Session F46: Focus Session: Shuttling and Readout in Spin Qubit Arrays

Valley-splitting mapping by conveyor-mode spin-coherent single electron shuttling

In Si/SiGe heterostructures, the low-lying excited valley state causes spin-dephasing for spin qubits. Coherent electron shuttling [1,2] may serve as a cornerstone for scaling spin qubits [3], offering spatial control over electrons, but is in itself prone to information loss at points of low valley splitting [4]. Hence, for characterizing and understanding the local variations in valley splitting across a Si/SiGe wafer, the valley splitting needs to be measured efficiently with high spatial and energy resolution.  

Leveraging the spatial control granted by conveyor-mode spin-coherent electron shuttling [1], we map valley splittings at various positions in the shuttling path by detecting magnetic anticrossings of ground and excited valley states. Our new method has sub μeV energy accuracy and a lateral resolution limited by quantum dot size and potential disorder. In addition to shuttling, we orthogonally displace the shuttle path by 6 nm steps in order to gain a 2D valley splitting map of 210 nm by 18 nm size. Its correlation length is given by the dot size and its energy spectrum agrees well with magneto-spectroscopy data for the same wafer, which, however, requires approximately 100 times longer measurement time.   

Coherent spin qubit shuttling through germanium quantum dots

Quantum links can interconnect qubit registers and are therefore essential in networked quantum computing. Semiconductor quantum dot qubits have seen significant progress in the high-fidelity operation of small qubit registers but establishing a compelling quantum link remains a challenge. Here, we show that a spin qubit can be shuttled through multiple quantum dots while preserving its quantum information. Remarkably, we achieve these results using hole spin qubits in germanium, despite the presence of strong spin-orbit interaction. We accomplish the shuttling of spin basis states over effective lengths beyond 300 μm and demonstrate the coherent shuttling of superposition states over effective lengths corresponding to 9 μm, which we can extend to 49 μm by incorporating dynamical decoupling. These findings indicate qubit shuttling as an effective approach to route qubits within registers and to establish quantum links between registers.   

Benefits and perspective of conveyor-mode single electron shuttling in Si/SiGe

Long-ranged coherent qubit coupling is a missing functional block for a scalable architecture of a spin-qubit based quantum computer. In a conveyor-mode shuttle, the spin-qubit is adiabatically transported while confined to a propagating sinusoidal potential in a gate-defined quantum channel [1]. Its key feature is the all-electrical operation by only few easily tunable input terminals and compatibility with industrial gate-fabrication. Spin-coherent conveyor-mode electron-shuttling could enable spin quantum-chips with scalable and sparse qubit-architecture hosting millions of spin-qubits [2].

 

I will summarize our progress on conveyor-mode single electron shuttling in Si/SiGe: In a 10 µm long shuttle device, we experimentally demonstrate a shuttle fidelity of 99.7±0.3% across the full device and back with a total distance of 19 μm [3]. By shuttling, we initialize and readout a register of 34 quantum dots with arbitrarily chosen patterns of zero and single-electrons [3] despite the presence of charge disorder [1] and lattice deformation [4]. In a 1 µm long shuttle device, we investigate the spin coherence during conveyor-mode shuttling by separation and rejoining an EPR spin-pair. We boost the shuttle velocity to 2.8 m/s and observe a rising spin-qubit dephasing time with the longer shuttle distances due to motional narrowing. We estimate the spin-shuttle infidelity due to dephasing to be 0.7 % for a total shuttle distance of at least 420 nm [5]. By spin-shuttling, we map material properties e.g., the valley splitting with unprecedented lateral resolution. Concerning a shuttle-based scalable quantum computing architecture, our device simulations for all relevant operations predict that operation fidelities exceeding 99.9 % are in reach [6].

 

[1] V. Langrock and J. A. Krzywda et al., PRX Quantum 4, 020305 (2023).

[2] J. M. Boter et al., Phys. Rev. Appl. 18, 024053 (2022).  

[3] R. Xue et al., arXiv:2306.16375 (2023).

