Thrifty Shadow Estimation: Reusing Quantum Circuits and Bounding Tails.

Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from "classical shadows," obtained by applying random quantum circuits and computational basis measurements. In this Letter we study the statistical efficiency of this approach in light of near-term quantum computing. We propose a more practical variant of the protocol, thrifty shadow estimation, in which quantum circuits are reused many times instead of having to be freshly generated for each measurement. We show that reuse is maximally effective when sampling Haar random unitaries, and maximally ineffective when sampling from the Clifford group, i.e., one should not reuse circuits when performing shadow estimation with the Clifford group. We provide an efficiently simulable family of quantum circuits that interpolates between these extremes, which we believe should be used instead of the Clifford group. Finally, we consider tail bounds for shadow estimation and discuss when median-of-means estimation can be replaced with standard mean estimation.

A crossbar network for silicon quantum dot qubits.

The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle electrons as a mechanism for on-chip flying qubits. To increase the number of qubits to the thousands or millions of qubits needed for practical quantum information, we present an architecture based on shared control and a scalable number of lines. Crucially, the control lines define the qubit grid, such that no local components are required. Our design enables qubit coupling beyond nearest neighbors, providing prospects for nonplanar quantum error correction protocols. Fabrication is based on a three-layer design to define qubit and tunnel barrier gates. We show that a double stripline on top of the structure can drive high-fidelity single-qubit rotations. Self-aligned inhomogeneous magnetic fields induced by direct currents through superconducting gates enable qubit addressability and readout. Qubit coupling is based on the exchange interaction, and we show that parallel two-qubit gates can be performed at the detuning-noise insensitive point. While the architecture requires a high level of uniformity in the materials and critical dimensions to enable shared control, it stands out for its simplicity and provides prospects for large-scale quantum computation in the near future.