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Register a new userFast Bayesian tomography of a two-qubit gate set in silicon
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Added by
Stephen D. Bartlett
Publication date
2021
fields
Physics
and research's language is
English
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Benchmarking and characterising quantum states and logic gates is essential in the development of devices for quantum computing. We introduce a Bayesian approach to self-consistent process tomography, called fast Bayesian tomography (FBT), and experimentally demonstrate its performance in characterising a two-qubit gate set on a silicon-based spin qubit device. FBT is built on an adaptive self-consistent linearisation that is robust to model approximation errors. Our method offers several advantages over other self-consistent tomographic methods. Most notably, FBT can leverage prior information from randomised benchmarking (or other characterisation measurements), and can be performed in real time, providing continuously updated estimates of full process matrices while data is acquired.
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Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Ear
Measurements that occur within the internal layers of a quantum circuit -- mid-circuit measurements -- are an important quantum computing primitive, most notably for quantum error correction. Mid-circuit measurements have both classical and quantum outputs, so they can be subject to error modes that do not exist for measurements that terminate quantum circuits. Here we show how to characterize mid-circuit measurements, modelled by quantum instruments, using a technique that we call quantum instrument linear gate set tomography (QILGST). We then apply this technique to characterize a dispersive measurement on a superconducting transmon qubit within a multiqubit system. By varying the delay time between the measurement pulse and subsequent gates, we explore the impact of residual cavity photon population on measurement error. QILGST can resolve different error modes and quantify the total error from a measurement; in our experiment, for delay times above 1000 ns we measured a total error rate (i.e., half diamond distance) of $epsilon_{diamond} = 8.1 pm 1.4 %$, a readout fidelity of $97.0 pm 0.3%$, and output quantum state fidelities of $96.7 pm 0.6%$ and $93.7 pm 0.7%$ when measuring $0$ and $1$, respectively.
Quantum computation requires qubits that can be coupled and realized in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates cite{DiVincenzo2000, Loss1998}. Strong effort across several fields have led to an impressive array of qubit realizations, including trapped ions cite{Brown2011}, superconducting circuits cite{Barends2014}, single photonscite{Kok2007}, single defects or atoms in diamond cite{Waldherr2014, Dolde2014} and silicon cite{Muhonen2014}, and semiconductor quantum dots cite{Veldhorst2014}, all with single qubit fidelities exceeding the stringent thresholds required for fault-tolerant quantum computing cite{Fowler2012}. Despite this, high-fidelity two-qubit gates in the solid-state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits cite{Barends2014}, as semiconductor systems have suffered from difficulties in coupling qubits and dephasing cite{Nowack2011, Brunner2011, Shulman2012}. Here, we show that these issues can be eliminated altogether using single spins in isotopically enriched siliconcite{Itoh2014} by demonstrating single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the original Loss-DiVincenzo proposal cite{Loss1998}. We realize CNOT gates via either controlled rotation (CROT) or controlled phase (CZ) operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is employed in the two-qubit CZ gate. The speed of the two-qubit CZ operations is controlled electrically via the detuning energy and we find that over 100 two-qubit gates can be performed within a two-qubit coherence time of 8 textmu s, thereby satisfying the criteria required for scalable quantum computation.
We propose a new protocol to implement ultra-fast two-qubit phase gates with trapped ions using spin-dependent kicks induced by resonant transitions. By only optimizing the allocation of the arrival times in a pulse train sequence the gate is implemented in times faster than the trapping oscillation period $T<2pi/omega$. Such gates allow us to increase the number of gate operations that can be completed within the coherence time of the ion-qubits favoring the development of scalable quantum computers.
Nuclear spins were among the first physical platforms to be considered for quantum information processing, because of their exceptional quantum coherence and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, due to the lack of methods to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted $^{31}$P nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterised using gate set tomography (GST), yielding one-qubit gate fidelities up to 99.93(3)%, two-qubit gate fidelity of 99.21(14)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Since electron spin qubits in semiconductors can be further coupled to other electrons or physically shuttled across different locations, these results establish a viable route for scalable quantum information processing using nuclear spins.
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