Superconducting flux qubit operating at zero magnetic field

  1. Sunmi Kim,
  2. Leonid V. Abdurakhimov,
  3. Duong Pham,
  4. Wei Qiu,
  5. Hirotaka Terai,
  6. Sahel Ashhab,
  7. Shiro Saito,
  8. Taro Yamashita,
  9. and Kouichi Semba
The operation of a conventional superconducting flux qubit requires the application of a precisely tuned magnetic field to set the operation point at half a flux quantum through the
qubit loop, which makes the scaling of quantum circuits based on this type of qubits difficult. It has been proposed that, by inducing a pi phase shift in the superconducting order parameter using a precisely controlled nanoscale-thickness superconductor/ferromagnet/superconductor Josephson junction, commonly referred to as pi-junction, it is possible to realize a flux qubit operating at zero magnetic flux. We report the realization of a zero-flux-biased flux qubit based on three NbN/AlN/NbN Josephson junctions and a NbN/PdNi/NbN ferromagnetic pi-junction. The qubit lifetime is in the microsecond range, which we argue is limited by quasiparticle excitations in the metallic ferromagnet layer. With further improvements in the materials of the ferromagnetic junction, the zero-flux-biased flux qubits can become a promising platform for quantum computing.

High-frequency suppression of inductive coupling between flux qubit and transmission line resonator

  1. Sahel Ashhab,
  2. Ziqiao Ao,
  3. Fumiki Yoshihara,
  4. and Kouichi Semba
We perform theoretical calculations to investigate the naturally occurring high-frequency cutoff in a circuit comprising a flux qubit coupled inductively to a transmission line resonator
(TLR). Our results agree with those of past studies that considered somewhat similar circuit designs. In particular, a decoupling occurs between the qubit and the high-frequency modes. As a result, the coupling strength between the qubit and resonator modes increases with mode frequency ω as ω‾‾√ at low frequencies and decreases as 1/ω‾‾√ at high frequencies. We derive expressions for the multimode-resonator-induced Lamb shift in the qubit’s characteristic frequency. Because of the natural decoupling between the qubit and high-frequency modes, the Lamb-shift-renormalized qubit frequency remains finite.

Extremely Large Lamb Shift in a Deep-strongly Coupled Circuit QED System with a Multimode Resonator

  1. Ziqiao Ao,
  2. Sahel Ashhab,
  3. Fumiki Yoshihara,
  4. Tomoko Fuse,
  5. Kosuke Kakuyanagi,
  6. Shiro Saito,
  7. Takao Aoki,
  8. and Kouichi Semba
We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime,
where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator (λ/4 CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency ωcutoff for the coupling between the FQ and the modes in the CPWR, where the coupling grows as ωn‾‾‾√ for ωn/ωcutoff≪1 and decreases as 1/ωn‾‾‾√ for ωn/ωcutoff≫1. Here ωn is the frequency of the nth mode. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3\% and the total Lamb shift from all the modes is 96.5\%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.

Speed limits for quantum gates with weakly anharmonic qubits

  1. Sahel Ashhab,
  2. Fumiki Yoshihara,
  3. Tomoko Fuse,
  4. Naoki Yamamoto,
  5. Adrian Lupascu,
  6. and Kouichi Semba
We consider the implementation of two-qubit gates when the physical systems used to realize the qubits are weakly anharmonic and therefore possess additional quantum states in the accessible
energy range. We analyze the effect of the additional quantum states on the maximum achievable speed for quantum gates in the qubit state space. By calculating the minimum gate time using optimal control theory, we find that higher energy levels can help make two-qubit gates significantly faster than the reference value based on simple qubits. This speedup is a result of the higher coupling strength between higher energy levels. We then analyze the situation where the pulse optimization algorithm avoids pulses that excite the higher levels. We find that in this case the presence of the additional states can lead to a significant reduction in the maximum achievable gate speed. We also compare the optimal control gate times with those obtained using the cross-resonance/selective-darkening gate protocol. We find that the latter, with some parameter optimization, can be used to achieve a relatively fast implementation of the CNOT gate. These results can help the search for optimized gate implementations in realistic quantum computing architectures, such as those based on superconducting qubits. They also provide guidelines for desirable conditions on anharmonicity that would allow optimal utilization of the higher levels to achieve fast quantum gates.

