Achieving the Heisenberg limit in quantum metrology using quantum error correction

Abstract

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 magnetometry using two-stroke thermal machines

“…The recent experimental advances in the control of systems at the microscopic level enabled fascinating progress in quantum technologies [1][2][3][4]. This has, in turn, sparked rigorous theoretical [5][6][7][8] and experimental [9][10][11] progress in the field of quantum metrology, with the aim of developing sensors capable of probing systems in the quantum regime with high accuracy [12][13][14][15]; such accuracy is essential throughout different branches of physics, including quantum information processing [16][17][18][19], quantum optics [20,21] and condensed matter physics [22][23][24][25]. One of the major challenges in quantum metrology is the precise estimation of small parameters [5,26].…”

The dynamical-decoupling-based spatiotemporal noise spectroscopy

“…Such investigations are currently of high importance for ongoing and nearfuture development of multi-qubit quantum registers for various applications. The cross-correlations of local noises are known to have significant influence on quantum metrological applications of systems of multiple entangled qubits [45][46][47][48][49][50][51][52], and quantum error correction [53,54]-a central issue for long-term prospects of quantum computation-that crucially relies on assumptions about correlations in decoherence processes of multiple qubits [55][56][57][58][59][60].…”

Robust symmetry-protected metrology with the Haldane phase

“…The challenge with quantum metrology schemes based on single quantum systems is the considerable susceptibility to noise associated with such sensitive probes. Recent work into quantum metrology schemes that make use of quantum error correction [6][7][8][9][10] attempts to address this issue. The control requirements and experimental complexity for such schemes, however, are quite daunting with current experimental techniques.…”

“…In comparison to schemes for metrology that use quantum error correction or other techniques with fast control [6][7][8][9][10]20], our method removes the requirements for active error correction and the local control associated with it, instead using the passive error-preventing properties of the SP phase. We present a sensing protocol that measures the direction of the field only, and then extend this protocol to measure both direction and strength.…”