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arXiv:2306.03564 · Physical review. B./Physical review. B

Simultaneous transient dispersive readout of multiple spin qubits

Florian Ginzel, Guido Burkard

Published Sep 28, 2023• 3 citations
arXivHTMLPDF

Abstract

We propose a paradigm of multiplexed dispersive qubit measurement performed while the qubits dephase. A Laplace transformation of the time-dependent cavity response allows to separate contributions from multiple qubits coupled to the same resonator mode, thus allowing for simultaneous single-shot readout. With realistic parameters for silicon spin qubits we find a competitive readout fidelity, while the measurement time compares favorably to conventional dispersive readout. We extend the multiplexed readout method to quantum nondemolition measurements using auxiliary qubits.

DOI
10.1103/physrevb.108.125437

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We propose a paradigm of multiplexed dispersive qubit measurement performed while the qubits dephase. A Laplace transformation of the time-dependent cavity response allows to separate contributions from multiple qubits coupled to the same resonator mode, thus allowing for simultaneous single-shot readout. With realistic parameters for silicon spin qubits we find a competitive readout fidelity, while the measurement time compares favorably to conventional dispersive readout. We extend the multiplexed readout method to quantum nondemolition measurements using auxiliary qubits.
Dispersive readout, the current standard for measuring superconducting qubits, relies on relatively easy to engineer, static transverse coupling between a qubit and a detuned cavity mode. However, this method requires circuit design trade-offs between qubit-cavity coupling, cavity-feedline coupling, detuning, and the resultant decoherence introduced by the cavity mode. Additionally, the criteria for performing quantum nondemolition measurements, including reduced cavity photon numbers, further limits speed and fidelity. In this work, we introduce a circuit with pulse-tunable qubit-cavity and cavity-feedline couplings so that the entire qubit-measurement process can be fully optimized. Here, the core measurement process resembles a quantum gate operation between the qubit and the cavity, with the cavity acting like an ancilla, storing the qubit-state information. To fully explore time-dependent effects of the full qubit-cavity dynamics, we go beyond the rotating-wave, Jaynes-Cummings, or dispersive approximations, to develop a pulsed-measurement protocol. In addition, we propose a realistic circuit architecture that can provide a very fast, high-fidelity, QND measurement with near-unit efficiency.
We introduce a frequency-multiplexed readout scheme for superconducting phase qubits. Using a quantum circuit with four phase qubits, we couple each qubit to a separate lumped-element superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four qubits can be read out simultaneously using frequency multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple qubits, a significant advantage for scaling up to larger numbers of qubits.
For some cavity-quantum-electrodynamics systems, such as a single-electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can exhibit a parity-time-symmetric phase transition at the exceptional point (EP). Because the EP can amplify the perturbation induced by the qubit and the parity-time symmetry can narrow the linewidths of the peaks in the transmission spectrum of the passive cavity, we can measure the quantum states of the weakly coupled qubit via this transmission spectrum. Owing to the weak coupling between the qubit and the passive cavity, the backaction due to the measurement of the qubit can also be reduced in comparison with the conventional dispersive readout technique in the strong-coupling regime.
The ability to perform high-fidelity quantum nondemolition qubit readout is pivotal for the realization of large and powerful quantum computers. Such readout of superconducting qubits is generally enabled by amplifying the weak dispersive measurement signals using phase-preserving quantum-limited Josephson amplifiers with sufficient gain to dilute the contribution of the added noise by the output chain. Here, we further enhance the qubit readout fidelity by (1) simultaneously measuring the two-mode squeezed states of the amplified readout signals at the signal and idler frequencies of the nondegenerate amplifier and (2) coherently combining them at the classical processing stage following a relative rotation that maximizes the signal to noise ratio of the qubit-encoded readout quadrature. Such readout scheme exhibits enhancement in the readout fidelity for all practical values of amplifier gain and noise added by the output chain and is fully compatible with frequency multiplexed setups used in large quantum processors.
We present experimental results on a dispersive scheme for reading out a Josephson phase qubit. A capacitively shunted dc-SQUID is used as a nonlinear resonator which is inductively coupled to the qubit. We detect the flux state of the qubit by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, we reduce the qubit state measurement time down to 25 microseconds, which is much faster than using the conventional readout performed by switching the SQUID to its non-zero dc voltage state. The demonstrated readout scheme allows for reading out multiple qubits using a single microwave line by employing frequency-division multiplexing.
Existing schemes for semiconductor spin qubit readout involve either spin-to-charge conversion or electric dipole coupling to a superconducting resonator. The former requires destructive readout while the latter suffers from enhanced qubit dephasing, limiting the potential performance of quantum measurement: an open challenge in semiconductor quantum computing. Here we propose a coupling to a superconducting resonator based on qubit energy curvature versus gate voltage, which enables quantum nondemolition (QND) readout while the qubit resides in its full sweet spot and with zero dipole coupling (offering resilience to charge noise). Readout strengths of tens to hundred megahertz (MHz) can be reached, at least ten times larger than in the previously proposed schemes. We show how this curvature interaction generates two strictly QND readout approaches: (i) via a ``dispersive-like'' (quantum capacitance) spin-dependent resonator energy shift, similar in implementation to circuit-QED dispersive readout, but avoiding the Purcell effect; and (ii) with the addition of qubit gate voltage modulation, a longitudinal readout which can be selectively switched on, for a chosen n-qubit subsystem. Neither scheme requires the qubit and resonator to be close in frequency.