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arXiv:quant-ph/0401066 · Physical Review Letters

Charge Detection Enables Free-Electron Quantum Computation

C. W. J. Beenakker, David Peter Divincenzo, Clive Emary, M. Kindermann

Published Jul 6, 2004• 195 citations
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Abstract

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.

DOI
10.1103/physrevlett.93.020501

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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.
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 investigate how to carry out universal quantum computation deterministically with free electrons in decoherence-free subspace by using polarizing beam splitters, charge detectors, and single-spin rotations. Quantum information in our case is encoded in spin degrees of freedom of the electron-pairs which construct a decoherence-free subspace. We design building blocks for two noncommutable single-logic-qubit gates and a logic controlled phase gate, based on which a universal and scalable quantum information processing robust to dephasing is available in a deterministic way.
The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyze the parity gate (PPP gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with PPP gates and show that native networks simplify considerably the resources required for producing multiqubit entanglement, such as nnn--Greenberg-Horne-Zellinger (GHZ) states. Other applications include a Bell-state analyzer and teleportation. We also show that cluster state fusion can be performed deterministically with parity measurements. We then extend this analysis to hybrid quantum networks containing spin and mode qubits. Starting from an easy-to-prepare resource (spin-mode entanglement of single electrons) we show how to produce a spin nnn-GHZ state with linear elements (beam splitters and local spin flips) and charge-parity detectors; this state can be used as a resource in a spin quantum computer or as a precursor for constructing cluster states. Finally, we construct an alternative spin-controlled-ZZZ gate by using the mode degrees of freedom as ancill\ae{}.
Based on electron spins in semiconductor quantum dots as qubits, a new quantum controlled-NOT (CNOT) gate is constructed in solid nanostructure without resorting to spin-spin interactions. Single-electron tunneling technology and coherent quantum-dot cellular-automaton architecture are used to generate an ancillary charge entangled state. Using the ancillary charge entangled state as an intermediate state, we obtain a spin entangled state and design a CNOT gate by using only single-spin rotations.
We discuss a measurement-based implementation of a controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins 1/2 or in equivalent systems. The key to such an extension is to find a feasible qubit-parity meter. We present a general scheme for reducing this qubit-parity meter to a local spin-parity measurement performed on two spins, one from each qubit. Two possible realizations of a multiparticle CNOT gate are further discussed: electron spins in double quantum dots in the singlet-triplet encoding, and $\ensuremath{\nu}=5/2$ Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.