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arXiv:1205.2490 · Physical Review Letters

Experimental Characterization of Quantum Dynamics Through Many-Body Interactions

Daniel Nigg, Julio T. Barreiro, Philipp Schindler, Masoud Mohseni, Thomas Monz, Michael Chwalla, Markus Hennrich, R. Blatt

Published Feb 5, 2013• 8 citations
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Abstract

We report on the implementation of a quantum process tomography technique known as direct characterization of quantum dynamics applied on coherent and incoherent single-qubit processes in a system of trapped (40)Ca(+) ions. Using quantum correlations with an ancilla qubit, direct characterization of quantum dynamics reduces substantially the number of experimental configurations required for a full quantum process tomography and all diagonal elements of the process matrix can be estimated with a single setting. With this technique, the system's relaxation times T(1) and T(2) were measured with a single experimental configuration. We further show the first, complete characterization of single-qubit processes using a single generalized measurement realized through multibody correlations with three ancilla qubits.

DOI
10.1103/physrevlett.110.060403

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We report on the implementation of a quantum process tomography technique known as direct characterization of quantum dynamics applied on coherent and incoherent single-qubit processes in a system of trapped (40)Ca(+) ions. Using quantum correlations with an ancilla qubit, direct characterization of quantum dynamics reduces substantially the number of experimental configurations required for a full quantum process tomography and all diagonal elements of the process matrix can be estimated with a single setting. With this technique, the system's relaxation times T(1) and T(2) were measured with a single experimental configuration. We further show the first, complete characterization of single-qubit processes using a single generalized measurement realized through multibody correlations with three ancilla qubits.
We experimentally implement direct characterization of quantum dynamics (DCQD) algorithm of a single qubit proposed in M. Mohseni and D. A. Lidar [Phys. Rev. Lett. 97, 170501 (2006)], which does not require quantum state tomography. The number of experimental configurations is reduced by a factor of 2 compared with that of standard quantum process tomography, which can be increased four times with an ideal Bell state analyzer. We combine the DCQD algorithm with maximum-likelihood estimation to give the physical characterization of quantum dynamics. It can also be applied to obtaining partial information about quantum dynamics.
We use hyperentangled photons to experimentally implement an entanglement-assisted quantum process tomography technique known as direct characterization of quantum dynamics. Specifically, hyperentanglement-assisted Bell-state analysis enabled us to characterize a variety of single-qubit quantum processes using far fewer experimental configurations than are required by standard quantum process tomography. Furthermore, we demonstrate how known errors in Bell-state measurement may be compensated for in the data analysis. Using these techniques, we have obtained single-qubit process fidelities over 98% but with one-third the number of experimental configurations required for standard quantum process tomography. Extensions of these techniques to multiqubit quantum processes are discussed.
Direct characterization of quantum dynamics (DCQD) introduced by Mohseni and Lidar [Phys. Rev. Lett. 97, 170501 (2006)] offers an effective way for estimation of quantum dynamical systems. Employing single-photon two-qubit states, we experimentally implement DCQD of one-qubit dynamics. The requirement of two-body interactions is thus eliminated such that the algorithm can be realized more conveniently. Both DCQD and standard quantum process tomography (SQPT) measurements are performed for several processes. The data from both methods show good agreement. Although the average process fidelities of the data obtained via DCQD are a little lower than that of SQPT, the number of experimental configurations is quadratically reduced evidencing the quadratic advantage of DCQD scheme. Partial information of the quantum dynamics can also be directly extracted via DCQD with fewer measurements.
Characterising multi-time quantum processes is essential for analysing temporally correlated noise and for designing effective control and mitigation strategies. A complete operational description through multi-time process tomography requires an informationally complete set of probes, which necessarily includes non-deterministic intermediate operations. On present-day quantum devices, such operations are commonly implemented using mid-circuit measurements and reset, which are technologically limited and can introduce noise and overhead in terms of ancilla requirement. In this work, we study the minimal ancillary dimension required for complete characterisation of multi-time processes. We show that sequential interactions with a single qubit ancilla can generate an informationally complete family of correlated probes for processes of arbitrary length, without requiring mid-circuit measurements or reset. Our result provides a resource-efficient route for complete multi-time process tomography and establishes that one qubit of coherent ancillary memory suffices for full reconstruction of arbitrary multi-time dynamics.
The standard procedure for quantum process tomography (QPT) requires a series of experiments. Each experiment involves initialization of the system to a particular basis state, applying the quantum process $\ensuremath{\varepsilon}$ on the system, and finally characterizing the output state by quantum state tomography (QST). The output states collected for a complete set of basis states enable us to calculate the $\ensuremath{\chi}$ matrix characterizing the process $\ensuremath{\varepsilon}$. The standard procedure for QST itself requires independent experiments, each involving measurement of a set of commuting observables. Thus QPT procedure demands a number of independent measurements and, moreover, this number increases rapidly with the size of the system. However, in ensemble systems, the total number of independent measurements can be greatly reduced with the availability of ancilla qubits. Ancilla-assisted process tomography (AAPT) has earlier been shown to require a single QST of system-ancilla space. Ancilla-assisted quantum state tomography (AAQST) has also been shown to perform QST in a single-scan measurement of an ensemble system. Here we combine AAPT with AAQST to realize a single-scan QPT (SSPT), a procedure to characterize a general quantum process in a single ensemble measurement. We demonstrate experimental SSPT by characterizing several single-qubit processes using a three-qubit NMR quantum register. Furthermore, using the SSPT procedure, we experimentally characterize the twirling process and compare the results with theory.
The characterization of the dynamics of quantum systems is a task of both fundamental and practical importance. A general class of methods which have been developed in quantum information theory to accomplish this task is known as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A. Lidar Phys. Rev. Lett. 97, 170501 (2006)] we presented an algorithm for direct characterization of quantum dynamics (DCQD) of two-level quantum systems. Here we provide a generalization by developing a theory for direct and complete characterization of the dynamics of arbitrary quantum systems. In contrast to other QPT schemes, DCQD relies on quantum error-detection techniques and does not require any quantum state tomography. We demonstrate that for the full characterization of the dynamics of nnn ddd-level quantum systems (with ddd prime), the minimal number of required experimental configurations is reduced quadratically from d4n{d}^{4n}d4n in separable QPT schemes to d2n{d}^{2n}d2n in DCQD.