Enhanced-coherence all-nitride superconducting qubit epitaxially grown on Si Substrate

  1. Sunmi Kim,
  2. Hirotaka Terai,
  3. Taro Yamashita,
  4. Wei Qiu,
  5. Tomoko Fuse,
  6. Fumiki Yoshihara,
  7. Sahel Ashhab,
  8. Kunihiro Inomata,
  9. and Kouichi Semba
We have developed superconducting qubits based on NbN/AlN/NbN epitaxial Josephson junctions on Si substrates which promise to overcome the drawbacks of qubits based on Al/AlOx/Al junctions.
The all-nitride qubits have great advantages such as chemical stability against oxidation (resulting in fewer two-level fluctuators), feasibility for epitaxial tunnel barriers (further reducing energy relaxation and dephasing), and a larger superconducting gap of ∼5.2 meV for NbN compared to ∼0.3 meV for Al (suppressing the excitation of quasiparticles). Replacing conventional MgO by a Si substrate with a TiN buffer layer for epitaxial growth of nitride junctions, we demonstrate a qubit energy relaxation time T1=16.3 μs and a spin-echo dephasing time T2=21.5 μs. These significant improvements in quantum coherence are explained by the reduced dielectric loss compared to previously reported NbN-based qubits with MgO substrates (T1≈T2≈0.5 μs). These results are an important step towards constructing a new platform for superconducting quantum hardware.

Hamiltonian of a flux qubit-LC oscillator circuit in the deep-strong-coupling regime

  1. Fumiki Yoshihara,
  2. Sahel Ashhab,
  3. Tomoko Fuse,
  4. Motoaki Bamba,
  5. and Kouichi Semba
We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit and an LC oscillator. If we keep the qubit’s lowest two energy levels,
the derived circuit Hamiltonian takes the form of the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator, regardless of the coupling strength. To investigate contributions from the qubit’s higher energy levels, we numerically calculate the transition frequencies of the circuit Hamiltonian. We find that the qubit’s higher energy levels mainly cause an overall shift of the entire spectrum, but the energy level structure up to the seventh excited states can still be fitted well by the quantum Rabi Hamiltonian even in the case where the coupling strength is larger than the frequencies of the qubit and the oscillator, i.e., when the qubit-oscillator circuit is in the deep-strong-coupling regime. We also confirm that some of the paradoxical properties of the quantum Rabi Hamiltonian in the deep-strong-coupling regime, e.g. the non-negligible number of photons and the nonzero expectation value of the flux in the oscillator in the ground state, arise from the circuit Hamiltonian as well.

Effects of an environment on the ground state of circuit QED systems in the deep-strong coupling regime

  1. Tomohiro Shitara,
  2. Motoaki Bamba,
  3. Fumiki Yoshihara,
  4. Tomoko Fuse,
  5. Sahel Ashhab,
  6. Kouichi Semba,
  7. and Kazuki Koshino
We investigate theoretically how the ground state of a qubit-resonator system in the deep-strong coupling (DSC) regime is affected by the coupling to an environment. We employ a superposition
of coherent states displaced in the qubit-state-dependent directions as a variational ansatz for the ground state of the qubit-resonator-environment system. We show that the reduced density matrix of the qubit-resonator system strongly depends on types of the resonator-waveguide and resonator-qubit coupling, i.e., capacitive or inductive, because of the broken rotational symmetry of the eigenstates of the DSC system in the resonator phase space. When the resonator couples to the qubit and the environment in different ways (for instance, one is inductive and the other is capacitive), the system is almost unaffected by the resonator-waveguide coupling. In contrast, when the types of two couplings are the same (for instance, both are inductive), by increasing the resonator-waveguide coupling strength, the average number of virtual photons increases and the quantum superposition realized in the qubit-resonator entangled ground state is partially degraded. Since the superposition becomes more fragile when the qubit-resonator coupling strength gets large, there exists an optimal strength of the qubit-resonator coupling to maximize the nonclassicality of the qubit-resonator system.

