Dynamics of a superconducting qubit coupled to quantum two-level systems in its environment Robert Johansson (RIKEN, The Institute of Physical and Chemical Research, Japan) In collaboration with: Sahel Ashhab (RIKEN) Alexandre Zagoskin (UBC, RIKEN, Loughborough U.) Franco Nori (The University of Michigan, RIKEN) 1

Overview Decoherence of qubit coupled to two-level systems (TLS). Physica C 444, 45-52. Driven dynamics of qubit coupled to a TLS. New J. Phys. 8, 103. Using TLSs with long coherence times as qubits. PRL 97, 077001. Robert Johansson 11/29/2019

Overview Decoherence of qubit coupled to two-level systems (TLS). Physica C 444, 45-52. Driven dynamics of qubit coupled to a TLS. New J. Phys. 8, 103. Using TLSs with long coherence times as qubits. PRL 97, 077001. Robert Johansson 11/29/2019

Superconducting phase qubit Energy Phase across Josephson junction Robert Johansson Physica C 444, 45-52 11/29/2019 4

Evidence of TLSs in the environment Strong coupling Long coherence times Bias current Simmonds et al., PRL (2004) Cooper et al., PRL (2004) Robert Johansson Physica C 444, 45-52 11/29/2019 5

What if there are no visible splittings, but many invisibly small splittings? Small splittings should still contribute to relaxation. Each TLS contributes a small relaxation peak at its natural frequency. Total noise spectrum could still look smooth. Also weakly coupled TLSs could have long coherence times Bias current Simmonds et al., PRL (2004) Robert Johansson Physica C 444, 45-52 11/29/2019 6

Quantum degrees of freedom in the environment If an environmental degree of freedom has a longer decoherence time than its coupling strength to the qubit, it must be treated as a quantum object, i.e., the noise power spectrum is not enough to describe it. Model of a qubit coupled to a single TLS: We must treat this combined system quantum mechanically. Robert Johansson Physica C 444, 45-52 11/29/2019 7

Model of a qubit coupled to a TLS The qubit is in resonance with the TLS: We use a Bloch-Redfield master equation without the secular approximation to model the background decoherence rates and for the qubit and TLS: Solving for and tracing out the TLS gives the qubit dynamics: and the corrections to the qubit decoherence rates can be extracted. Robert Johansson Physica C 444, 45-52 11/29/2019 8

Correction to qubit relaxation rate due to the TLS Perturbation theory in quantum picture Traditional weak-coupling approximation (noise power spectrum approach) Shnirman et al., PRL (2005) The two approaches differ when the condition: is not satisfied. (Similar results for correction to the dephasing rate) Robert Johansson Physica C 444, 45-52 11/29/2019

Relative corrections to relaxation rate as function of time Transient: Longer Þ More memory Þ Non-markovian behavior (Similar results for dephasing rates) Robert Johansson Physica C 444, 45-52 11/29/2019 10

Overview Decoherence of qubit coupled to two-level systems (TLS). Physica C 444, 45-52. Driven dynamics of qubit coupled to a TLS. New J. Phys. 8, 103. Using TLSs with long coherence times as qubits. PRL 97, 077001. Robert Johansson 11/29/2019

Characterizing the TLSs Distribution of: resonance frequencies energy splittings can be measured in experiments: Martinis et al., PRL (2005) Is it possible to find the distribution of values of n(q) and n(TLS)? Robert Johansson New J. Phys. 8, 103 11/29/2019 12

Driven Qubit+TLS system Let’s take: and small l q=angle between n and z Robert Johansson New J. Phys. 8, 103 11/29/2019 13

Driven Qubit+TLS system Let’s take: and small l Rabi resonance peaks at each eigenfrequency: q=angle between n and z Robert Johansson New J. Phys. 8, 103 11/29/2019 14

Qubit+TLS energy levels: how to probe them Time driving frequency driving frequency Robert Johansson New J. Phys. 8, 103 11/29/2019 15

Effects of decoherence - Oscillations are damped in the time domain, with an exponentially decaying envelope function. Resonance peaks are widened in the frequency domain. Solid line: no decoherence. Dashed line: strong TLS decoherence Þ TLS becomes weakly coupled. Dotted line: moderate decoherence on both. Þ Narrow features are suppressed. Dash-dotted line: strong qubit decoherence. Þ Qubit cannot perform Rabi oscillations. Robert Johansson New J. Phys. 8, 103 11/29/2019 16

Overview Decoherence of qubit coupled to two-level systems (TLS). Physica C 444, 45-52. Driven dynamics of qubit coupled to a TLS. New J. Phys. 8, 103. Using TLSs with long coherence times as qubits. PRL 97, 077001. Robert Johansson 11/29/2019

Can we use coherent TLSs as qubits? Superconducting phase qubit TLS impurities in the junction Josephson junction Experiments show that some environmental TLSs have coherence times comparable to, or even longer, than the qubit. Question: Can we use those TLSs as qubits? Warning: We have no control over the parameters of TLSs. They are formed accidentally during fabrication. Robert Johansson Phys. Rev. Lett. 97, 077001 11/29/2019 18

Can we use coherent TLSs as qubits? Superconducting phase qubit TLS impurities in the junction Josephson junction Experiments show that some environmental TLSs have coherence times comparable to, or even longer, than the qubit. Question: Can we use those TLSs as qubits? Yes, in principle. We do not need to control the TLS parameters, we only need to be able to measure them. Robert Johansson Phys. Rev. Lett. 97, 077001 11/29/2019 19

TLS parameters Need to know: resonance frequencies and coupling strengths for the different TLSs. Simmonds et al., PRL (2004) Cooper et al., PRL (2004) Robert Johansson Phys. Rev. Lett. 97, 077001 11/29/2019 20

Single qubit gate on the TLSs Qubit in ground state at t=0 Time Manipulate qubit Or: If you manipulate the qubit very fast, you do not need to go out of resonance in the middle. Robert Johansson Phys. Rev. Lett. 97, 077001 11/29/2019 21

i-SWAP operation on TLSs Time Qubit in ground state at t=0 Single qubit operations + i-SWAP = universal set of gates Robert Johansson Phys. Rev. Lett. 97, 077001 11/29/2019 22

Conclusions We find corrections to relaxation and dephasing rates of a qubit weakly coupled to a TLS with long coherence rates. We identify features in the dynamics of a driven qubit coupled to a TLS that can be used to characterize the TLS. We suggest that TLSs with long coherence times can be used as qubits, by using the Josephson junction qubit as a bus. Robert Johansson 11/29/2019