Abstract Noise is the greatest obstacle in quantum metrology that limits it achievable precision and sensitivity. There are many techniques to mitigate the effect of noise, but this can never be done completely. One commonly proposed technique is to repeatedly apply quantum error correction. Unfortunately, the required repetition frequency needed to recover the Heisenberg limit is unachievable with the existing quantum technologies. In this article we explore the discrete application of quantum error correction with current technological limitations in mind. We establish that quantum error correction can be beneficial and highlight the factors which need to be improved so one can reliably reach the Heisenberg limit level precision.
Abstract Noise is the greatest obstacle in quantum metrology that limits it achievable precision and sensitivity. There are many techniques to mitigate the effect of noise, but this can never be done completely. One commonly proposed technique is to repeatedly apply quantum error correction. Unfortunately, the required repetition frequency needed to recover the Heisenberg limit is unachievable with the existing quantum technologies. In this article we explore the discrete application of quantum error correction with current technological limitations in mind. We establish that quantum error correction can be beneficial and highlight the factors which need to be improved so one can reliably reach the Heisenberg limit level precision.
Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum error correction (QEC) can recover the HL in various scenarios. A notable example is estimating a Pauli-Z signal under bit-flip noise using the repetition code, which is both optimal for metrology and robust against noise. However, previous protocols often assume noise affects only the signal accumulation step, while the QEC operations -- including state preparation and measurement -- are noiseless. To overcome this limitation, we study fault-tolerant quantum metrology where all qubit operations are subject to noise. We focus on estimating a Pauli-Z signal under bit-flip noise, together with state preparation and measurement errors in all QEC operations. We propose a fault-tolerant metrological protocol where a repetition code is prepared via repeated syndrome measurements, followed by a fault-tolerant logical measurement. We demonstrate the existence of an error threshold, below which errors are effectively suppressed and the HL is attained.
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.
Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, the quantum error-correcting code achieving the best possible precision can be found by solving a semidefinite program. We also show that noiseless ancilla are not needed when the signal Hamiltonian and the error operators commute. Finally we provide two explicit, archetypal examples of quantum sensors: qubits undergoing dephasing and a lossy bosonic mode.
We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error correction this limitation can be overcome. This is demonstrated in two scenarios, including a many-body Hamiltonian with single-qubit dephasing or depolarizing noise and a single-body Hamiltonian with transversal noise. In both cases, we show that Heisenberg scaling, and hence a quadratic improvement over the classical case, can be retained. Moreover, for the case of frequency estimation we find that the inclusion of error correction allows, in certain instances, for a finite optimal interrogation time even in the asymptotic limit.
The main obstacle for practical quantum technology is the noise, which can induce the decoherence and destroy the potential quantum advantages. The fluctuation of a field, which induces the dephasing of the system, is one of the most common noises and widely regarded as detrimental to quantum technologies. Here we show, contrary to the conventional belief, the fluctuation can be used to improve the precision limits in quantum metrology for the estimation of various parameters. Specifically, we show that for the estimation of the direction and rotating frequency of a field, the achieved precisions at the presence of the fluctuation can even surpass the highest precision achievable under the unitary dynamics which have been widely taken as the ultimate limit. We provide explicit protocols, which employs the adaptive quantum error correction, to achieve the higher precision limits with the fluctuating fields. Our study provides a completely new perspective on the role of the noises in quantum metrology. It also opens the door for higher precisions beyond the limit that has been believed to be ultimate.