Inversion of qubit energy levels in qubit-oscillator circuits in the deep-strong-coupling regime

  1. Fumiki Yoshihara,
  2. Tomoko Fuse,
  3. Ziqiao Ao,
  4. Sahel Ashhab,
  5. Kosuke Kakuyanagi,
  6. Shiro Saito,
  7. Takao Aoki,
  8. Kazuki Koshino,
  9. and Kouichi Semba
We report on experimentally measured light shifts of superconducting flux qubits deep-strongly-coupled to an LC oscillator, where the coupling constant is comparable to the qubit’s
transition frequency and the oscillator’s resonance frequency. By using two-tone spectroscopy, the energies of the six-lowest levels of the coupled circuits are determined. We find a huge Lamb shift that exceeds 90% of the bare qubit frequencies and inversion of the qubits‘ ground and excited states when there is a finite number of photons in the oscillator. Our experimental results agree with theoretical predictions based on the quantum Rabi model.

Characteristic spectra of circuit quantum electrodynamics systems from the ultrastrong to the deep strong coupling regime

  1. Fumiki Yoshihara,
  2. Tomoko Fuse,
  3. Sahel Ashhab,
  4. Kosuke Kakuyanagi,
  5. Shiro Saito,
  6. and Kouichi Semba
We report on spectra of circuit quantum electrodynamics (QED) systems in an intermediate regime that lies between the ultrastrong and deep strong coupling regimes, which have been reported
previously in the literature. Our experimental results, along with numerical simulations, demonstrate that as the coupling strength increases, the spectrum of a circuit-QED system undergoes multiple qualitative transformations, such that several ranges are identified, each with its own unique spectral features. These results allow us to define characteristic features that distinguish several different regimes of coupling in circuit-QED systems.

Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime

  1. Fumiki Yoshihara,
  2. Tomoko Fuse,
  3. Sahel Ashhab,
  4. Kosuke Kakuyanagi,
  5. Shiro Saito,
  6. and Kouichi Semba
To control light-matter interaction at the single-quantum level in cavity quantum electrodynamics (cavity-QED) or circuit-QED, strong coupling between the light and matter components
is indispensable. Specifically, the coupling rate g must be larger than the decay rates. If g is increased further and becomes as large as the frequencies of light and matter excitations, the energy eigenstates including the ground state are predicted to be highly entangled. This qualitatively new coupling regime can be called the deep strong-coupling regime. One approach toward the deep strong-coupling regime is to use huge numbers of identical systems to take advantage of ensemble enhancement. With the emergence of so-called macroscopic artificial atoms, superconducting qubits for example, it has become possible for a single artificial atom to realize ultrastrong coupling, where ℏg exceeds ~10% of the energies of the qubit ℏωq and the harmonic oscillator ℏωo. By making use of the macroscopic magnetic dipole moment of a flux qubit, large zero-point-fluctuation current of an LC oscillator, and large Josephson inductance of a coupler junction, we have realized circuits in the deep strong-coupling regime, where g/ωo ranges from 0.72 to 1.34 and g/ωq >> 1. Using energy spectroscopy measurements, we have observed unconventional transition spectra between Schrodinger cat-like energy eigenstates. These states involve quantum superpositions of Fock states with phase-space displacements of ±g/ωo and remarkably survive with environmental noise. Our results provide a basis for ground-state-based entangled-pair generation and open a new direction in circuit-QED.