True experimental reconstruction of quantum states and processes via convex optimization

Gaikwad, Akshay; Arvind, .; Dorai, Kavita

doi:10.1007/s11128-020-02930-z

Cited by 14 publications

(16 citation statements)

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“…Using the MSQPT method, the matrix is Hermitian by construction, however there is no guarantee that it will satisfy the last two conditions. One can use the constrained convex optimization (CCO) technique 10 to obtain a valid matrix from as follows: where is the experimentally obtained process matrix using the MSQPT protocol and is the variable process matrix which represents the underlying true quantum process.…”

Section: Preliminariesmentioning

confidence: 99%

“…Resource requirements for standard QST and QPT methods grow exponentially with increasing system size, and hence several novel methods have been designed that focus on simplifying and reducing experimental complexity such as maximum likelihood estimation 3 , adaptive quantum tomography 4 , self-guided tomography 5 , ancilla-assisted tomography 6 , compressed sensing tomography 7 , 8 , and least square optimization based tomography 9 , 10 . These novel tomography protocols have been experimentally demonstrated on various physical configurations such as NMR 11 , 12 , linear-optics 13 , NV-centers 14 , ion-trap based quantum processors 15 , photonic qubits 16 , and superconducting qubits 17 – 20 .…”

Section: Introductionmentioning

confidence: 99%

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Implementing efficient selective quantum process tomography of superconducting quantum gates on IBM quantum experience

Gaikwad

Shende

Arvind

et al. 2022

Sci Rep

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The experimental implementation of selective quantum process tomography (SQPT) involves computing individual elements of the process matrix with the help of a special set of states called quantum 2-design states. However, the number of experimental settings required to prepare input states from quantum 2-design states to selectively and precisely compute a desired element of the process matrix is still high, and hence constructing the corresponding unitary operations in the lab is a daunting task. In order to reduce the experimental complexity, we mathematically reformulated the standard SQPT problem, which we term the modified SQPT (MSQPT) method. We designed the generalized quantum circuit to prepare the required set of input states and formulated an efficient measurement strategy aimed at minimizing the experimental cost of SQPT. We experimentally demonstrated the MSQPT protocol on the IBM QX2 cloud quantum processor and selectively characterized various two- and three-qubit quantum gates.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implementing efficient selective quantum process tomography of superconducting quantum gates on IBM quantum experience

Gaikwad

Shende

Arvind

et al. 2022

Sci Rep

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“…The density matrix of the initial state was reconstructed using least square constrained convex optimization method [48] by performing full quantum state tomography using a set of seven preparatory pulses {III, XXX, IIY , XY X, Y II, XXY , IY Y } where I represents 'no-operation' and X(Y ) is the local π/2 unitary operator with phases x(y) and local operations The quantum circuit to implement PT-symmetric Hamiltonian is shown in Fig. 1(a).…”

Section: Experimental Demonstration Of the Dynamics Of Quantum Cohere...mentioning

confidence: 99%

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

Gautam¹,

Dorai²,

Arvind³

2022

Preprint

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In this work, we study the dynamics of quantum coherence (total coherence, global coherence and local coherence) evolving under a local PT-symmetric Hamiltonian in maximally entangled bipartite and tripartite states. Our results indicate that quantum coherence in the bipartite state oscillates in the unbroken phase regime of the PT-symmetric Hamiltonian. Interestingly, in the broken phase regime, while the global coherence decays exponentially, the local and total coherences enter a "freezing" regime where they attain a stable value over time. A similar pattern is observed for the dynamics of total and local coherences in the maximally entangled tripartite state, while the dynamics of global coherence in this state differs from that of the bipartite state. These results were experimentally validated for a maximally entangled bipartite state on a three-qubit nuclear magnetic resonance (NMR) quantum processor, with one of the qubits acting as an ancilla. The experimental results match well with the theoretical predictions, upto experimental errors.

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“…We note here that using the standard QPT method may not always lead to a positive semi-definite experimentally constructed χ matrix, due to experimental uncertainties. This problem can be resolved by reformulating the linear inversion problem as a constrained convex optimization problem as follows [19]:…”

Section: A Standard Qpt and χ Matrix Representationmentioning

confidence: 99%

“…Several QST protocols have been extended to perform QPT, which include MLE-based QPT [9], LS-based QPT [10], simplified QPT [11], convex optimization-based QPT [12], selective and efficient QPT [13], adaptive QPT [14], and ancillaassisted QPT [15]. These protocols have been successfully demonstrated on various physical systems such as NMR [16][17][18][19][20], NV-centers [21], linear optics [22], superconducting qubits [23][24][25] and ion trap-based quantum processors [26].…”

Section: Introductionmentioning

confidence: 99%

Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

Gaikwad¹,

Arvind²,

Dorai³

2021

Preprint

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We employ the compressed sensing (CS) algorithm and a heavily reduced data set to experimentally perform true quantum process tomography (QPT) on an NMR quantum processor. We obtain the estimate of the process matrix χ corresponding to various two-and three-qubit quantum gates with a high fidelity. The CS algorithm is implemented using two different operator bases, namely, the standard Pauli basis and the Pauli-error basis. We experimentally demonstrate that the performance of the CS algorithm is significantly better in the Pauli-error basis, where the constructed χ matrix is maximally sparse. We compare the standard least square (LS) optimization QPT method with the CS-QPT method and observe that, provided an appropriate basis is chosen, the CS-QPT method performs significantly better as compared to the LS-QPT method. In all the cases considered, we obtained experimental fidelities greater than 0.9 from a reduced data set, which was approximately five to six times smaller in size than a full data set. We also experimentally characterized the reduced dynamics of a two-qubit subsystem embedded in a three-qubit system, and used the CS-QPT method to characterize processes corresponding to the evolution of two-qubit states under various J-coupling interactions.

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True experimental reconstruction of quantum states and processes via convex optimization

Cited by 14 publications

References 50 publications

Implementing efficient selective quantum process tomography of superconducting quantum gates on IBM quantum experience

Implementing efficient selective quantum process tomography of superconducting quantum gates on IBM quantum experience

Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor

Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

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