Floquet-enhanced spin swaps

Abstract

The transfer of information between quantum systems is essential for quantum communication and computation. In quantum computers, high connectivity between qubits can improve the efficiency of algorithms, assist in error correction, and enable high-fidelity readout. However, as with all quantum gates, operations to transfer information between qubits can suffer from errors associated with spurious interactions and disorder between qubits, among other things. Here, we harness interactions and disorder between qubits to improve a swap operation for spin eigenstates in semiconductor gate-defined quantum-dot spins. We use a system of four electron spins, which we configure as two exchange-coupled singlet-triplet qubits. Our approach, which relies on the physics underlying discrete time crystals, enhances the quality factor of spin-eigenstate swaps by up to an order of magnitude. Our results show how interactions and disorder in multi-qubit systems can stabilize non-trivial quantum operations and suggest potential uses for non-equilibrium quantum phenomena, like time crystals, in quantum information processing applications. Our results also confirm the long-predicted emergence of effective Ising interactions between exchange-coupled singlet-triplet qubits.

Fig. 1. Experimental setup.

a Scanning electron micrograph of the quadruple quantum dot device. The locations of the electron spins are overlaid. b Schematic showing the two-qubit Ising system in a four-spin Heisenberg chain. c The pulse sequence used in the experiments.

Fig. 2. Floquet-enhanced π rotations.

a, b Measured ground-state return probabilities of (a) ST qubit 1 and (b) ST qubit 2, after four Floquet steps, with interaction time τ = 1.4 μs. The ranges of J₁ and J₃ center around $J_1^{\pi }$ and $J_3^{\pi }$. The values of J₁ and J₃ are swept simultaneously. In both figures, the red cross marks the condition for the Floquet-enhanced π rotations. The black ovals are the semiclassical phase boundaries. c, d Simulated return probabilities of (c) ST qubit 1 and (d) ST qubit 2, corresponding to the data in (a) and (b), respectively. e, f Measured ground-state return probabilities of (e) ST qubit 1 and (f) ST qubit 2, after four Floquet steps, with interaction time τ = 1.0 μs. J₁ and J₃ values are the same as in a and b. g, h Simulated return probabilities of (g) ST qubit 1 and (h) ST qubit 2, corresponding to the data in (e) and (f), respectively. The experimental data in (a, b, e, f) are averaged over 8192 realizations. In all figures, $P_g^k$ indicates the ground-state return probability for ST qubit k.

Fig. 3. Absence of Floquet enhancement due to the omission of a π pulse.

a, b Measured ground-state return probabilities of (a) ST qubit 1 and (b) ST qubit 2, after four Floquet steps, with interaction time τ = 1.4 μs. The ranges of J₁ and J₃ center around $J_1^{\pi }$ and $J_3^{2\pi }$, respectively. The values of J₁ and J₃ are swept simultaneously. The data are averaged over 8192 realizations.

Fig. 4. Floquet-enhanced spin swaps.

a–d Quality-factor enhancement of spin-eigenstate swaps for different initial states. In each figure, the top panel shows the measurements of ST qubit 1, and the bottom panel shows the measurements of ST qubit 2. The initial states are shown on the top, where $∣g⟩$ and $∣e⟩$ represent the ground state and the excited state of the ST qubit, respectively. The Floquet-enhanced π-pulse data are shown in blue, and the non-enhanced regular π-pulse data are shown in red. The fitted exponential decay envelopes are overlaid as dashed lines for all data except for the bottom panel in (d). The data are averaged over 4096 realizations.

Fig. 5. Preserving and generating entangled states.

a Return probability for the singlet state of an ST qubit defined on sites 3 and 4 of an L = 6 spin chain. The two remaining ST qubits are initialized in the state $∣\uparrow \downarrow ⟩$. b Two-qubit probabilities before and after the execution of a two-qubit CZ gate, using the modified DTC protocol (for a chain of length L = 4). The initial state of ST qubit 1 is the triplet $∣T_0⟩$ and of qubit 2 is the singlet. The x coordinate of each point is the total time of all the pulse sequences. The y coordinate of each point is the joint two-qubit probability. The “expected post-CZ state'' is an entangled state of the two ST qubits. The results in both panels are averaged over 4096 realizations.