Floquet-engineered enhancement of coherence times in a driven fluxonium qubit

  1. Pranav S. Mundada,
  2. András Gyenis,
  3. Ziwen Huang,
  4. Jens Koch,
  5. and Andrew A. Houck
vWe use the quasienergy structure that emerges when a fluxonium superconducting circuit is driven periodically to encode quantum information with dynamically induced flux-insensitive
sweet spots. The framework of Floquet theory provides an intuitive description of these high-coherence working points located away from the half-flux symmetry point of the undriven qubit. This approach offers flexibility in choosing the flux bias point and the energy of the logical qubit states as shown in [\textit{Huang et al., 2020}]. We characterize the response of the system to noise in the modulation amplitude and DC flux bias, and experimentally demonstrate an optimal working point which is simultaneously insensitive against fluctuations in both. We observe a 40-fold enhancement of the qubit coherence times measured with Ramsey-type interferometry at the dynamical sweet spot compared with static operation at the same bias point.

Engineering Dynamical Sweet Spots to Protect Qubits from 1/f Noise

  1. Ziwen Huang,
  2. Pranav S. Mundada,
  3. András Gyenis,
  4. David I. Schuster,
  5. Andrew A. Houck,
  6. and Jens Koch
Protecting superconducting qubits from low-frequency noise is essential for advancing superconducting quantum computation. We here introduce a protocol for engineering dynamical sweet
spots which reduce the susceptibility of a qubit to low-frequency noise. Based on the application of periodic drives, the location of the dynamical sweet spots can be obtained analytically in the framework of Floquet theory. In particular, for the example of fluxonium biased slightly away from half a flux quantum, we predict an enhancement of pure-dephasing by three orders of magnitude. Employing the Floquet eigenstates as the computational basis, we show that high-fidelity single-qubit gates can be implemented while maintaining dynamical sweet-spot operation. We further confirm that qubit readout can be performed by adiabatically mapping the Floquet states back to the static qubit states, and subsequently applying standard measurement techniques. Our work provides an intuitive tool to encode quantum information in robust, time-dependent states, and may be extended to alternative architectures for quantum information processing.

Universal fast flux control of a coherent, low-frequency qubit

  1. Helin Zhang,
  2. Srivatsan Chakram,
  3. Tanay Roy,
  4. Nathan Earnest,
  5. Yao Lu,
  6. Ziwen Huang,
  7. Daniel Weiss,
  8. Jens Koch,
  9. and David I. Schuster
The extit{heavy-fluxonium} circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the half-flux frustration
point. However, the suppressed charge matrix elements and low transition frequency have made it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control, and readout, that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize higher levels of the fluxonium to initialize the qubit with 97\% fidelity, corresponding to cooling it to 190 μK. We realize high-fidelity control using a universal set of single-cycle flux gates, which are comprised of directly synthesizable fast pulses, while plasmon-assisted readout is used for measurements. On a qubit with T1,T2e∼~300~μs, we realize single-qubit gates in 20−60~ns with an average gate fidelity of 99.8% as characterized by randomized benchmarking.

Experimental realization of an intrinsically error-protected superconducting qubit

  1. Andras Gyenis,
  2. Pranav S. Mundada,
  3. Agustin Di Paolo,
  4. Thomas M. Hazard,
  5. Xinyuan You,
  6. David I. Schuster,
  7. Jens Koch,
  8. Alexandre Blais,
  9. and Andrew A. Houck
Encoding a qubit in logical quantum states with wavefunctions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing.
Using a circuit-quantum-electrodynamics architecture, we experimentally realize a superconducting 0−π qubit, which hosts protected states suitable for quantum-information processing. Multi-tone spectroscopy measurements reveal the energy level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. We find that the parity symmetry of the qubit results in charge-insensitive levels connecting the protected states, allowing for logical operations. The measured relaxation (1.6 ms) and dephasing times (25 μs) demonstrate that our implementation of the 0−π circuit not only broadens the family of superconducting qubits, but also represents a promising candidate for the building block of a fault-tolerant quantum processor.

Universal gates for protected superconducting qubits using optimal control

  1. Mohamed Abdelhafez,
  2. Brian Baker,
  3. Andras Gyenis,
  4. Pranav Mundada,
  5. Andrew A. Houck,
  6. David Schuster,
  7. and Jens Koch
We employ quantum optimal control theory to realize quantum gates for two protected superconducting circuits: the heavy-fluxonium qubit and the 0-π qubit. Utilizing automatic differentiation
facilitates the simultaneous inclusion of multiple optimization targets, allowing one to obtain high-fidelity gates with realistic pulse shapes. For both qubits, disjoint support of low-lying wave functions prevents direct population transfer between the computational-basis states. Instead, optimal control favors dynamics involving higher-lying levels, effectively lifting the protection for a fraction of the gate duration. For the 0-π qubit, offset-charge dependence of matrix elements among higher levels poses an additional challenge for gate protocols. To mitigate this issue, we randomize the offset charge during the optimization process, steering the system towards pulse shapes insensitive to charge variations. Closed-system fidelities obtained are 99% or higher, and show slight reductions in open-system simulations.