[4] C. Corley-Wiciak et al., Phys. Rev. Appl. 20, 024056 (2023).

[5] T. Struck et al., arXiv:2307.04897 (2023).

[6] M. Künne and A. Willmes et al., arXiv:2306.16348 (2023).   

Bucket brigade and conveyor-mode coherent electron spin shuttling in Si/SiGe quantum dots

Long-range quantum links between spin qubits in gate-defined quantum dots are a key aspect in architectures that scale to the thousands of qubits that are required for practical quantum computation. Such coherent qubit connections, which we envision to span on the order of ten to tens of microns, provide space for on-chip classical control electronics [1, 2] and thereby alleviate the wiring bottleneck. 

 In this work we create a quantum link by shuttling a single electron spin across a linear array of six tunnel-coupled quantum dots in an isotopically enriched 28Si/SiGe heterostructure. An electron can be shuttled through the array in bucket brigade mode by sequentially pulsing both the electrochemical potential of each quantum dot and the interdot tunnel barriers [3,4,5]. Alternatively, sinusoidal voltage signals can be applied to all the channel gates to create a traveling-wave potential (conveyor-mode) [6,7]. We benchmark both bucket brigade and conveyor-mode shuttling while transporting the electron back and forth across the device. In bucket brigade, the (echoed) spin can be shuttled with an average single hop fidelity of 99.45% (99.62%), consistent with earlier work on shuttling between two dots [4,5]. The fidelity is significantly boosted when operating in conveyor mode, where one round trip from quantum dot two to five and back using a conveyor operated at 300 MHz yields a spin echo fidelity of up to 99.76%. This corresponds to a fidelity of 99.96% for transport over the same distance as in an interdot hop. 

 [1] J.M. Taylor et al., Nature Physics 1, 177–183 (2005) 

[2] L.M.K. Vandersypen et al., npj Quantum Information 3, 34 (2017) 

[3] T. Fujita et al., npj Quantum Information 3, 22 (2017) 

[4] J. Yoneda et al., Nature Communications 12, 4114 (2021) 

[5] A. Noiri et al., Nature Communications 13, 5740 (2022) 

[6] I. Seidler et al., npj Quantum Information 8, 100 (2022) 

[7] T. Struck et al., arXiv:2307.04897 (2023)    

Hilbert Space Fragmentation and Scar Time Crystallinity in Driven Homogeneous Central Spin Models

We study the stroboscopic non-equilibrium quantum dynamics of periodically driven central spin systems with XXZ-type interaction. The system exhibits a strong fragmentation of Hilbert space into a four-dimensional Floquet Krylov subspace and discrete time-translation symmetry breaking due to oscillations between two disjoint regions within each Krylov subspace. Analytical and numerical analyses of the stability of the fragmented subspaces reveal the existence of scar states corresponding to fully polarized satellite spins, which also possess high overlap with Floquet eigenstates having atypically low bipartite entanglement entropy. We show that the period-doubling indicative of time crystalline behavior arises for highly polarized initial states and persists in the presence of magnetic field disorder, pulse errors, and other perturbative effects. Our work is relevant for experiments on semiconductor quantum dots or defect spins hyperfine-coupled to surrounding nuclei.    

Variability mitigation in epitaxial-heterostructure-based spin qubit arrays via gate layout optimization

 The scalability of spin qubit devices may be compromised due to variability induced by disorder in the host materials. Charge traps, in particular, are particularly problematic due to their strong Coulomb interaction with the carriers of the qubits. In this sense, epitaxial heterostructures are of high interest given their low level of disorder at the vicinities of the active layer. The charge traps in these devices are indeed mostly located at the top GeSi/oxide interface, which is a few tens of nanometers away from the qubits. Their presence may still induce non-negligible inhomogeneities in the qubits chemical potentials and couplings, which complicates the management of spin qubit arrays.  

In this work, we focus on hole qubits in Ge/SiGe heterostructures and simulate the impact of variability on the chemical potential, detuning, and tunnel coupling between qubit pairs in a prototypical 2D spin qubit array.  We unveil the key role of gate coverage on screening the charge traps, and propose alternative designs to minimize the variability figures. These findings emphasize the importance of device design in enhancing resilience against interface traps and provide valuable insights in the quest for scalable spin qubit architectures.   

