Investigating Entanglement Rates of Coupled Superconducting QubitsJ. Howard1, K. Clark1, C. Haack1, J. Long2, M. Bal2, R. Zhao2, T. Zhao2, D. Pappas2, Z. Gong1, M. Singh1

1Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA

2National Institute of Standards and Technology, Boulder, CO, 80305, USA

Overview

Quantum entanglement, the operation by which multiple qubits enter a

non-separable quantum state, is the defining operation that distinguishes

quantum from classical computation. Due to finite coherence windows in

which to perform operations, the maximum rate at which entanglement

can be generated is an important metric. Theoretical predictions from Dr.

Gong’s group show that this rate can be boosted via coupling to a third

ancillary qubit. The goal of this work is to experimentally demonstrate this

increase in the entanglement speed limit on a superconducting qubit

platform.

Theory

Current work focuses on demonstrating an entangling speed limit for

reaching the Bell state |00〉+|11〉√2

for two σzσz-coupled qubits (see “Devices”

section). There are two available methods for determining a theoretical

speed limit. The first is to design a pulse sequence that consists of a free

evolution flanked by single qubit rotations. This offers an analytical limit so

long as the single-qubit rotations are approximately instantaneous

compared to the free evolution time.

The second method, which we are currently pursuing, is to numerically

optimize the drive pulses for fidelity to the target state. Sweeping over

total gate duration we get the curve shown in Fig.1.

Figure 1: Graph of infidelity to the Bell state as a function of gate duration when using

numerically optimized pulses.

Device

The two-qubit coupled concentric transmon system currently being

measured (see Fig.2) has the following Hamiltonian:H~

=gz

4σ1

z +gz

4σ2

z +gz

4σ1

zσ2z (1)

+ Ω1x(t)(σ1

x |0〉 〈0| + r1σ1x |1〉 〈1|

)+ Ω1y(t)

(σ1

y |0〉 〈0| + r1σ1y |1〉 〈1|

)+ Ω2x(t)

(|0〉 〈0|σ2

x + r2 |1〉 〈1|σ2x)

+ Ω2y(t)(|0〉 〈0|σ2

y + r2 |1〉 〈1|σ2y)

with gz = 9.75MHz, r1 = 1.14, r2 = 0.77 and Rabi strengths Ω[1,2],[x ,y ]

determined by our optimized drive pulses.

Figure 2: Concentric transmon device micrograph

Experiment

The numerically-optimized pulses intended to generate the target Bell

state are shown in figure 3. These will be followed by tomographic

sequences and projective readout.

Figure 3: Entangling gate consisting of numerically-optimized pulses applied to each qubit

Current Progress

We have so far run full spectroscopy on the qubit system but are seeing

beating patterns in our Ramsey experiments (Fig. 5) that indicate qubit

transition frequencies changing due to quasiparticle tunneling at a rate of

about 31 kHZ. This effect needs to be suppressed in order to achieve

acceptable phase coherence times for our experiment.

Figure 4: T1 measurementFigure 5: Ramsey fringe beating for the

|01〉 → |11〉 transition

Future Work

IBecause the dipole ratios (r1, r2 in the “Devices” section) are not both unity,

there exists drive coupling in addition to the σzσz interaction that affect the

entangling speed limit. Future experimental efforts will focus on bringing

these ratios closer to unity, with theory efforts focusing on developing a

means to account for this drive coupling in the speed limit prediction.

IUpon successfully generating a fidelity curve for the two qubit system that

matches the theoretical speed limit predictions work will begin on

designing a three-qubit system to demonstrate the predicted speedup.

Acknowledgements

The authors thank the NIST-Boulder Physical Measurement Laboratory

division as well as NSF CCF grant no. 1839232 for supporting this project.

Singh Group | Department of Physics | Colorado School of Mines

Pappas Group | Quantum Processing Division | NIST-Boulder