An integrated tool-set for Control, Calibration and Characterization of quantum devices applied to superconducting qubits

  1. Nicolas Wittler,
  2. Federico Roy,
  3. Kevin Pack,
  4. Max Werninghaus,
  5. Anurag Saha Roy,
  6. Daniel J. Egger,
  7. Stefan Filipp,
  8. Frank K. Wilhelm,
  9. and Shai Machnes
Efforts to scale-up quantum computation have reached a point where the principal limiting factor is not the number of qubits, but the entangling gate infidelity. However, a highly detailedsystem characterization required to understand the underlying errors is an arduous process and impractical with increasing chip size. Open-loop optimal control techniques allow for the improvement of gates but are limited by the models they are based on. To rectify the situation, we provide a new integrated open-source tool-set for Control, Calibration and Characterization (C3), capable of open-loop pulse optimization, model-free calibration, model fitting and refinement. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates and an approximate error budget, all based on a high-performance, feature-rich simulator. We illustrate our methods using fixed-frequency superconducting qubits for which we learn model parameters to an accuracy of <1% and derive a coherence limited cross-resonance (CR) gate that achieves 99.6% fidelity without need for calibration. [/expand]

Leakage reduction in fast superconducting qubit gates via optimal control

  1. Max Werninghaus,
  2. Daniel J. Egger,
  3. Federico Roy,
  4. Shai Machnes,
  5. Frank K. Wilhelm,
  6. and Stefan Filipp
Reaching high speed, high fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon
qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. By parameterizing pulses with a piecewise-constant representation that matches the capabilities of the control hardware we create a 4.16 ns single-qubit pulse with 99.76% fidelity and 0.044% leakage. This is a seven-fold reduction of the leakage rate of the best DRAG pulse we have calibrated at such short durations on the same system.

Gate-efficient simulation of molecular eigenstates on a quantum computer

  1. Marc Ganzhorn,
  2. Daniel J. Egger,
  3. Panagiotis Kl. Barkoutsos,
  4. Pauline Ollitrault,
  5. Gian Salis,
  6. Nikolaj Moll,
  7. Andreas Fuhrer,
  8. Peter Müller,
  9. Stefan Woerner,
  10. Ivano Tavernelli,
  11. and Stefan Filipp
A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available
coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Complementing the theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95% we are able to compute the eigenstates within an accuracy of 50 mHartree on average, a limit set by the coherence time of the tunable coupler.

Adiabatic quantum simulations with driven superconducting qubits

  1. Marco Roth,
  2. Nikolaj Moll,
  3. Gian Salis,
  4. Marc Ganzhorn,
  5. Daniel J. Egger,
  6. Stefan Filipp,
  7. and Sebastian Schmidt
We propose a quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by a polychromatic magnetic flux modulation of a tunable bus
element. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multi-qubit Hamiltonian which features independently tunable XX and YY-type interactions as well as local bias fields over a large parameter range. We demonstrate the adiabatic simulation of the ground state of a hydrogen molecule using two superconducting qubits and one tunable bus element. The time required to reach chemical accuracy lies in the few microsecond range and therefore could be implemented on currently available superconducting circuits. Further applications of this technique may also be found in the simulation of interacting spin systems.

Pulsed reset protocol for fixed-frequency superconducting qubits

  1. Daniel J. Egger,
  2. Marc Ganzhorn,
  3. Gian Salis,
  4. Andreas Fuhrer,
  5. Peter Müller,
  6. and Stefan Filipp
Improving coherence times of quantum bits is a fundamental challenge in the field of quantum computing. With long-lived qubits it becomes, however, inefficient to wait until the qubits
have relaxed to their ground state after completion of an experiment. Moreover, for error-correction schemes it is import to rapidly re-initialize ancilla parity-check qubits. We present a simple pulsed qubit reset protocol based on a two-pulse sequence. A first pulse transfers the excited state population to a higher excited qubit state and a second pulse into a lossy environment provided by a low-Q transmission line resonator, which is also used for qubit readout. We show that the remaining excited state population can be suppressed to 2.2±0.8% and utilize the pulsed reset protocol to carry out experiments at enhanced rates.

Quantum optimization using variational algorithms on near-term quantum devices

  1. Nikolaj Moll,
  2. Panagiotis Barkoutsos,
  3. Lev S. Bishop,
  4. Jerry M. Chow,
  5. Andrew Cross,
  6. Daniel J. Egger,
  7. Stefan Filipp,
  8. Andreas Fuhrer,
  9. Jay M. Gambetta,
  10. Marc Ganzhorn,
  11. Abhinav Kandala,
  12. Antonio Mezzacapo,
  13. Peter Müller,
  14. Walter Riess,
  15. Gian Salis,
  16. John Smolin,
  17. Ivano Tavernelli,
  18. and Kristan Temme
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits.
Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.

Optimal Control of Quantum Measurement

  1. Daniel J. Egger,
  2. and Frank K. Wilhelm
Pulses to steer the time evolution of quantum systems can be designed with optimal control theory. In most cases it is the coherent processes that can be controlled and one optimizes
the time evolution towards a target unitary process, sometimes also in the presence of non-controllable incoherent processes. Here we show how to extend the GRAPE algorithm in the case where the incoherent processes are controllable and the target time evolution is a non-unitary quantum channel. We perform a gradient search on a fidelity measure based on Choi matrices. We illustrate our algorithm by optimizing a phase qubit measurement pulse. We show how this technique can lead to large measurement contrast close to 99%. We also show, within the validity of our model, that this algorithm can produce short 1.4 ns pulses with 98.2% contrast.

Multimode circuit QED with hybrid metamaterial transmission lines

  1. Daniel J. Egger,
  2. and Frank K. Wilhelm
Quantum transmission lines are a central to superconducting and hybrid quantum computing. Parallel to these developments are those of left-handed meta-materials. They have a wide variety
of applications in photonics from the microwave to the visible range such as invisibility cloaks and perfect flat lenses. For classical guided microwaves, left-handed transmission lines have been proposed and studied on the macroscopic scale. We combine these ideas in presenting a left-handed/right-handed hybrid transmission line for applications in quantum optics on a chip. The resulting system allows circuit QED to reach a new regime: multi-mode ultra-strong coupling. Out of the many potential applications of this novel device, we discuss two; the preparation of multipartite entangled states and its use as a quantum simulator for the spin-boson model where a quantum phase transition is reached up to finite size-effects.