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Journal of Physics Conference Series

NMR imaging analogue of the individual qubit operations in superconducting flux-qubit chains

Toshiyuki Fujii, Shigemasa Matsuo, Noriyuki Hatakenaka

Published Feb 1, 2009• 0 citations
Publisher

Abstract

A solid-state quantum computer conventionally requires the control lines for each qubit to operate individually. This makes quantum circuits complicated, especially in multi-qubit systems. Here we propose a simple single-qubit operation in a superconducting flux-qubit chain without control lines in an analogy of the Nuclear Magnetic Resonance (NMR) imaging technique. A superconducting flux qubit can be regarded as an artificial atom with spin 1/2 that can be manipulated by an external magnetic field. To identify the location of each qubit in the qubit chain, a static field gradient is introduced along the qubit chain. This magnetic field gradient causes differences in the Zeeman frequencies of each separate qubit. This allows a large number of distinct qubits to be individually addressed. Single-qubit operations are then possible when the external electromagnetic frequency is adjusted to the resulting energy-level separation of the target qubit.

DOI
10.1088/1742-6596/150/2/022011

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A solid-state quantum computer conventionally requires the control lines for each qubit to operate individually. This makes quantum circuits complicated, especially in multi-qubit systems. Here we propose a simple single-qubit operation in a superconducting flux-qubit chain without control lines in an analogy of the Nuclear Magnetic Resonance (NMR) imaging technique. A superconducting flux qubit can be regarded as an artificial atom with spin 1/2 that can be manipulated by an external magnetic field. To identify the location of each qubit in the qubit chain, a static field gradient is introduced along the qubit chain. This magnetic field gradient causes differences in the Zeeman frequencies of each separate qubit. This allows a large number of distinct qubits to be individually addressed. Single-qubit operations are then possible when the external electromagnetic frequency is adjusted to the resulting energy-level separation of the target qubit.
We theoretically analyze the performance of the nuclear magnetic resonance (NMR) spectroscopy with a superconducting flux qubit (FQ). Such NMR with the FQ is attractive because of the possibility to detect the relatively small number of nuclear spins in a local region ($\ensuremath{\approx}\ensuremath{\mu}\mathrm{m}$) with low temperatures ($\ensuremath{\approx}\mathrm{mK}$) and low magnetic fields ($\ensuremath{\approx}\mathrm{mT}$), in which other types of quantum sensing schemes cannot easily be accessed. A sample containing nuclear spins is directly attached on the FQ, and the FQ is used as a magnetometer to detect magnetic fields from the nuclear spins. Especially, we consider two types of approaches to NMR with the FQ. One of them is to use spatially inhomogeneous excitations of the nuclear spins, which are induced by a spatially asymmetric driving with radio-frequency (rf) pulses. Such an inhomogeneity causes a change in the dc magnetic flux penetrating a loop of the FQ, which can be detected by a standard Ramsey measurement on the FQ. The other approach is to use a dynamical decoupling on the FQ to measure ac magnetic fields induced by Larmor precession of the nuclear spins. In this case, neither a spin excitation nor a spin polarization is required since the signal comes from fluctuating magnetic fields of the nuclear spins. We calculate the minimum detectable density (number) of the nuclear spins for the FQ with experimentally feasible parameters. We show that the minimum detectable density (number) of the nuclear spins with these approaches is around 1021/cm3{10}^{21}/{\mathrm{cm}}^{3}1021/cm3 (108{10}^{8}108) with an accumulation time of 1 s.
Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.
We propose a decoupling-free nuclear-spin quantum computer installed on a quantum electron spin chain with a singlet ground state and a finite spin gap. Qubits are I=1/2I=1/2I=1/2 nuclear spins implanted periodically along the quantum spin chain. A magnetic field gradient is applied parallel to the chain, which allows individual access to each qubit. A single-qubit operation (rotation gate) is realized with the rf field tuned to the nuclear Larmor frequency at the qubit of interest, while a two-qubit operation (controlled-NOT gate) is achieved using the Suhl-Nakamura interaction through a packet of triplet magnons, which are excited by a microwave tuned to the spin gap energy (SN(SN(SN gate). The interaction can be switched off by turning off the microwave, and a decoupling-free quantum computer is realized. The initialization is achieved with an optical pumping qubit initializer, which has a multilayered structure of the quantum spin chain and a semiconductor. Spin polarizations created by the optical pumping in the semiconducting layers are transferred to the spin chain layers through a cross polarization and a spin diffusion. The scheme allows us to separate the initialization process from the computation, enabling us to optimize the latter independently of the former.
We propose a novel MRI (Magnetic Resonance Imaging) technique based quantum bit (qubit) generation with water proton NMR (1H-NMR), distinct from previously proposed NMR chemical shift or spectroscopic techniques based qubit generation. We briefly review prior NMR-based techniques in the context of quantum computing, focusing on MRI-related methods. The proposed technique utilizes MRI-based gradient methods combined with set of local reverse gradients to generate multiple qubits. This configuration enables the creation of multiple localized constant magnetic fields, each producing a qubit with highly homogeneous field, therefore, a unique single frequency. The RF electronics and signal processing techniques are analogous to those used in conventional MRI scanners, allowing operation at room temperature, with the exception of the main magnet, which remains identical to that of standard MRI systems. Additional advantages of this method include the ability to leverage the extensive pulse techniques and hardware developed for MRI scanners over the past 50 years. Furthermore, the wide array of MRI pulse sequences enables highly sophisticated signal processing for quantum computing applications, such as the spin purification.
We show that a superconducting circuit containing two loops, when treated with Macroscopic Quantum Coherence (MQC) theory, constitutes a complete two-bit quantum computer. The manipulation of the system is easily implemented with alternating magnetic fields. A \textit{universal} set of quantum gates is deemed available by means of all unitary single bit operations and a controlled-not (\textsc{cnot}) sequence. We use multi-dimensional MQC theory and time-dependent first order perturbation theory to analyze the model. Our calculations show that a two qubit arrangement, each having a diameter of 200nm, operating in the flux regime can be operated with a static magnetic field of ∼0.1\sim 0.1∼0.1T, and an alternating dynamic magnetic field of amplitude ∼1\sim 1∼1 Gauss and frequency ∼10\sim 10∼10Hz. The operational time τopτ_{op}τop​ is estimated to be ∼10\sim 10∼10ns.
Frequency-selective readout for superconducting qubits opens up the way towards scaling qubit circuits without increasing the number of measurement lines. Here we demonstrate the readout of an array of 7 flux qubits located on the same chip using a single measurement line. Each qubit is placed near an individual λ/4 resonator which, in turn, is coupled to a common microwave transmission line. We performed spectroscopy and coherent manipulation of all qubits and determined their parameters in a single measurement run.