Optimization of the resonator-induced phase gate for superconducting qubits

  1. Moein Malekakhlagh,
  2. William Shanks,
  3. and Hanhee Paik
The resonator-induced phase gate is a two-qubit operation in which driving a bus resonator induces a state-dependent phase shift on the qubits equivalent to an effective ZZ interaction.
In principle, the dispersive nature of the gate offers flexibility for qubit parameters. However, the drive can cause resonator and qubit leakage, the physics of which cannot be fully captured using either the existing Jaynes-Cummings or Kerr models. In this paper, we adopt an ab-initio model based on Josephson nonlinearity for transmon qubits. The ab-initio analysis agrees well with the Kerr model in terms of capturing the effective ZZ interaction in the weak-drive dispersive regime. In addition, however, it reveals numerous leakage transitions involving high-excitation qubit states. We analyze the physics behind such novel leakage channels, demonstrate the connection with specific qubits-resonator frequency collisions, and lay out a plan towards device parameter optimization. We show this type of leakage can be substantially suppressed using very weakly anharmonic transmons. In particular, weaker qubit anharmonicity mitigates both collision density and leakage amplitude, while larger qubit frequency moves the collisions to occur only at large anharmonicity not relevant to experiment. Our work is broadly applicable to the physics of weakly anharmonic transmon qubits coupled to linear resonators. In particular, our analysis confirms and generalizes the measurement-induced state transitions noted in Sank et al. (Phys. Rev. Lett. 117, 190503) and lays the groundwork for both strong-drive resonator-induced phase gate implementation and strong-drive dispersive qubit measurement.

Investigating microwave loss of SiGe using superconducting transmon qubits

  1. Martin Sandberg,
  2. Vivekananda P. Adiga,
  3. Markus Brink,
  4. Cihan Kurter,
  5. Conal Murray,
  6. Marinus Hopstaken,
  7. John Bruley,
  8. Jason Orcutt,
  9. and Hanhee Paik
Silicon-Germanium (SiGe) is a material that possesses a multitude of applications ranging from transistors to eletro-optical modulators and quantum dots. The diverse properties of SiGe
also make it attractive to implementations involving superconducting quantum computing. Here we demonstrate the fabrication of transmon quantum bits on SiGe layers and investigate the microwave loss properties of SiGe at cryogenic temperatures and single photon microwave powers. We find relaxation times of up to 100 μs, corresponding to a quality factor Q above 4 M for large pad transmons. The high Q values obtained indicate that the SiGe/Si heterostructure is compatible with state of the art performance of superconducting quantum circuits.

Experimental demonstration of a resonator-induced phase gate in a multi-qubit circuit QED system

  1. Hanhee Paik,
  2. A. Mezzacapo,
  3. Martin Sandberg,
  4. D. T. McClure,
  5. B. Abdo,
  6. A. D. Corcoles,
  7. O. Dial,
  8. D. F. Bogorin,
  9. B. L. T. Plourde,
  10. M. Steffen,
  11. A. W. Cross,
  12. J. M. Gambetta,
  13. and Jerry M. Chow
The resonator-induced phase (RIP) gate is a multi-qubit entangling gate that allows a high degree of flexibility in qubit frequencies, making it attractive for quantum operations in
large-scale architectures. We experimentally realize the RIP gate with four superconducting qubits in a three-dimensional (3D) circuit-quantum electrodynamics architecture, demonstrating high-fidelity controlled-Z (CZ) gates between all possible pairs of qubits from two different 4-qubit devices in pair subspaces. These qubits are arranged within a wide range of frequency detunings, up to as large as 1.8 GHz. We further show a dynamical multi-qubit refocusing scheme in order to isolate out 2-qubit interactions, and combine them to generate a four-qubit Greenberger-Horne-Zeilinger state.

