Preparing ground states of the XXZ model using the quantum annealing with inductively coupled superconducting flux qubits

  1. Takashi Imoto,
  2. Yuya Seki,
  3. and Yuichiro Matsuzaki
Preparing ground states of Hamiltonians is important in the condensed matter physics and the quantum chemistry. The interaction Hamiltonians typically contain not only diagonal but
also off-diagonal elements. Although quantum annealing provides a way to prepare a ground state of a Hamiltonian, we can only use the Hamiltonian with Ising interaction by using currently available commercial quantum annealing devices. In this work, we propose a quantum annealing for the XXZ model, which contains both Ising interaction and energy-exchange interaction, by using inductively coupled superconducting flux qubits. The key idea is to use a recently proposed spin-lock quantum annealing where the qubits are driven by microwave fields. As long as the rotating wave approximation is valid, the inductive coupling between the superconducting flux qubits produces the desired Hamiltonian in the rotating frame, and we can use such an interaction for the quantum annealing while the microwave fields driving play a role of the transverse fields. To quantify the performance of our scheme, we implement numerical simulations, and show that we can prepare ground states of the two-dimensional Heisenberg model with a high fidelity.

Identification of different types of high-frequency defects in superconducting qubits

  1. Leonid V. Abdurakhimov,
  2. Imran Mahboob,
  3. Hiraku Toida,
  4. Kosuke Kakuyanagi,
  5. Yuichiro Matsuzaki,
  6. and Shiro Saito
Parasitic two-level-system (TLS) defects are one of the major factors limiting the coherence times of superconducting qubits. Although there has been significant progress in characterizing
basic parameters of TLS defects, exact mechanisms of interactions between a qubit and various types of TLS defects remained largely unexplored due to the lack of experimental techniques able to probe the form of qubit-defect couplings. Here we present an experimental method of TLS defect spectroscopy using a strong qubit drive that allowed us to distinguish between various types of qubit-defect interactions. By applying this method to a capacitively shunted flux qubit, we detected a rare type of TLS defects with a nonlinear qubit-defect coupling due to critical-current fluctuations, as well as conventional TLS defects with a linear coupling to the qubit caused by charge fluctuations. The presented approach could become the routine method for high-frequency defect inspection and quality control in superconducting qubit fabrication, providing essential feedback for fabrication process optimization. The reported method is a powerful tool to uniquely identify the type of noise fluctuations caused by TLS defects, enabling the development of realistic noise models relevant to fault-tolerant quantum control.

Polarizing electron spins with a superconducting flux qubit

  1. Shingo Kukita,
  2. Hideaki Ookane,
  3. Yuichiro Matsuzaki,
  4. and Yasushi Kondo
Electron spin resonance (ESR) is a useful tool to investigate properties of materials in magnetic fields where high spin polarization of target electron spins is required in order to
obtain high sensitivity. However, the smaller magnetic fields becomes, the more difficult high polarization is passively obtained by thermalization. Here, we propose to employ a superconducting flux qubit (FQ) to polarize electron spins actively. We have to overcome a large energy difference between the FQ and electron spins for efficient energy transfer among them. For this purpose, we adopt a spin-lock technique on the FQ where the Rabi frequency associated with the spin-locking can match the resonance (Larmor) one of the electron spins. We find that adding dephasing on the spins is beneficial to obtain high polarization of them, because otherwise the electron spins are trapped in dark states that cannot be coupled with the FQ. We show that our scheme can achieve high polarization of electron spins in realistic experimental conditions.

Investigation of controls of a superconducting quantum parametron under a strong pump field

  1. Shumpei Masuda,
  2. Toyofumi Ishikawa,
  3. Yuichiro Matsuzaki,
  4. and Shiro Kawabata
Pumped at approximately twice the natural frequency, a Josephson parametric oscillator called parametron or Kerr parametric oscillator shows self-oscillation. Quantum annealing and
universal quantum computation using self-oscillating parametrons as qubits were proposed. However, controls of parametrons under the pump field are degraded by unwanted rapidly oscillating terms in the Hamiltonian, which is called counter rotating terms (CRTs) coming from the violation of the rotating wave approximation. Therefore, the pump field can be an intrinsic origin of the imperfection of controls of parameterons. Here, we theoretically study the effect of the CRTs on the accuracy of controls of a parametron: creation of a cat state and a single qubit gate along the x axis. It is shown that there is a trade-off relationship between the suppression of the nonadiabatic transitions and the validity of the rotating wave approximation in a conventional approach. We show that the tailored time dependence of the detuning of the pump field can suppress both of the nonadiabatic transitions and the disturbance of the state of the parametron due to the CRTs.

Control of transition frequency of a superconducting flux qubit by longitudinal coupling to the photon number degree of freedom in a resonator

  1. Hiraku Toida,
  2. Takuya Ohrai,
  3. Yuichiro Matsuzaki,
  4. Kosuke Kakuyanagi,
  5. and Shiro Saito
We control transition frequency of a superconducting flux qubit coupled to a frequency-tunable resonator comprising a direct current superconducting quantum interference device (dc-SQUID)
by microwave driving. The dc-SQUID mediates the coupling between microwave photons in the resonator and a flux qubit. The polarity of the frequency shift depends on the sign of the flux bias for the qubit and can be both positive and negative. The absolute value of the frequency shift becomes larger by increasing the photon number in the resonator. These behaviors are reproduced by a model considering the magnetic interaction between the flux qubit and dc-SQUID. The tuning range of the transition frequency of the flux qubit reaches ≈ 1.9 GHz, which is much larger than the ac Stark/Lamb shift observed in the dispersive regime using typical circuit quantum electrodynamics devices.

