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International Journal of Quantum Information

IMPLEMENTATION OF QUANTUM LOGIC OPERATIONS AND CREATION OF ENTANGLEMENT BETWEEN TWO NUCLEAR SPIN QUBITS WITH CONSTANT INTERACTION

G. P. Berman, Geoffrey W. Brown, M. E. Hawley, D. I. Kamenev, V. I. Tsifrinovich

Published Dec 1, 2006• 0 citations
Publisher

Abstract

We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear–electron hyperfine and electron–electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Controlled-NOT gate. The exchange interaction is constant, and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper, parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.

DOI
10.1142/s0219749906002353

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We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear–electron hyperfine and electron–electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Controlled-NOT gate. The exchange interaction is constant, and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper, parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.
We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear-electron hyperfine and electron-electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Control-Not gate. The exchange interaction is constant and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.
The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using controlled-NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a controlled-NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small.
The use of nuclear spins for quantum computation is limited by the difficulty in creating genuine quantum entanglement between distant nuclei. Current demonstrations of nuclear entanglement in semiconductors rely on coupling the nuclei to a common electron, which is not a scalable strategy. In this work, we demonstrated a two-qubit controlled-Z logic operation between the nuclei of two phosphorus atoms in a silicon device, separated by up to 20 nanometers. Each atom binds separate electrons, whose exchange interaction mediates the nuclear two-qubit gate. We prepared and measured a nuclear Bell state with a fidelity of [Formula: see text] and a concurrence of [Formula: see text]. With this method, future progress in scaling up semiconductor spin qubits can be extended to the development of nuclear spin-based quantum computers.
Abstract Phosphorus atoms in silicon are an outstanding platform for quantum computing as their nuclear spins exhibit coherence time over seconds [1, 2]. By placing multiple phosphorus atoms within a radius of a few nanometers, they couple via the hyperfine interaction to a single, shared electron. Such a nuclear spin register enables multi-qubit control above the fault-tolerant threshold [3] and the execution of small-scale quantum algorithms [4]. To achieve quantum error correction, fast and efficient interconnects have to be implemented between spin registers while maintaining high fidelity across all qubit metrics. Here, we demonstrate such integration with a fully controlled 11-qubit atom processor composed of two multi-nuclear spin registers which are linked via electron exchange interaction. Through the development of scalable calibration and control protocols, we achieve coherent coupling between nuclear spins using a combination of single- and multi-qubit gates with all fidelities ranging from 99.5% to 99.99%. We verify the efficient all-to-all connectivity by preparing both local and non-local Bell states with a record state fidelity beyond 99% and extend entanglement through the generation of Greenberger-Horne-Zeilinger (GHZ) states over all data qubits. By establishing high-fidelity operation across interconnected nuclear-spin registers, we ealise a key milestone towards fault-tolerant quantum computation with atom processors.
We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. Since the wavelength of the radio-frequency pulses is much larger than the distance between the spins, each pulse affects all spins in the chain and introduces the phase and probability errors, which occur even without the influence of the environment. These errors caused by the unwanted transitions are minimized and computed numerically.
We suggest an architecture for quantum computing with spin-pair encoded qubits in silicon. Electron-nuclear spin-pairs are controlled by a dc magnetic field and electrode-switched on and off hyperfine interaction. This digital processing is insensitive to tuning errors and easy to model. Electron shuttling between donors enables multiqubit logic. These hydrogenic spin qubits are transferable to nuclear spin-pairs, which have long coherence times, and electron spin-pairs, which are ideally suited for measurement and initialization. The architecture is scalable to a highly parallel operation.