Dissipative quantum error correction and application to quantum sensing with trapped ions

Abstract

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-flips or phase-flips. Our dissipative error correction scheme operates in a continuous 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.

Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation

“…where A β (t) are system operators, while B β (t) are bath operators 4 . If we make the change of variable t = -¢ t t and insert equation (12) in (11), after some algebra we obtain:…”

“…In this scenario, for  ¥ T the autocorrelation functions of the bath are proportional to a Dirac delta,  t d t µ bb¢ ( ) ( ), and we recover the so-called singular-coupling limit [31]. If now we calculate the integral in equation (13) for a sufficiently large time t * ?τ B , such that t * is still way smaller than the time τ R at which the state of the system in interaction picture changes appreciably, then we can safely replace ρ S (t−τ) with ρ S (t) in the same equation, since the dynamics of ρ S (t) is way slower than the decay 4 The bath operators B β in equation (12) should not be confused with B ( α) defined in equations (4) and (6): each B β is given by the product of the corresponding coupling constant a ( ) g k and the operator a…”

“…Open quantum systems of two coupled qubits are of fundamental importance in many disparate fields, being for instance at the basis of the realization of multi-qubit gates for quantum computation [1][2][3], distributed quantum sensing and metrology [4,5], and entanglement generation [6][7][8]. Such systems have been experimentally simulated in a variety of platforms, including trapped ions [9,10], superconducting qubits [11], or cavity QED arrays [12].…”

Quantum optimal control of the dissipative production of a maximally entangled state

“…Applications of this basic idea are many faceted-its use has been suggested, for example in generating entanglement [10][11][12][13][14][15][16][17][18][19][20][21][22][23], implementing universal quantum computing [9], driving phase transitions [24][25][26] and autonomous quantum error correction [27][28][29]. Experimentally, the generation of non-classical states [30], entangled states [31][32][33][34], and non-equilibrium quantum phases [35][36][37] have successfully been demonstrated.…”

Optimal approximate quantum error correction for quantum metrology

“…The task involves preparing a suitable initial state of the system, allowing it to evolve under quantum controls for a specific time, performing a suitable measurement, and inferring the value of the unknown system parameter from the measurement outcome. To enhance the estimation precision, a variety of quantum strategies have been proposed, such as squeezing the initial state [7][8][9][10][11][12], optimizing the probing time [13], monitoring the environment [14][15][16], exploiting non-Markovian effects [17][18][19], optimizing the control Hamiltonian [20][21][22] and quantum error correction [23][24][25][26][27][28][29][30][31][32][33][34].Quantum mechanics places a fundamental limit on estimation precision, the Heisenberg limit (HL), where the estimation precision scales like 1/N for N probes; or equivalently, 1/t for a total probing time t. In the noiseless case, the HL is achievable using the maximally entangled state among probes [1,35]. In practice, decoherence plays an indispensible role.…”