Electron Spin Resonance with up to 20 Spin Sensitivity Measured using a Superconducting Flux Qubit

  1. Rangga P. Budoyo,
  2. Kosuke Kakuyanagi,
  3. Hiraku Toida,
  4. Yuichiro Matsuzaki,
  5. and Shiro Saito
We report on electron spin resonance spectroscopy measurements using a superconducting flux qubit with a sensing volume of 6 fl. The qubit is read out using a frequency-tunable Josephson
bifurcation amplifier, which leads to an inferred measurement sensitivity of about 20 spins in a 1 s measurement. This sensitivity represents an order of magnitude improvement when compared with flux-qubit schemes using a dc-SQUID switching readout. Furthermore, noise spectroscopy reveals that the sensitivity is limited by flicker (1/f) flux noise.

Quantum annealing with capacitive-shunted flux qubits

  1. Yuichiro Matsuzaki,
  2. Hideaki Hakoshima,
  3. Yuya Seki,
  4. and Shiro Kawabata
Quantum annealing (QA) provides us with a way to solve combinatorial optimization problems. In the previous demonstration of the QA, a superconducting flux qubit (FQ) was used. However,
the flux qubits in these demonstrations have a short coherence time such as tens of nano seconds. For the purpose to utilize quantum properties, it is necessary to use another qubit with a better coherence time. Here, we propose to use a capacitive-shunted flux qubit (CSFQ) for the implementation of the QA. The CSFQ has a few order of magnitude better coherence time than the FQ used in the QA. We theoretically show that, although it is difficult to perform the conventional QA with the CSFQ due to the form and strength of the interaction between the CSFQs, a spin-lock based QA can be implemented with the CSFQ even with the current technology. Our results pave the way for the realization of the practical QA that exploits quantum advantage with long-lived qubits.

Nuclear magnetic resonance spectroscopy with a superconducting flux qubit

  1. Koichiro Miyanishi,
  2. Yuichiro Matsuzaki,
  3. Hiraku Toida,
  4. Kosuke Kakuyanagi,
  5. Makoto Negoro,
  6. Masahiro Kitagawa,
  7. and Shiro Saito
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 (∼μm) with low temperatures (∼ mK) and low magnetic fields (∼ mT), in which other types of quantum sensing schemes cannot easily access. 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 (108) with an accumulation time of a second.

Electron paramagnetic resonance spectroscopy using a single artificial atom

  1. Hiraku Toida,
  2. Yuichiro Matsuzaki,
  3. Kosuke Kakuyanagi,
  4. Xiaobo Zhu,
  5. William J. Munro,
  6. Hiroshi Yamaguchi,
  7. and Shiro Saito
Electron paramagnetic resonance (EPR) spectroscopy is an important technology in physics, chemistry, materials science, and biology. Sensitive detection with a small sample volume is
a key objective in these areas, because it is crucial, for example, for the readout of a highly packed spin based quantum memory or the detection of unlabeled metalloproteins in a single cell. In conventional EPR spectrometers, the energy transfer from the spins to the cavity at a Purcell enhanced rate plays an essential role and requires the spins to be resonant with the cavity, however the size of the cavity (limited by the wavelength) makes it difficult to improve the spatial resolution. Here, we demonstrate a novel EPR spectrometer using a single artificial atom as a sensitive detector of spin magnetization. The artificial atom, a superconducting flux qubit, provides advantages both in terms of its quantum properties and its much stronger coupling with magnetic fields. We have achieved a sensitivity of ∼400 spins/Hz‾‾‾√ with a magnetic sensing volume around 10−14λ3 (50 femto-liters). This corresponds to an improvement of two-order of magnitude in the magnetic sensing volume compared with the best cavity based spectrometers while maintaining a similar sensitivity as those spectrometers . Our artificial atom is suitable for scaling down and thus paves the way for measuring single spins on the nanometer scale.

Superradiance with an ensemble of superconducting flux qubits

  1. Neill Lambert,
  2. Yuichiro Matsuzaki,
  3. Kosuke Kakuyanagi,
  4. Natsuko Ishida,
  5. Shiro Saito,
  6. and Franco Nori
Superconducting flux qubits are a promising candidate for realizing quantum information processing and quantum simulations. Such devices behave like artificial atoms, with the advantage
that one can easily tune the „atoms“ internal properties. Here, by harnessing this flexibility, we propose a technique to minimize the inhomogeneous broadening of a large ensemble of flux qubits by tuning only the external flux. In addition, as an example of many-body physics in such an ensemble, we show how to observe superradiance, and its quadratic scaling with ensemble size, using a tailored microwave control pulse that takes advantage of the inhomogeneous broadening itself to excite only a sub-ensemble of the qubits. Our scheme opens up an approach to using superconducting circuits to explore the properties of quantum many-body systems.