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Chinese Physics B

Deterministic implementations of fermionic quantum SWAP and Fredkin gates for spin qubits based on charge detection

Hong‐Fu Wang, Shou Zhang, Ai‐Dong Zhu

Published Apr 1, 2012• 4 citations
Publisher

Abstract

We propose a scheme to implement fermionic quantum SWAP and Fredkin gates for spin qubits with the aid of charge detection. The scheme is deterministic without the need of qubit—qubit interaction, and the proposed setups consist of simple polarizing beam splitters, single-spin rotations, and charge detectors. Compared with linear optics quantum computation, this charge-measurement-based qubit scheme greatly enhances the success probability for implementing quantum SWAP and Fredkin gates and greatly simplifies the experimental realization of scalable quantum computers with noninteracting electrons.

DOI
10.1088/1674-1056/21/4/040306

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We propose a scheme to implement fermionic quantum SWAP and Fredkin gates for spin qubits with the aid of charge detection. The scheme is deterministic without the need of qubit—qubit interaction, and the proposed setups consist of simple polarizing beam splitters, single-spin rotations, and charge detectors. Compared with linear optics quantum computation, this charge-measurement-based qubit scheme greatly enhances the success probability for implementing quantum SWAP and Fredkin gates and greatly simplifies the experimental realization of scalable quantum computers with noninteracting electrons.
We propose a scheme to implement fermionic quantum SWAP and Fredkin gates for spin qubits with the aid of charge detection. The scheme is deterministic without the need of qubit–qubit interaction, and the proposed setups consist of simple polarizing beam splitters, single-spin rotations, and charge detectors. Compared with linear optics quantum computation, this charge-measurement-based qubit scheme greatly enhances the success probability for im- plementing quantum SWAP and Fredkin gates and greatly simplifies the experimental realization of scalable quantum computers with noninteracting electrons.
We propose a protocol and physical implementation for partial Bell-state measurements of Fermionic qubits, allowing for deterministic quantum computing in solid-state systems without the need for two-qubit gates. Our scheme consists of two spin qubits in a double quantum dot where the two dots have different Zeeman splittings and resonant tunneling between the dots is only allowed when the spins are antiparallel. This converts spin parity into charge information by means of a projective measurement and can be implemented with established technologies. This measurement-based qubit scheme greatly simplifies the experimental realization of scalable quantum computers in electronic nanostructures.
This paper proposes a fermionic linear optical scheme for the teleportation and entanglement concentration via entanglement swapping based on charge detection. It also proves that this method is useful in generating entangled states such as GHZ states, W states, and cluster states by using fermionic polarizing beam splitters and single spin rotations assisted by a parity check on the fermionic qubits. This scheme is nearly deterministic (i.e., with 100% successful probability) and does not need the joint Bell state measurement required in the previous schemes.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only ddd PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to their relatively easy manipulation and realization. We present efficient schemes to implement controlled-not (cnot) gates and controlled-swap (Fredkin) gates by using solely linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd level), respectively. On the basis of the hybrid encoding, cnot and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a cnot gate has been reduced to one polarizing beam splitter, while only ddd polarizing beam splitters are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to 1 and and are dimension independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7% under realistic conditions, which is higher than in previous schemes.
It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speedup of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a CNOT (controlled NOT) gate for free fermions, using only beam splitters and spin rotations. The gate is nearly deterministic if the charge detector counts the number of electrons in a mode, and fully deterministic if it only measures the parity of that number.