Ten Milliseconds for Aluminum Cavities in the Quantum Regime

  1. M. Reagor,
  2. Hanhee Paik,
  3. G. Catelani,
  4. L. Sun,
  5. C. Axline,
  6. E. Holland,
  7. I.M. Pop,
  8. N.A. Masluk,
  9. T. Brecht,
  10. L. Frunzio,
  11. M.H. Devoret,
  12. L.I. Glazman,
  13. and R. J. Schoelkopf
A promising quantum computing architecture couples superconducting qubits to microwave resonators (circuit QED), a system in which three-dimensional microwave cavities have become a
valuable resource. Such cavities have surface-to-volume ratios, or participation ratios a thousandfold smaller than in planar devices, deemphasizing potentially lossy surface elements by an equal amount. Motivated by this principle, we have tested aluminum superconducting cavity resonators with internal quality factors greater than 0.5 billion and intrinsic lifetimes reaching 0.01 seconds at single photon power and millikelvin temperatures. These results are the first to explore the use of superconducting aluminum, a ubiquitous material in circuit QED, as the basis of highly coherent (Q~10^7-10^9) cavity resonators. Measurements confirm the cavities‘ predicted insensitivity to quasiparticles (kinetic inductance fraction-5ppm) and an absence of two level dielectric fluctuations.

Observation of quantum state collapse and revival due to the single-photon Kerr effect

  1. Gerhard Kirchmair,
  2. Brian Vlastakis,
  3. Zaki Leghtas,
  4. Simon E. Nigg,
  5. Hanhee Paik,
  6. Eran Ginossar,
  7. Mazyar Mirrahimi,
  8. Luigi Frunzio,
  9. S. M. Girvin,
  10. and R. J. Schoelkopf
Photons are ideal carriers for quantum information as they can have a long coherence time and can be transmitted over long distances. These properties are a consequence of their weak
interactions within a nearly linear medium. To create and manipulate nonclassical states of light, however, one requires a strong, nonlinear interaction at the single photon level. One approach to generate suitable interactions is to couple photons to atoms, as in the strong coupling regime of cavity QED systems. In these systems, however, one only indirectly controls the quantum state of the light by manipulating the atoms. A direct photon-photon interaction occurs in so-called Kerr media, which typically induce only weak nonlinearity at the cost of significant loss. So far, it has not been possible to reach the single-photon Kerr regime, where the interaction strength between individual photons exceeds the loss rate. Here, using a 3D circuit QED architecture, we engineer an artificial Kerr medium which enters this regime and allows the observation of new quantum effects. We realize a Gedankenexperiment proposed by Yurke and Stoler, in which the collapse and revival of a coherent state can be observed. This time evolution is a consequence of the quantization of the light field in the cavity and the nonlinear interaction between individual photons. During this evolution non-classical superpositions of coherent states, i.e. multi-component Schroedinger cat states, are formed. We visualize this evolution by measuring the Husimi Q-function and confirm the non-classical properties of these transient states by Wigner tomography. The single-photon Kerr effect could be employed in QND measurement of photons, single photon generation, autonomous quantum feedback schemes and quantum logic operations.

Photon Shot Noise Dephasing in the Strong-Dispersive Limit of Circuit QED

  1. A. P. Sears,
  2. A. Petrenko,
  3. G. Catelani,
  4. L. Sun,
  5. Hanhee Paik,
  6. G. Kirchmair,
  7. L. Frunzio,
  8. L. I. Glazman,
  9. S. M. Girvin,
  10. and R. J. Schoelkopf
We study the photon shot noise dephasing of a superconducting transmon qubit in the strong-dispersive limit, due to the coupling of the qubit to its readout cavity. As each random arrival
or departure of a photon is expected to completely dephase the qubit, we can control the rate at which the qubit experiences dephasing events by varying textit{in situ} the cavity mode population and decay rate. This allows us to verify a pure dephasing mechanism that matches theoretical predictions, and in fact explains the increased dephasing seen in recent transmon experiments as a function of cryostat temperature. We investigate photon dynamics in this limit and observe large increases in coherence times as the cavity is decoupled from the environment. Our experiments suggest that the intrinsic coherence of small Josephson junctions, when corrected with a single Hahn echo, is greater than several hundred microseconds.

Black-box superconducting circuit quantization

  1. Simon E. Nigg,
  2. Hanhee Paik,
  3. Brian Vlastakis,
  4. Gerhard Kirchmair,
  5. Shyam Shankar,
  6. Luigi Frunzio,
  7. Michel Devoret,
  8. Robert Schoelkopf,
  9. and Steven Girvin
We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions
coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found.