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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.)

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dynamics of a superconducting qubit coupled to quantum two level systems in its environment

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)

overview
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

overview1
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

superconducting phase qubit
Superconducting phase qubit

Energy

Phase across

Josephson junction

Robert Johansson

Physica C 444, 45-52

evidence of tlss in the environment
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

what if there are no visible splittings but many invisibly small splittings
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

quantum degrees of freedom in the environment
Quantum degrees of freedom inthe 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

model of a qubit coupled to a tls
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

slide9

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

relative corrections to relaxation rate as function of time
Relative corrections to relaxation rate as function of time

Relative correction

Transient:

Longer Þ More memory Þ Non-markovian behavior

(Similar results for dephasing rates)

Robert Johansson

Physica C 444, 45-52

overview2
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

characterizing the tlss
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

driven qubit tls system
Driven Qubit+TLS system

and small l

Let’s take:

q=angle between n and z

Robert Johansson

New J. Phys. 8, 103

driven qubit tls system1
Driven Qubit+TLS system

and small l

Let’s take:

Rabi resonance peaks at each eigenfrequency:

q=angle between n and z

Robert Johansson

New J. Phys. 8, 103

qubit tls energy levels how to probe them
Qubit+TLS energy levels: how to probe them

Time

driving frequency

driving frequency

Robert Johansson

New J. Phys. 8, 103

slide16

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

overview3
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

can we use coherent tlss as qubits
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

can we use coherent tlss as qubits1
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

tls parameters
TLS parameters

Need to know: resonance frequencies and coupling strengths for the different TLSs.

Cooper et al., PRL (2004)

Simmonds et al., PRL (2004)

Robert Johansson

Phys. Rev. Lett. 97, 077001

slide21

Single qubit gate on the TLSs

Time

Qubit in ground state at t=0

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

i swap operation on tlss
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

conclusions
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