Spin Kerr-cat qubits

summary

Video file (mp4)

The gist

The spin Kerr-cat encoding introduces a noise-robust qubit design leveraging clock transitions in quadrupolar nuclei to achieve first-order suppression of noise, potentially extending coherence times

In short

The spin Kerr-cat encoding uses a clock transition in quadrupolar nuclei to make qubits robust against charge and magnetic noise, potentially extending coherence times significantly. This method suppresses dominant error sources by tuning the qubit splitting based on external fields. The work demonstrates that this encoding allows for high-fidelity two-qubit gates between nuclear spins and electron spins.

Key concepts

Spin Kerr-cat Encoding
This design uses the two lowest energy levels of a $\mathbb{Z}_2$-symmetric nuclear spin Hamiltonian to define qubit states. These states are approximated by 'spin cat' states, which are highly distinguishable in their orientation, providing a way to encode quantum information robustly against noise.
Clock Transition
The encoding exploits a specific transition frequency in the spectrum of quadrupolar nuclei. By tuning external magnetic fields relative to this transition strength, the energy splitting ($\Delta$) is made insensitive to small fluctuations in charge noise, effectively suppressing dephasing caused by $1/f$ noise.
Two-Qubit Gate via Electron Shuttling
A novel gate is proposed by coupling a spin Kerr-cat qubit with a mobile electron spin. By adiabatically moving an electron on and off a donor potential, the nuclear spin state can be entangled with the electron's state, enabling high-fidelity two-qubit operations.
$1/f$ Noise Suppression
The clock transition is designed so that its first derivative with respect to small variations in the quadrupolar coupling strength vanishes. This mathematical property ensures that the qubit's energy splitting remains stable even when subjected to charge noise, leading to a quadratic enhancement in dephasing time.

Terminology used across episodes

This episode discusses

The paper

Spin Kerr-cat qubits · Read on arXiv

Department of Physics, University of Basel · Physics Department, King Fahd University of Petroleum and Minerals · Quantum Center, King Fahd University of Petroleum and Minerals · RDIA Chair in Quantum Computing

The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a sweet spot near a clock transition in the spectrum of quadrupolar nuclei (having spin I at least 1) to achieve a suppression of charge and magnetic noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a Z 2-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states for sufficiently high asymmetry parameters. For nuclei in highly asymmetric electric-field gradients, the nuclear spin could therefore be initialized in the spin-Kerr-cat subspace using SU(2) rotations and measurement rather than full SU(2I+1) control. We calculate the dephasing time of the spin Kerr-cat qubit under a model of 1/f noise, as well as relaxation of the qubit due to breaking of the Z 2 symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (123 Sb) donors in silicon, we estimate that second-scale T 2* times could be achieved with this encoding, with bitflips and leakage occurring on significantly longer timescales. We propose a two-qubit gate acting on spin Kerr-cat qubits and electron-spin qubits, enabled by adiabatically moving an electron on and off the donor potential. Based on numerical simulations, we estimate that with an enhancement of measured quadrupolar couplings by a factor of about 2, a gate fidelity exceeding 99% could be achieved for spin Kerr cats encoded in 123 Sb, with a gate time under 100 ns. By entangling the nuclear spin with an electron spin in this way, the spin Kerr-cat qubit could then be measured using a Pauli spin blockade readout of the electron.

DOI: 10.1103/z3dj-95j6

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Spin Kerr-cat qubits".

Mira: Here's the gist of the paper. The spin Kerr-cat encoding introduces a noise-robust qubit design leveraging clock transitions in quadrupolar nuclei to achieve first-order suppression of noise, potentially extending coherence times significantly.

Mira: The basis states of the spin Kerr-cat qubit are defined by the two lowest levels of a Z2-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states.

Paper summary: Kai: We've seen how they introduce the spin Kerr-cat encoding and what it claims about extending lifetime at the hardware level. Now let's look closer at how this actually works.

Mira: The thesis is that by leveraging a clock transition in the spectrum of quadrupolar nuclei, having spin I greater than or equal to one, they can achieve a first-order suppression of noise that leads to qubit dephasing.

Lev: To get there, the basis states are defined by the two lowest levels of a Z two-symmetric nuclear-spin Hamiltonian and these states are well approximated by spin cat states for sufficiently high asymmetry parameters <ref:2604.19687#pg1,by the two lowest levels of a>.

Kai: They ensure the definite z parity of these qubit basis states is kept by an overall Z two symmetry of the nuclear-spin Hamiltonian, which they realize through proper alignment of the applied magnetic field in relation to the EFG tensor <ref:2604.19687#pg1>.

Mira: The spin cat states, phi plus or minus are defined as symmetric and anti-symmetric linear combinations of two spin coherent states that are maximally distinguishable in their azimuthal coordinate.

Lev: The qubit splitting is tuned to a local maximum by tuning the magnetic field strength so that B zero = gamma n B zero assumes a particular value in units of Q <ref:2604.19687#pg3>.

Kai: Then the basis states of the spin Kerr-cat qubit are given by one = zero pi/two plus and zero = zero pi/two- <ref:2604.19687#pg3>.

Mira: The dephasing is suppressed because the clock transition is determined by the strength of the applied magnetic field relative to Q, causing its first derivative with respect to small variations in Q to vanish.

Lev: That vanishing first derivative ensures robustness against charge noise as well, which contrasts with what they are trying to do for superconducting resonators where photon loss is the dominant error source.

Conclusion: Kai: We've seen the basics of how the encoding works, so now we look at how it handles real noise sources like one/f noise <ref:2604.19687#pg1>.

Mira: The spin Kerr-cat encoding is designed to suppress the dominant error source affecting spin qubits, which is different from what they do for Kerr-cat encodings in superconducting resonators where photon loss causes bitflip errors instead of phase flips.

Lev: The paper shows that this strategy alone could enhance the decoherence time of encoded quantum information by several orders of magnitude without active quantum error correction or dynamical decoupling.

Kai: one/f noise, which couples the nuclear spin to non-uniform electric fields, is addressed because the clock transition is determined by the strength of the applied magnetic field relative to Q, causing its first derivative with respect to small variations in Q to vanish <ref:2604.19687#pg1>.

Mira: This vanishing first derivative ensures robustness against charge noise as well, and they found that the enhancement in dephasing time T two ct relative to T two* is quadratic, described by T two ct > A(I, eta) sqrt two pi Q (T two*) <ref:2604.19687#pg1>

Lev: Relaxation due to charge noise results from coupling between the nuclear spin and electric-field gradients. For a two-level charge fluctuator located at a distance of ten nanometers, bitflip errors zero one due to random movements of the charge will only occur on a timescale exceeding one thousand seconds for Q = one hundred kilohertz.

Kai: The generalization to an ensemble of two-level charge fluctuators shows that the transition rate ten scales like beta two max, which falls off rapidly with increasing r min and will ultimately be set predominantly by this one specific fluctuator <ref:2604.19687#pg3>.

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