Quantum information can be protected from noise and decoherence by encoding it into a decoherence-free subspace of the full Hilbert space. In this approach, it is important to devise implementations of quantum logic gates acting on the encoded logical qubits. Here, we experimentally investigate the implementation of an entangling linear optical controlled- $Z$ gate on two logical qubits encoded into pairs of physical qubits, which protects the quantum information from collective dephasing. This decoherence-resilient two-qubit gate on logical qubits is realized using a suitable four-qubit quantum gate on the physical qubits, which may help to protect the encoded quantum information from systematic errors arising due to imperfect operations on single logical qubits. We characterize the gate operation on input superposition states and demonstrate its ability to protect quantum coherence even under complete collective dephasing.Quantum information can be protected from noise and decoherence by encoding it into a decoherence-free subspace of the full Hilbert space. In this approach, it is important to devise implementations of quantum logic gates acting on the encoded logical qubits. Here, we experimentally investigate the implementation of an entangling linear optical controlled-$Z$ gate on two logical qubits encoded into pairs of physical qubits, which protects the quantum information from collective dephasing. This decoherence-resilient two-qubit gate on logical qubits is realized using a suitable four-qubit quantum gate on the physical qubits, which may help to protect the encoded quantum information from systematic errors arising due to imperfect operations on single logical qubits. We characterize the gate operation on input superposition states and demonstrate its ability to protect quantum coherence even under complete collective dephasing.

Physical Review AppliedNov 25, 20203 citations

Single-loop realization of universal nonadiabatic holonomic gates in decoherence-free subspaces

Chang Wang, Zhenping Guo

Control errors and decoherence are two main obstacles for realization of quantum computation. Nonadiabatic holonomic quantum computation in decoherence-free subspaces can protect quantum gates from both control errors and decoherence, and, therefore, it has received increasing attention. The original protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces needs two loops in the Grassmann manifold to generate an arbitrary nonadiabatic holonomic one-qubit gate. In this paper, we proposed a protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, where an arbitrary one-qubit gate is generated by only a single loop in the Grassmann manifold and an entangling two-qubit gate assisted by two single-qubit gates can be used to construct a two-qubit controlled unitary gate. In addition, the encoding of our protocol for nonadiabatic holonomic gates requires a lower number of physical qubits compared with previous schemes. Our scheme not only maintains the merits of the original protocol but it also avoids the extra work of combining two gates to realize an arbitrary one-qubit gate.Control errors and decoherence are two main obstacles for realization of quantum computation. Nonadiabatic holonomic quantum computation in decoherence-free subspaces can protect quantum gates from both control errors and decoherence, and, therefore, it has received increasing attention. The original protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces needs two loops in the Grassmann manifold to generate an arbitrary nonadiabatic holonomic one-qubit gate. In this paper, we proposed a protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, where an arbitrary one-qubit gate is generated by only a single loop in the Grassmann manifold and an entangling two-qubit gate assisted by two single-qubit gates can be used to construct a two-qubit controlled unitary gate. In addition, the encoding of our protocol for nonadiabatic holonomic gates requires a lower number of physical qubits compared with previous schemes. Our scheme not only maintains the merits of the original protocol but it also avoids the extra work of combining two gates to realize an arbitrary one-qubit gate.

Europhysics Letters (EPL)Dec 10, 201810 citations

Two-Qubit Gate Theory

Christopher J. Ballance

Springer thesesJan 1, 20170 citations

Infidelity Induced by Ground-Rydberg Decoherence of the Control Qubit in a Two-Qubit Rydberg-Blockade Gate

Yangyang Liu, Yuan Sun, Zhuo Fu +5 more

For neutral-atom qubits, two-qubit gates are typically realized via the Rydberg-blockade effect, which hints at the special status of Rydberg levels compared with regular qubit register states. However, the experimental and theoretical studies that have been done to reveal how the ground-Rydberg coherence of the control-qubit atom affects the fidelity of a two-qubit gate are not yet adequate, especially when all experimental two-qubit gates feature a single atom that stays in the Rydberg state for a certain time. Here, we perform a careful investigation of decoherence in ground-Rydberg transitions in a single atom with various pulse sequences. In particular, based on the commonly used controlled- $Z$ ( ${C}_{Z}$ ) gate sequence proposed by D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000), we observe that a control-qubit atom subject to a two-qubit entangling process with the $H$ - ${C}_{Z}$ controlled-not gate scheme experiences a process that is essentially similar to ground-Rydberg Ramsey interference. Then, we build a straightforward theoretical model to link the decoherence time ${\ensuremath{\tau}}_{\mathrm{gr}}$ of the control qubit (extracted from Ramsey fringes of the ground-Rydberg transition) to this ${C}_{Z}$ pulse sequence, and also analyze the typical origins of decoherence effects. Finally, we discuss the loss of fidelity of the ${C}_{Z}$ gate due to the limits imposed by the ground-Rydberg coherence properties, and the prospect of improving fidelity with refined gate protocols.For neutral-atom qubits, two-qubit gates are typically realized via the Rydberg-blockade effect, which hints at the special status of Rydberg levels compared with regular qubit register states. However, the experimental and theoretical studies that have been done to reveal how the ground-Rydberg coherence of the control-qubit atom affects the fidelity of a two-qubit gate are not yet adequate, especially when all experimental two-qubit gates feature a single atom that stays in the Rydberg state for a certain time. Here, we perform a careful investigation of decoherence in ground-Rydberg transitions in a single atom with various pulse sequences. In particular, based on the commonly used controlled-$Z$ (${C}_{Z}$) gate sequence proposed by D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000), we observe that a control-qubit atom subject to a two-qubit entangling process with the $H$-${C}_{Z}$ controlled-not gate scheme experiences a process that is essentially similar to ground-Rydberg Ramsey interference. Then, we build a straightforward theoretical model to link the decoherence time ${\ensuremath{\tau}}_{\mathrm{gr}}$ of the control qubit (extracted from Ramsey fringes of the ground-Rydberg transition) to this ${C}_{Z}$ pulse sequence, and also analyze the typical origins of decoherence effects. Finally, we discuss the loss of fidelity of the ${C}_{Z}$ gate due to the limits imposed by the ground-Rydberg coherence properties, and the prospect of improving fidelity with refined gate protocols.

arXiv:2012.12589Physical Review AppliedMay 11, 202128 citations

Decoherence in Josephson Qubits

R. McDermott

Bulletin of the American Physical SocietyMar 14, 20060 citations

Z

gate on two logical qubits encoded into pairs of physical qubits, which protects the quantum information from collective dephasing. This decoherence-resilient two-qubit gate on logical qubits is realized using a suitable four-qubit quantum gate on the physical qubits, which may help to protect the encoded quantum information from systematic errors arising due to imperfect operations on single logical qubits. We characterize the gate operation on input superposition states and demonstrate its ability to protect quantum coherence even under complete collective dephasing.

Z

(

{C}_{Z}

) gate sequence proposed by D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000), we observe that a control-qubit atom subject to a two-qubit entangling process with the

H

{C}_{Z}

controlled-not gate scheme experiences a process that is essentially similar to ground-Rydberg Ramsey interference. Then, we build a straightforward theoretical model to link the decoherence time ${\ensuremath{\tau}}_{\mathrm{gr}}$ of the control qubit (extracted from Ramsey fringes of the ground-Rydberg transition) to this

{C}_{Z}

pulse sequence, and also analyze the typical origins of decoherence effects. Finally, we discuss the loss of fidelity of the

{C}_{Z}

gate due to the limits imposed by the ground-Rydberg coherence properties, and the prospect of improving fidelity with refined gate protocols.