Circuit QED architecture for quantum control and measurement

Strong interaction between artificial atoms (qubits or qutrits) and microwave photons in a cavity gave birth one of the leading platforms for quantum control and computing, called circuit Quantum Electrodynamics (QED). In these systems the superconducting qubits based on Josephson junctions are manipulated with local magnetic and electric fields while the resonators serve a as quantum bus and for read out of the qubit quantum states.

In the past our group members have strongly contributed to implementing key elements for quantum information processing with the superconducting circuits. This includes the first implementations of: the gap tunable flux qubit1, multiplex read out of multi-qubit sample2, the three-qubit Toffoli gate3 and quantum teleportation in solid state4.

At UQ we continue to investigate new regimes of circuit QED systems to get a better grip on quantum mechanics. To perform experiments in this field our laboratory has installed a sophisticated measurement appartus with extensive list of the microwave and digital electronics, custom build measurement software with unlimited functionality and parametric amplifiers.

  1. F.G. Paauw, A. Fedorov, C.J.P.M. Harmans, and J.E. Mooij, Tuning the gap of a superconducting flux qubit, Phys. Rev. Lett. 102, 090501 (2009).

  2. M. Jerger, S. Poletto, P. Macha, U. Hübner, A. Lukashenko, E. Il'ichev and A. V. Ustinov, Readout of a qubit array via a single transmission line, EPL 96, 40012 (2011).

  3. A. Fedorov, L. Steffen, M. Baur, M. P. da Silva and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature 481, 170 (2012).

  4. L. Steffen, Y. Salathe, M. Oppliger, P. Kurpiers, M. Baur, C. Eichler, G. Puebla-Hellmann, A. Fedorov  and A. Wallraff, Realization of deterministic quantum teleportation with solid state qubits, Nature 500, 319 (2013).

Karpov D et al, 2020
EPJ B, 93, pp. 49

In a continuous measurement scheme a spin-1/2 particle can be measured and simultaneously driven by an external resonant signal.

Szombati D. et al, 2020
Phys. Rev. Lett, 124, pp. 70401

Quantum mechanics postulates that measuring the qubit's wave function results in its collapse, with the recorded discrete outcome designating the particular eigenstate the qubit collapsed into. We show this picture breaks down when the qubit is strongly driven during measurement. More specifically, for a fast evolving qubit the measurement returns the time-averaged expectation value of the measurement operator, erasing information about the initial state of the qubit, while completely suppressing the measurement back-action. We call this regime `quantum rifling', as the fast spinning of the Bloch vector protects it from deflection into either of its two eigenstates. We study this phenomenon with two superconducting qubits coupled to the same probe field and demonstrate that quantum rifling allows us to measure either one of the two qubits on demand while protecting the state of the other from measurement back-action. Our results allow for the implementation of selective read out multiplexing of several qubits, contributing to efficient scaling up of quantum processors for future quantum technologies.

Kulikov A, Navarathna R and Fedorov A, 2020
arxiv.org/abs/1906.02658

Initialization of a qubit in a pure state is a prerequisite for quantum computer operation. Qubits are commonly initialized by cooling to their ground states through passive thermalization or by using active reset protocols.

We present a technique to measure the transfer function of a control line using a qubit as a vector network analyzer. Our method requires coupling the line under test to the the longitudinal component of the Hamiltonian of the qubit and the ability to induce Rabi oscillations through simultaneous driving of the transversal component. We used this technique to characterize the 'flux' control of a superconducting Transmon qubit in the range of 8 to 400\,MHz. Our method can be used for the qubit 'flux' line calibration to increase the fidelity of entangling gates for the quantum processor. The qubit can be also used as a microscopic probe of the electro-magnetic fields on a chip. 

Hamann A.R. et al, 2018
Phys. Rev. Lett., 121, pp. 123601

Our experiment comprises the first experimental implemenation of a so called "optical rectifier" or a non-reciprocal device based on quantum nonlinearity of two-level atoms. Our device is also the simplest possible device which can behave non-reciprocally and shows the connection between non-reciprocty and entangelement.

Hamann A.R. et al
,
2018
Phys. Rev. Lett.
,
121
, pp.
123601

Our experiment comprises the first experimental implemenation of a so called "optical rectifier" or a non-reciprocal device based on quantum nonlinearity of two-level atoms. Our device is also the simplest possible device which can behave non-reciprocally and shows the connection between non-reciprocty and entangelement.

Müller C. et al, 2017
Phys. Rev. A, 96, pp. 53817

Recent theoretical studies of a pair of atoms in a 1D waveguide find that the system responds asymmetrically to incident fields from opposing directions at low powers. Since there is no explicit time-reversal symmetry breaking elements in the device, this has caused some debate. Here we show that the asymmetry arises from the formation of a quasi-dark-state of the two atoms, which saturates at extremely low power. In this case the nonlinear saturability explicitly breaks the assumptions of the Lorentz reciprocity theorem. Moreover, we show that the statistics of the output field from the driven system can be explained by a very simple stochastic mirror model and that at steady state, the two atoms and the local field are driven to an entangled, tripartite |W⟩ state. Because of this, we argue that the device is better understood as a saturable Yagi-Uda antenna, a distributed system of differentially-tuned dipoles that couples asymmetrically to external fields. 

Kulikov A. et al, 2017
Physical Review Letters, 119, pp. 240501

We experimentally realize a quantum random number generator (QRNG) with randomness of each generated number certified by the Kochen-Specker theorem. Employing this novel certification scheme eliminates the necessity for input seed random numbers and lifts the non-locality requirement for the certified QRNG. Implementation on the base of superconducting qubits allows achieving a bit rate of 25 kBit/s, two orders of magnitude higher than previously reported certified QRNGs. These improvements make our result a major step towards realization a practical certified quantum QRNG with implications for digital security and modelling algorithms.

The ability to determine whether a multi-level quantum system is in a certain state while preserving quantum coherence between all orthorgonal states is necessary to realize binary-outcome compatible measurements which are, in turn, a prerequisite for testing the contextuality of quantum mechanics. In this paper, we use a three-level superconducting system (a qutrit) coupled to a microwave cavity to explore different regimes of quantum measurement. In particular, we engineer the dispersive shifts of the cavity frequency to be identical for the first and second excited states of the qutrit which allows us to realize a strong projective binary-outcome measurement onto its ground state with a fidelity of 94.3%. Complemented with standard microwave control and low-noise parametric amplification, this scheme can be used to create sets of compatible measurements to reveal the contextual nature of superconducting circuits. 

The ability to determine whether a multi-level quantum system is in a certain state while preserving quantum coherence between all orthorgonal states is necessary to realize binary-outcome compatible measurements which are, in turn, a prerequisite for testing the contextuality of quantum mechanics. In this paper, we use a three-level superconducting system (a qutrit) coupled to a microwave cavity to explore different regimes of quantum measurement. In particular, we engineer the dispersive shifts of the cavity frequency to be identical for the first and second excited states of the qutrit which allows us to realize a strong projective binary-outcome measurement onto its ground state with a fidelity of 94.3%. Complemented with standard microwave control and low-noise parametric amplification, this scheme can be used to create sets of compatible measurements to reveal the contextual nature of superconducting circuits. 

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