A two-qubit conditional quantum gate with single spins

Fedor Jelezko, T. Gaebel, I. Popa, Michael Domhan, Achim Dieter Gruber, Jörg Wrachtrup

Published Feb 12, 2004• 0 citations

Abstract

A quantum logical NOT and a conditional two-qubit gate (CROT), are implemented with single spins in a solid. As quantum bits a single electron spin and a single 13C nuclear spin of a single nitrogen vacancy defect center in diamond are used. The quantum state of the electron spin can be read out optically. Owing to long decoherence and relaxation times the systems meets the requirements of hardware for quantum computation. Density matrix tomography of the CROT gate shows that the achieved performance of the two bit conditional quantum gate is promising. The gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms. Further on, the system may allow for solid-state room temperature quantum computation

Related papers

Observation of Coherent Oscillation of a Single Nuclear Spin and Realization of a Two-Qubit Conditional Quantum Gate

Fedor Jelezko, T. Gaebel, I. Popa +3 more

Rabi nutations of a single nuclear spin in a solid have been observed. The experiments were carried out on a single electron and a single 13C nuclear spin of a single nitrogen-vacancy defect center in diamond. The system was used for implementation of quantum logical NOT and a conditional two-qubit gate (CROT). Density matrix tomography of the CROT gate shows that the gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms.

arXiv:quant-ph/0402087Physical Review LettersSep 20, 2004735 citations

Single-Qubit Operations with the Nitrogen-Vacancy Center in Diamond

Thomas A. Kennedy, Forrest T. Charnock, John S. Colton +3 more

A concept combining optics and microwave pulses with the negative charge-state of the nitrogen-vacancy (NV—) center in diamond is demonstrated through experiments that are equivalent to single-qubit gates, and decoherence for this qubit is examined. The spin levels of the ground state provide the two-level system. Optical excitation provides polarization of these states. The polarized state is operated coherently by 35 GHz microwave pulses. The final state is read out through the photoluminescence intensity. Decoherence arises from different sources for different samples. For high-pressure, high-temperature synthetic diamonds, the high concentration of substitutional N limits the phase-memory to a few μs. In a single-crystal CVD diamond, the phase memory time is at least 32 μs at 100 K. 14N is tightly coupled to the electronic spin and produces modulation of the electron–spin echo decay under certain conditions. A two-qubit gate is proposed using this nuclear spin. This demonstration provides a great deal of insight into quantum devices in the solid state with some possibility for real application.

physica status solidi (b)Oct 1, 200243 citations

Universal high-fidelity quantum gates for spin qubits in diamond

Hans P. Bartling, Jiwon Yun, Kai-Niklas Schymik +8 more

Spins associated to solid-state color centers are a promising platform for investigating quantum computation and quantum networks. Recent experiments have demonstrated multiqubit quantum processors, optical interconnects, and basic quantum error-correction protocols. One of the key open challenges towards larger-scale systems is to realize high-fidelity universal quantum gates. In this work, we design and demonstrate a complete high-fidelity gate set for the two-qubit system formed by the electron and nuclear spin of a nitrogen-vacancy center in diamond. We use gate set tomography (GST) to systematically optimize the gates and demonstrate single-qubit gate fidelities of up to 99.999 ( 1 ) % and a two-qubit gate fidelity of 99.93 ( 5 ) % . Our gates are designed to decouple unwanted interactions and can be extended to other electron-nuclear spin systems. The high fidelities demonstrated provide opportunities towards larger-scale quantum processing with color-center qubits.

arXiv:2403.10633Physical Review AppliedMar 21, 202534 citations

Quantum computation using the 13C nuclear spins near the single NV defect center in diamond

Jörg Wrachtrup, S. Ya. Kilin, Alexander P. Nizovtsev

We discuss the possibility of realizing quantum computation on the basis of a cluster of single interacting nuclear spins in solids. This idea seems to be feasible because of the combination of two techniques—Single Molecule Spectroscopy and Optically Detected Electron Nuclear Double Resonance. Compared to the well-known bulk Nuclear Magnetic Resonance (NMR), the proposed method of quantum computation has the advantage that quantum computation is performed with pure spin states and the quantum processor is more easily scalable. At the same time, the advantages of NMR quantum computation are kept: long coherence time and easy construction of quantum gates. As a specific system to implement the above idea, we discuss the 13 C-nuclear spins in the nearest vicinity of a single nitrogen-vacancy (NV) defect center in diamond, which can be optically detected using the technique of scanning confocal microscopy. Owing to the hyperfine coupling of the ground state electron paramagnetic spin S =1 of the center to 13 C nuclear spins in a diamond lattice, the states of nuclear spins in the vicinity of the defect-center can be addressed individually. Preliminary consideration shows that it should be possible to address up to 12 individual 13 C nuclear spins. The dephasing time of the nuclear spin states at low temperatures allows realization up to 10 5 gates.

