest that the protocol can be effective against errors due to both energy relaxation and the low-frequency dephasing noise, except at a reduced probability of success.

DOI
10.1063/1.4885836

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We demonstrate a protocol, that combines quantum uncollapsing and dynamical decoupling, to protect the quantum state stored in a qubit against decoherence errors. The protocol can simultaneously suppress the two kinds of decoherence processes: the energy relaxation and the low-frequency noise induced dephasing. We present the analytical derivation and numerical simulations in detail. We also provide a preliminary experimental test in superconducting phase qubits, using the process fidelity to calibrate the performance of the protocol. Our results suggest that the protocol can be effective against errors due to both energy relaxation and the low-frequency dephasing noise, except at a reduced probability of success.
A central task towards building a practical quantum computer is to protect individual qubits from decoherence while retaining the ability to perform high-fidelity entangling gates involving arbitrary two qubits. Here we propose and demonstrate a dephasing-insensitive procedure for storing and processing quantum information in an all-to-all connected superconducting circuit involving multiple frequency-tunable qubits, each of which can be controllably coupled to any other through a central bus resonator. Although it is generally believed that the extra frequency tunability enhances the control freedom but induces more dephasing impact for superconducting qubits, our results show that any individual qubit can be dynamically decoupled from dephasing noise by applying a weak continuous and resonant driving field whose phase is reversed in the middle of the pulse. More importantly, we demonstrate a new method for realizing a two-qubit phase gate with inherent dynamical decoupling via the combination of continuous driving and qubit-qubit swapping coupling. We find that the weak continuous driving fields not only enable the conditional dynamics essential for quantum information processing, but also protect both qubits from dephasing during the gate operation.
A fundamental challenge for quantum information processing is reducing the impact of environmentally induced errors. Here we demonstrate a quantum error detection and rejection protocol based on the idea of quantum uncollapsing, using this protocol to reduce the impact of energy relaxation owing to the environment in a three-qubit superconducting circuit. We encode quantum information in a target qubit, and use the other two qubits to detect and reject errors caused by energy relaxation. This protocol improves the storage time of a quantum state by a factor of roughly three, at the cost of a reduced probability of success. This constitutes the first experimental demonstration of the algorithm-based improvement in the lifetime of a quantum state stored in a qubit. © 2014 Macmillan Publishers Limited. All rights reserved.
We investigate the capability of dynamical decoupling techniques to reduce decoherence from a realistic environment generating 1/f noise. The predominance of low frequency modes in the noise profile allows for decoherence scenarios where relatively slow control rates suffice for a drastic improvement. However, the actual figure of merit is very sensitive to the details of the dynamics, with decoupling performance which may deteriorate for non-Gaussian noise and/or high frequency working points. Our results are promising for robust solid-state qubits and beyond.
This dissertation presents a theoretical analysis of protocols relevant for quantum information processing with superconducting qubits. The purpose of these protocols is decoherence suppression and quantum information transfer. Our analysis makes use of the standard density matrix formalism and Kraus operator (operator-sum) representation of quantum operations. We also use the mathematical trick of unravelling continuous evolution into discrete scenarios with corresponding probabilities.We show that decoherence due to zero-temperature energy relaxation can be almost completely suppressed, probabilistically, by weak measurement reversal (also known as quantum uncollapsing). To protect a qubit, a weak (partial) quantum measurement moves it towards the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength.We also analyze several simple quantum error correction (QEC) and quantum error detection (QED) protocols, relevant to superconducting qubits. We show that for energy relaxation the repetitive N-qubit quantum codes cannot be used for QEC, but can be used for QED (also known as probabilistic error correction). Moreover, the repetitive code with only two qubits is sufficient for QED. We also present several other two-qubit algorithms realizable with the current technology of superconducting phase qubits; these algorithms can demonstrate QEC for intentional errors and QED for real decoherence.We also analyze a procedure designed to transfer the state of a microwave qubit from one superconducting resonator to another resonator via a transmission line; the emission and capture of the microwave energy is achieved using tunable couplers. The procedure is shown to be robust against experimental imperfections of required pulse shapes. Our results also indicate that a successful state transfer requires nearly equal resonator frequencies for the entire duration of the procedure.
We show that qubit decoherence due to zero-temperature energy relaxation can be almost completely suppressed by using the quantum uncollapsing (measurement reversal) procedure. To protect a qubit state, a partial quantum measurement moves it toward the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength. The experiment can be realized in a straightforward way using the superconducting phase qubit.
Hybrid systems consisting of different types of qubits are promising for building quantum computers if they combine useful properties of their constituent qubits. However, they also pose additional challenges if one type of qubits is more susceptible to environmental noise than the others. Dynamical decoupling can help to protect such systems by reducing the decoherence due to the environmental noise, but the protection must be designed such that it does not interfere with the control fields driving the logical operations. Here, we test such a protection scheme on a quantum register consisting of the electronic and nuclear spins of a nitrogen-vacancy center in diamond. The results show that processing is compatible with protection: The dephasing time was extended almost to the limit given by the longitudinal relaxation time of the electron spin.