Self-protected quantum algorithms based on quantum state tomography

Wu, Lian-Ao; Byrd, Mark

doi:10.1007/s11128-008-0090-9

Cited by 17 publications

(10 citation statements)

References 49 publications

(66 reference statements)

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“…Quantum information is stored not only in the strings of 0's and 1's representing the state of the entire system in the computational basis, but also in the relative phase between superpositions of computational basis states. While models of circuit model quantum computation exist which allow for a high degree of decoherence and still enable a speedup over classical algorithms [40,41], it is clear that in general T 2 represents an upper limit on the time it takes to perform a circuit model quantum computation, in the absence of quantum error correction [42].…”

Section: Timescales and Decoherence In The Circuit Vs The Adiabatmentioning

confidence: 99%

Decoherence in adiabatic quantum computation

2015

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Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time-scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed system setting, remain beneficial in the open system setting. To address the high computational cost of master equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.

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Section: Timescales and Decoherence In The Circuit Vs The Adiabatmentioning

confidence: 99%

Decoherence in adiabatic quantum computation

2015

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“…One example of the utility is given in Ref. [32], where the robust simulation of quantum systems with quantum systems was considered. In addition, the preferred basis given here provides a connection between quantum error correcting codes and direct application thereof.…”

Section: Discussionmentioning

confidence: 99%

General open-system quantum evolution in terms of affine maps of the polarization vector

Byrd

Bishop

2011

Phys. Rev. A

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The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the density matrix in terms of the polarization vector representation. This has been thoroughly explored for qubits since the components of the polarization vector are measurable quantities (corresponding to expectation values of Hermitian operators) and also because it enables the description of map domains geometrically. Here we extend the OS-affine map correspondence to qudits, briefly discuss general properties of the map, the form for particular important cases, and provide several explicit results for qutrit maps. We use the affine map and a singular-value-like decomposition, to find positivity constraints that provide a symmetry for small polarization vector magnitudes (states which are closer to the maximally mixed state) which is broken as the polarization vector increases in magnitude (a state becomes more pure). The dependence of this symmetry on the magnitude of the polarization vector implies the polar decomposition of the map can not be used as it can for the qubit case. However, it still leads us to a connection between positivity and purity for general d-state systems. Contents

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“…We now proceed to carry out state tomography [27] to check how well the quantum states are teleported in our experiment. In this process, by comparing both the theoretical and experimental density matrices of a quantum state, the accuracy of implementation can be tested.…”

Section: Quantum State Tomographymentioning

confidence: 99%

Experimental realization of quantum teleportation using coined quantum walks

Chatterjee

Devrari

Behera

et al. 2019

Quantum Inf Process

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The goal of teleportation is to transfer the state of one particle to another particle. In coined quantum walks, conditional shift operators can introduce entanglement between position space and coin space. This entanglement resource can be used as a quantum channel for teleportation, as proposed by Wang, Shang and Xue [Quantum Inf. Process. 16, 221 (2017)]. Here, we demonstrate the implementation of quantum teleportation using quantum walks on a five-qubit quantum computer and a 32-qubit simulator provided by IBM quantum experience beta platform. We show the teleportation of singlequbit, two-qubit and three-qubit quantum states with circuit implementation on the quantum devices. The teleportation of Bell, W and GHZ states has also been demonstrated as special cases of the above states.

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Self-protected quantum algorithms based on quantum state tomography

Cited by 17 publications

References 49 publications

Decoherence in adiabatic quantum computation

Decoherence in adiabatic quantum computation

General open-system quantum evolution in terms of affine maps of the polarization vector

Experimental realization of quantum teleportation using coined quantum walks

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