Fast and high-fidelity dispersive readout of a spin qubit via squeezing and resonator nonlinearity

We investigate dispersive measurement of an individual electron spin in a semiconductor double quantum dot that is coupled to a nonlinear microwave resonator. By employing displaced squeezed vacuum states, we achieve rapid and high-fidelity readout for semiconductor spin qubits. Our findings reveal that the introduction of modest squeezing and mild nonlinearity can significantly improve both the signal-to-noise ratio (SNR) and the fidelity of the qubit-state readout. By properly matching the phases of squeezing, the nonlinear coupling coefficient, and the local oscillator, the optimal readout time can be reduced to the sub-microsecond range. For example, with currently accessible parameters ($kappaapprox 2chi_s$, $chi_sapprox 2pi imes 0.15 :mbox{MHz}$), utilizing a displaced squeezed vacuum state with $30$ photons and a moderate squeezing parameter $rapprox 0.85$, along with a nonlinearity strength of $lambda approx -1.2 chi_s$, a readout fidelity of $98\%$ can be attained within a readout time of around $0.6:mumbox{s}$.   

Proposing a New Set of Optimal Entanglement Witnesses

Quantum entanglement can be utilized for quantum information applications, super dense coding, and secure communications. Understanding whether a state is entangled is imperative for both near and far term quantum computing. An entanglement witness is an observable whose expectation value becomes negative only for entangled states. Riccardi et al. define a set of 6 entanglement witnesses {W}. We develop two-qubit entanglement witnessing protocols that rely on a subset of the full measurements required for full state tomography, with adaptive choice of measurements if a first set fails to witness entanglement. For states whose entanglement is not witnessed by {W}, we define additional witnesses {W',W''} and use the results of the first set of measurements to choose which {W',W''} witnesses to test next, with the goal of witnessing entanglement as much as possible in a limited set of measurements. We present strategies, including one based on training a neural network, to make the adaptive choice of the second witness set.   

Lieb-Robinson correlation function in large qubit chains

The Lieb-Robinson (LR) correlation function is a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum entanglement between spatially separated qubits. The finite propagation velocity for this correlator defines a “light-cone” of quantum influence.  We calculate the LR correlation function for one-dimensional qubit arrays described by the transverse field Ising model. Direct calculations of the LR correlation function have been limited by the exponential increase in the size of the state space with the number of qubits. We introduce a new technique that avoids this barrier by transforming the calculation to a sum over Pauli walks which results in linear scaling with system size. We can then explore propagation in arrays of many hundreds of qubits and observe the effects of the quantum phase transition in the system. We see the emergence of two velocities of propagation, one which is affected by the phase transition and one which is not. For the semi-infinite chain of qubits  at the quantum critical point, we derive an analytical result for the correlation function.   

Permutation-invariant quantum circuits

Permutation invariant quantum circuits are SWAP invariant circuits. They form a closed subgroup of SU(n) with a corresponding subalgebra. We show how all possible circuit elements can be constructure, the structure of the group and characterize the algebra with a symmetrized construction. The structure hints at a more general mathematical structure of two-qubit-operation invariant circuits. Permutation invariant quantum circuits have a completely different scaling compared to arbitrary circuits with only a polynomial growth in the number of parameters. The reduction in parameters connects to results of the simulatability of this class of circuits and their lack of barren plateaus. We provide some applications of permutation-invariant circuits and indicate how the construction is an important stepping stone to the implementation of any discrete symmetry onto a quantum circuit.   

Approximate t-design in general architectures

A key point of interest in quantum circuit design is understanding the rate at which a random circuit architecture approaches a globally uniform distribution. Previous works have proven that a one-dimensional brickwork architecture becomes an approximate t-design within a depth that is linear in system size. Using a cluster-linking picture, we show how to reduce more general architectures to this one-dimensional case while preserving the linear nature of the unitary t-designs.