Spectrum and Coherence Properties of the Current-Mirror Qubit

  1. D. K. Weiss,
  2. Andy C. Y. Li,
  3. D.G. Ferguson,
  4. and Jens Koch
exhibits a robust ground-state degeneracy and wave functions with disjoint support for appropriate circuit parameters."]In this protected regime, Cooper-pair excitons form the relevant low-energy excitations. Based on a full circuit analysis of the current-mirror device, we introduce an effective model that systematically captures the relevant low-energy degrees of freedom, and is amenable to diagonalization using Density Matrix Renormalization Group (DMRG) methods. We find excellent agreement between DMRG and exact diagonalization, and can push DMRG simulations to much larger circuit sizes than feasible for exact diagonalization. We discuss the spectral properties of the current-mirror circuit, and predict coherence times exceeding 1 ms in parameter regimes believed to be within reach of experiments.

Circuit quantization in the presence of time-dependent external flux

  1. Xinyuan You,
  2. J. A. Sauls,
  3. and Jens Koch
Circuit quantization links a physical circuit to its corresponding quantum Hamiltonian. The standard quantization procedure generally assumes any external magnetic flux to be static.
Time dependence naturally arises, however, when flux is modulated or when flux noise is considered. In this case, application of the existing quantization procedure can lead to inconsistencies. To resolve these, we generalize circuit quantization to incorporate time-dependent external flux.

Control and Coherence Time Enhancement of the 0- π Qubit

  1. Agustin Di Paolo,
  2. Arne L. Grimsmo,
  3. Peter Groszkowski,
  4. Jens Koch,
  5. and Alexandre Blais
Kitaev’s 0-π qubit encodes quantum information in two protected, near-degenerate states of a superconducting quantum circuit. In a recent work, we have shown that the coherence
times of a realistic 0-π device can surpass that of today’s best superconducting qubits [Groszkowski et al., New Journal of Physics 20 043053 (2018)]. Here we address controllability of the 0-π qubit. Specifically, we investigate the potential for dispersive control and readout, and introduce a new, fast and high-fidelity single-qubit gate that can interpolate smoothly between logical X and Z. We characterize the action of this gate using a multi-level treatment of the device, and analyze the impact of circuit element disorder and deviations in control and circuit parameters from their optimal values. Furthermore, we propose a cooling scheme to decrease the photon shot-noise dephasing rate, which we previously found to limit the coherence times of 0-π devices within reach of current experiments. Using this approach, we predict coherence time enhancements between one and three orders of magnitude, depending on parameter regime.

Quantum control of an oscillator using stimulated nonlinearity

  1. Andrei Vrajitoarea,
  2. Ziwen Huang,
  3. Peter Groszkowski,
  4. Jens Koch,
  5. and Andrew A. Houck
Superconducting circuits extensively rely on the Josephson junction as a nonlinear electronic element for manipulating quantum information and mediating photon interactions. Despite
continuing efforts in designing anharmonic Josephson circuits with improved coherence times, the best photon lifetimes have been demonstrated in microwave cavities. Nevertheless, architectures based on quantum memories need a qubit element for addressing these harmonic modules at the cost of introducing additional loss channels and limiting process fidelities. This work focuses on tailoring the oscillator Hilbert space to enable a direct Rabi drive on individual energy levels. For this purpose we implement a flux-tunable inductive coupling between two linear resonators using a superconducting quantum interference device. We dynamically activate a three-wave mixing process through parametric flux modulation in order to selectively address the lowest eigenstates as an isolated two-level system. Measuring the Wigner function confirms we can prepare arbitrary states confined in the single photon manifold, with measured coherence times limited by the oscillator intrinsic quality factor. This architectural shift in engineering oscillators with stimulated nonlinearity can be exploited for designing long-lived quantum modules and offers flexibility in studying non-equilibrium physics with photons in a field-programmable simulator.

Universal stabilization of single-qubit states using a tunable coupler

  1. Ziwen Huang,
  2. Yao Lu,
  3. Eliot Kapit,
  4. David I. Schuster,
  5. and Jens Koch
We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally. Our scheme utilized
red and blue sideband transitions in a system composed of a fluxonium qubit, a low-Q LC-oscillator, and a coupler enabling us to tune the interaction between them. Under parametric modulations of the coupling strength, the qubit can be steered into any desired pure or mixed single-qubit state. For realistic circuit parameters, we predict that stabilization can be achieved within 100 ns. By varying the ratio between the oscillator’s damping rate and the effective qubit-oscillator coupling strength, we can switch between under-damped, critically-damped, and over-damped stabilization and find optimal working points. We further analyze the effect of thermal fluctuations and show that the stabilization scheme remains robust for realistic temperatures.