One hundred seconds bit-flip time in a superconducting circuit

Posted on 10 March 2022

TL ; DR :

Together with the team of Zaki Leghtas at LPENS, Paris, we have demonstrated how to correct one of the two kinds of errors that cripple quantum computers, eliminating one of the main barriers to delivering a functional quantum computer.
Here is the preprint.

A quantum computer so close we can touch it

Qubits are the fundamental building blocks of quantum computers in the same way as bits are the foundation of their classical counterparts. A qubit with computational states |0\rangle and |1\rangle undergoes two types of errors: bit-flips that randomly swap |0\rangle and |1\rangle, and phase-flips that scramble the phase of quantum superpositions of |0\rangle and |1\rangle . Unlike phase-flips, bit-flips have an obvious classical analogue and interestingly classical bits in typical memory devices have tremendous bit-flip times compared to state of the art quantum system. In this work, we demonstrate that our stabilization scheme is compatible with macroscopic bit-flip times: we increased the resilience to bit-flip errors from a previous record of a few milliseconds to 2 minutes.

Why do we want a quantum computer

The idea of quantum computers has been around since the 1980’s. Richard Feynman had the intuition that quantum physics could enable computations out of the reach of classical machines. The invention by Peter Shor in 1994 of a quantum algorithm capable of factoring integers with an exponential speed-up proved him right. Since then the race has been on to build a usable quantum computer based on different qubit technologies : neutral atoms, spins, photons, trapped ions, superconducting qubits, etc. In that latter platform, one of the most recent advances is the superconducting cat qubit, which Alice&Bob chose to build a quantum computer.

How do cat qubits help

The dissipative cat-qubits scheme consists in stabilizing two oscillatory states of a superconducting resonator thanks to a combination of non-linear drive and dissipation. These two states, commonly called coherent states, have the same amplitude but opposite signs and are denoted |α⟩ and |-α⟩ and serve as the computational basis for the cat-qubit. Increasing α, or equivalently |α|² the cat-qubit photon number, has two opposing effect:

  1. it becomes harder for an external perturbation to disrupt the system enough to make the oscillation change sign completely. The bit-flip time increases exponentially in |α|²
  2. it becomes harder to hide the system from the environment. The phase-flip time decreases linearly in |α|².

Overall, the exponential versus linear scaling is an excellent trade-off to get error correction with a single physical qubit. Remarkably, the exponential scaling of bit-flips means it is theoretically possible to reach macroscopic bit-flip times with computational states containing only a small number of photons.

Cat qubits, as never seen before

However, the non-linear drive and dissipation that is required to stabilize the cat-qubit needs to be engineered quite accurately to be able to demonstrate such a scaling. Also, in previous implementations the measurement apparatus tended to bring too many perturbation to be able to observe stable operation over long time scales.

In order to overcome these limitations, we chose to engineer the driven-dissipation in a very stable regime and introduced a measurement scheme based on the continuous detection of the radiated field of the cat-qubit via an overcoupled antenna. This measurement scheme allows us to extract the lifetime of the coherent states |α⟩ and |-α⟩ that serve as a computationnal basis for the cat-qubit.

What we measured

We have measured a bit-flip time exceeding 100 seconds, for coherent states containing about 40 photons. As shown in the figure below, this was done by recording single trajectories showing the coherent state randomly and very rarely changing sign i.e. the circuit experiencing a bit-flip.

Real-time 40-photon coherent state dynamics.
(Left) Histogram of the detected field demonstrating two oscillatory states with opposite sign.
(Center) Single time trajectory of the circuit state revealing seldom jumps between the coherent states.
(Right) Cumulative distribution function of τjump the duration in between two consecutive jumps, labelled with the average.

For various coherent state sizes, we record time trajectories and extract the bit-flip time. The overall results are displayed in the graph below from which we distinguish two regimes. First with a limited number of photons the bit-flip time increases exponentially with the photon number. Then, when the bit-flip time reaches 2 minutes, it stops increasing with the photon number and saturates.

Exponential suppression of bit flips.
The bit-flip time (y-axis, log-scale) is measured as a function of the coherent state size in photon number (x-axis).

Even though, this detection scheme cannot reveal phase-flip times, the independent photon number calibration illustrates the quantum scale at which these macroscopic durations are achieved. The next implementation of this experiment will enable us to measure the phase-flip time along with the bit-flip time.

What’s next

This experiment was performed in a regime that favors the stability over the controllability of the system in order to demonstrate that our building blocks for engineering driven-dissipative stabilization will not be a limitation in the future.

The remaining roadmap for Alice&Bob is clear: we need to tackle phase-flip errors and plan to do this by implementing linear error correction codes. Stay tuned for more !