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Register a new userMagnetic field sensing with quantum error detection under the effect of energy relaxation
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A solid state spin is an attractive system with which to realize an ultra-sensitive magnetic field sensor. A spin superposition state will acquire a phase induced by the target field, and we can estimate the field strength from this phase. Recent studies have aimed at improving sensitivity through the use of quantum error correction (QEC) to detect and correct any bit-flip errors that may occur during the sensing period. Here, we investigate the performance of a two-qubit sensor employing QEC and under the effect of energy relaxation. Surprisingly, we find that the standard QEC technique to detect and recover from an error does not improve the sensitivity compared with the single-qubit sensors. This is a consequence of the fact that the energy relaxation induces both a phase-flip and a bit-flip noise where the former noise cannot be distinguished from the relative phase induced from the target fields. However, we have found that we can improve the sensitivity if we adopt postselection to discard the state when error is detected. Even when quantum error detection is moderately noisy, and allowing for the cost of the postselection technique, we find that this two-qubit system shows an advantage in sensing over a single qubit in the same conditions.
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Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen vacancy (NV) center in diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC field can be generally obtained when the $pi$-pulse period in the sequences matches the half time period of the field and the relative phase difference between the sequences and the field is zero. By contrast, the NV quantum sensor acquires no phase accumulation if the relative phase difference is $pi/2$. Thus, this phase-accumulation condition does not have any advantage for the magnetometry. However, we revealed that the non-phase-accumulation condition is available for detecting a very small phase shift of an AC field from its initial phase. This finding is expected to provide a guide for realizing sensitive measurement of a complex AC magnetic field in micrometer and nanometer scales.
We investigate the effect of quantum errors on a monitored Brownian Sachdev-Ye-Kitaev (SYK) model featuring a measurement-induced phase transition that can be understood as a symmetry-breaking transition of an effective $Z_4$ magnet in the replica space. The errors describe the loss of information about the measurement outcomes and are applied during the non-unitary evolution or at the end of the evolution. In the former case, we find that this error can be mapped to an emergent magnetic field in the $Z_4$ magnet, and as a consequence, the symmetry is explicitly broken independent of the measurement rate. Renyi entropies computed by twisting boundary conditions now generate domain walls even in the would-be symmetric phase at a high measurement rate. The entropy is therefore volume-law irrespective of the measurement rate. In the latter case, the error-induced magnetic field only exists near the boundary of the magnet. Varying the magnetic field leads to a pinning transition of domain walls, corresponding to error threshold of the quantum code prepared by the non-unitary SYK dynamics.
Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin- or phase flips. Our dissipative error correction scheme operates in a fully autonomous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
The energy resolution per bandwidth $E_R$ is a figure of merit that combines the field resolution, bandwidth or duration of the measurement, and size of the sensed region. Several different dc magnetometer technologies approach $E_R = hbar$, while to date none has surpassed this level. This suggests a technology-spanning quantum limit, a suggestion that is strengthened by model-based calculations for nitrogen-vacancy centres in diamond, for superconducting quantum interference device (SQUID) sensors, and for some optically-pumped alkali-vapor magnetometers, all of which predict a quantum limit close to $E_R = hbar$. Here we review what is known about energy resolution limits, with the aim to understand when and how $E_R$ is limited by quantum effects. We include a survey of reported sensitivity versus size of the sensed region for more than twenty magnetometer technologies, review the known model-based quantum limits, and critically assess possible sources for a technology-spanning limit, including zero-point fluctuations, magnetic self-interaction, and quantum speed limits. Finally, we describe sensing approaches that appear to be unconstrained by any of the known limits, and thus are candidates to surpass $E_R = hbar$.
The concept of entanglement, in which coherent quantum states become inextricably correlated, has evolved from one of the most startling and controversial outcomes of quantum mechanics to the enabling principle of emerging technologies such as quantum computation and quantum sensors. The use of entangled particles in measurement permits the transcendence of the standard quantum limit in sensitivity, which scales as N^1/2 for N particles, to the Heisenberg limit, which scales as N. This approach has been applied to optical interferometry using entangled photons and spin pairs for the measurement of magnetic fields and improvements on atomic clocks. Here, we demonstrate experimentally an 9.4-fold increase in sensitivity to an external magnetic field of a 10-spin entangled state, compared with an isolated spin, using nuclear spins in a highly symmetric molecule. This approach scales in a favourable way compared to systems where qubit loss is prevalent, and paves the way for enhanced precision in magnetic field sensing
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