Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit

Xin, Tao; Liang, Hao; Hou, Shi-Yao; Feng, Guoliang; Long, Gui Lu

doi:10.1007/s11433-019-9366-7

Cited by 17 publications

(7 citation statements)

References 46 publications

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“…Such special quantum states have interesting properties and have recently found several applications in the area of quantum information processing [41]. While standard schemes for pseudopure state preparation involve a large number of experiments and lead to reduced signal, recently a few schemes have been proposed that use only one ancilla spin and fewer number of experiments [52,53]. The relaxation behavior of twospin pseudopure states have been investigated and it was noted that cross-correlated spin relaxation plays an important role in accelerating or retarding the lifetimes of such states [54].…”

Section: B State Initialization Schemesmentioning

confidence: 99%

Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels

Singh,

Dorai

2020

Preprint

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In this work, we studied the relaxation dynamics of coherences of different order present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, single-and double-quantum coherences in several two-spin systems and performed a complete state tomography and computed state fidelity. We experimentally measured the decay of zero-and double-quantum coherences in these systems. The experimental data fitted well to a model that considers the main noise channels to be a correlated phase damping channel acting simultaneously on both spins in conjunction with a generalized amplitude damping channel acting independently on both spins. The differential relaxation of multiple-quantum coherences can be ascribed to the action of a correlated phase damping channel acting simultaneously on both the spins.

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Section: B State Initialization Schemesmentioning

confidence: 99%

Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels

Singh,

Dorai

2020

Preprint

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“…Quantum computers can effectively simulate the dynamics of quantum systems [1][2][3], prepare quantum states [4,5] and solve machine learning tasks [6][7][8][9][10][11][12], although the related algorithms generally require deep gate sequences. In the past years, rapid advances in the construction of large-scale faulttolerate universal quantum computers have been made based on, for instance, superconducting qubits [13][14][15], photos [16], silicon quantum dots [17] and ultracold trapped ions [18,19].…”

Section: Introductionmentioning

confidence: 99%

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

Liang,

Wei,

Fei

2022

Preprint

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The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions. Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism, we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems. Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states. Moreover, we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications, by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians. Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.

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“…Example applications of quantum computers include factorization, 3 database search, 4,5 solving linear equations, 6,7 query‐based eigensolver, 8 and full quantum eigensolver 9 . Proof‐of‐principle experiments of these quantum algorithms have been demonstrated on different physical platforms, such as optical system, 10‐13 ion‐trap system, 14,15 superconducting circuits, 16,17 NMR system, 18‐25 NV center, 26 and so on. However, it remains a major challenge in solving practical problems with these quantum algorithms at present, which is related to the limited number of qubits and the relative low gates fidelity under the current noisy intermediate‐scale quantum (NISQ) devices 27 …”

Section: Introductionmentioning

confidence: 99%

Variational quantum packaged deflation for arbitrary excited states

Wen

Yung

et al. 2021

Quantum Engineering

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Determining the spectral structure of molecular Hamiltonians is one of the most important and challenging research fields in quantum chemistry. In the near future, such a problem may be solvable by means of quantum simulation. However, constrained by a handful of qubits and noisy quantum gates available in the near‐term quantum devices, hybrid quantum‐classical algorithms based on variational methods such as variational quantum eigensolver have become a preferable choice. Here we propose an interesting variational quantum algorithm for obtaining the excited states of many‐body Hamiltonians. To obtain the kth excited states, the previous variational quantum deflation algorithm requires the use of k different variational circuits, which is now reduced to only two circuits with our algorithm. The feasibility of the algorithm was numerically tested on the hydrogen molecule with and without random noise, where the chemical accuracy is reached for both cases. This algorithm is expected to significantly reduce the resource requirements of quantum simulation.

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Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit

Cited by 17 publications

References 46 publications

Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels

Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

Variational quantum packaged deflation for arbitrary excited states

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