Multi-qubit gates and Schrödinger cat states in an optical clock

Multi-qubit gates and Schrödinger cat states in an optical clock

July 25, 2024 | Alec Cao, William J. Eckner, Theodor Lukin Yelin, Aaron W. Young, Sven Jandura, Lingfeng Yan, Kyungtae Kim, Guido Pupillo, Jun Ye, Nelson Darkwah Oppong, and Adam M. Kaufman
This paper presents a study on multi-qubit gates and Schrödinger cat states in an optical clock. The researchers developed and employed a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 9 optical clock qubits in a programmable atom array. They demonstrated a fractional frequency instability below the standard quantum limit using GHZ states of up to 4 qubits in an atom-laser comparison. However, due to their reduced dynamic range, GHZ states of a single size failed to improve the achievable clock precision at the optimal dark time compared to unentangled atoms. To overcome this, they simultaneously prepared a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision. Quantum systems have revolutionized sensing and measurement technologies, spanning applications from nanoscale imaging with nitrogen vacancy centers to gravimetry with atom interferometers and timekeeping based on optical atomic clocks. A major precision barrier for such devices is the quantum projection noise (QPN) arising from inherently probabilistic quantum measurements. Because of QPN, a measurement on N independent and identical quantum sensors will have an uncertainty scaling as 1/√N, known as the standard quantum limit (SQL). However, the fundamental precision bound given by quantum theory is the Heisenberg limit (HL) with 1/N scaling for linear observables. Improving measurements from the SQL towards the HL using entangled or non-classical resources is the central thrust of quantum-enhanced metrology. The intersection of programmable atom arrays with optical atomic clocks provides a novel opportunity in this endeavor. The former have emerged as one of the leading architectures for quantum information processing, with advances in Rydberg-gate design now enabling controlled-phase (CZ) gate fidelities as high as 0.995. The latter now routinely achieve fractional frequency uncertainties at or below the 10^-18 level, with synchronous comparisons allowing for stability near or at the SQL. Merging these capabilities becomes possible with tweezer-controlled optical atomic clocks, which have demonstrated a relative instability of 5 × 10^-17/√τ. The integration of high-fidelity entangling gates for generating metrologically useful many-body states in a clock-qubit atom array serves as a natural path towards entanglement-enhanced measurements at the precision frontier. The paper also explores the generation and use of Schrödinger cats, coherent superpositions of two macroscopically distinct quantum states. Specifically, the maximally entangled GHZ-type cat state of N qubits accumulates phase N-times faster than unentangled qubits and saturates the HL. However, GHZ states also suffer from increased sensitivity to dephasing noise and fragility to decay andThis paper presents a study on multi-qubit gates and Schrödinger cat states in an optical clock. The researchers developed and employed a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 9 optical clock qubits in a programmable atom array. They demonstrated a fractional frequency instability below the standard quantum limit using GHZ states of up to 4 qubits in an atom-laser comparison. However, due to their reduced dynamic range, GHZ states of a single size failed to improve the achievable clock precision at the optimal dark time compared to unentangled atoms. To overcome this, they simultaneously prepared a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision. Quantum systems have revolutionized sensing and measurement technologies, spanning applications from nanoscale imaging with nitrogen vacancy centers to gravimetry with atom interferometers and timekeeping based on optical atomic clocks. A major precision barrier for such devices is the quantum projection noise (QPN) arising from inherently probabilistic quantum measurements. Because of QPN, a measurement on N independent and identical quantum sensors will have an uncertainty scaling as 1/√N, known as the standard quantum limit (SQL). However, the fundamental precision bound given by quantum theory is the Heisenberg limit (HL) with 1/N scaling for linear observables. Improving measurements from the SQL towards the HL using entangled or non-classical resources is the central thrust of quantum-enhanced metrology. The intersection of programmable atom arrays with optical atomic clocks provides a novel opportunity in this endeavor. The former have emerged as one of the leading architectures for quantum information processing, with advances in Rydberg-gate design now enabling controlled-phase (CZ) gate fidelities as high as 0.995. The latter now routinely achieve fractional frequency uncertainties at or below the 10^-18 level, with synchronous comparisons allowing for stability near or at the SQL. Merging these capabilities becomes possible with tweezer-controlled optical atomic clocks, which have demonstrated a relative instability of 5 × 10^-17/√τ. The integration of high-fidelity entangling gates for generating metrologically useful many-body states in a clock-qubit atom array serves as a natural path towards entanglement-enhanced measurements at the precision frontier. The paper also explores the generation and use of Schrödinger cats, coherent superpositions of two macroscopically distinct quantum states. Specifically, the maximally entangled GHZ-type cat state of N qubits accumulates phase N-times faster than unentangled qubits and saturates the HL. However, GHZ states also suffer from increased sensitivity to dephasing noise and fragility to decay and
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