Optics and SpectroscopySep 1, 2001134 citations

Towards a room temperature solid state quantum processor - the nitrogen-vacancy center in diamond

Philipp Neumann

This work investigates the applicability of the nitrogen-vacancy (NV) defect center in diamond for quantum computation and metrology purposes. The NV center is a molecule like defect in the diamond lattice which is optically active and possesses an electron spin in its ground state. The spin can be used as a quantum bit and as a field sensor. The NV center has three major properties enabling individual control of single defects. Its optical properties depend on the spin state, the spin can be polarized optically and the spin state has an exceptionally long lifetime. Single NV centers can be controlled by optical and microwave radiation. Generally, the research on individually controllable quantum systems is not only motivated by quantum computation and communication. With the ongoing miniaturization nowadays electronic and electro-optic devices will soon reach the limit of single quantum building blocks. While in these applications the full complexity of single quantum systems might not be needed, small sensors based on single atoms or molecules might very well take advantage of the susceptibility of quantum coherences to environmental conditions. Major challenges for all approaches towards single quantum system control are the individual addressing, the measurement of the quantum state and the protection of quantum coherence from environmental noise. Today, there is a variety of systems (including the NV center) that allow control on the single quantum level. These are for example single photons, single ions and atoms in traps, single spins in semiconductors or single molecules in solid state systems. Rather mesoscopic examples are superconducting devices, nanomechanical oscillators or surface plasmon polaritons. Regarding the NV center it has been shown that the magnetic moment of its electron spin allows individual sensing and coupling to other surrounding electron and nuclear spins. Especially single nuclear spins were shown to be exceptional quantum memories. In this work small quantum registers of up to 5 spins have been used to test major requirements for a feasible quantum processor. Therefore, mainly artificially created high purity diamond samples with controlled spin and impurity concentration were used. The NV centers were either grown in or created via ion implantation techniques in a controlled fashion. As a first requirement for quantum computation entanglement among up to three spins has been generated and was verified by quantum state tomography. This proves the access of the full Hilbert space. Especially, entanglement among nuclear spins was very long-living. In further experiments this processor was used for first quantum algorithms like super-dense coding and the Deutsch algorithm. In addition, this work demonstrates new methods to initialize nuclear spin qubits into a desired quantum state. This is particularly important as improper initialization inhibits quantum computation. One of these methods is related to dynamic nuclear spin polarization and the other to measurement based state preparation. Nuclear spins in the diamond lattice originate mainly from the C-13 isotope. By artificially altering its content the influence on the NV center spin was investigated. The coherence times of the NV center were increasing inversely with the nuclear spin density. Even increasing nuclear spin density to offer more nuclear spin qubits to an operational quantum register was possible. As an alternative route of scaling up the quantum register pairs of closely spaced NV centers were investigated. For the first time two qubit gates among two NV centers mediated by magnetic dipolar coupling have been realized. Furthermore the sensing ability was demonstrated by measuring the relative distance of the two centers (10 nm) with sub-nm precision. Eventually, this work contains new insight into the electronically excited state of the NV center which allowed a more advanced control of the electron and nuclear spins. A comparably high magnetic field was used to decouple electron and nuclear spins. Finally, this allowed quantum nondemolition measurements on single nuclear spins which manifests in the observation of quantum jumps. The new insight was used to drastically improve the performance of quantum state readout. Summarizing, it was shown that single NV centers and proximal nuclear spins form versatile small quantum registers which can be interconnected with neighboring such NV quantum registers. Although the number of qubits used in this work is still small the experimental results propose a way of how to proceed when building a quantum computer. Regarding quantum metrology, however, the use of such a small register which can sense fields and store and process the results would already outperform a single NV electron spin by orders of magnitude.

Jan 1, 20128 citations

High-fidelity entangling gates for electron and nuclear spin qubits in diamond

Regina Finsterhoelzl, Wolf-Rüdiger Hannes, Guido Burkard

Motivated by the recent experimental progress in exploring the use of a nitrogen-vacancy (NV) center in diamond as a quantum computing platform, we propose schemes for fast and high-fidelity entangling gates on this platform. Using both analytical and numerical calculations, we demonstrate that synchronization effects between resonant and off-resonant transitions may be exploited such that spin-flip errors due to strong driving may be eliminated by adjusting the gate time or the driving field. This allows for fast, high-fidelity entangling operations between the electron spin and one or several nuclear spins. We investigate a two-qubit system where the NV center comprises a N 15 atom and a qubit-qutrit system for the case of a N 14 atom. In both cases, we predict a complete suppression of off-resonant driving errors for two-qubit gates when addressing the NV electron spin conditioned on states of nuclear spins of the nitrogen atom of the defect. Additionally, we predict fidelities > 0.99 for multiqubit gates when including the surrounding C 13 atoms in the diamond lattice in the conditioned logic.

arXiv:2403.11553Physical review. B./Physical review. BJun 3, 20256 citations