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Quantum Circuit Design Gate Engineering

Schmidt representation of 3-qubits with real amplitudes

arXiv

Authors: Oscar Perdomo

Year

2020

Paper ID

495

Status

Preprint

Abstract Read

~2 min

Abstract Words

150

Citations

N/A

Abstract

From the Schmidt representation we have that, up to local gates, every 2-qubit state can be written as [φrangle=λ₁ [00rangle+λ₂ [11rangle with λ₁ and λ₂ real numbers. For 3-qubits states, it is known, PRL 2000 85, that up to local gates every 3-qubit state can be written as [φrangle=λ₁ [000rangle+λ₂ e^{i θ}[100rangle+λ₃[101rangle+λ₄[110rangle+λ₅[111rangle with λ_ige0 and 0le θle π. In this paper, we show that no every 3-qubit state with real amplitudes can be transform in the form [φrangle=λ₁ [000rangle+λ₂ [100rangle+λ₃[101rangle+λ₄[110rangle+λ₅[111rangle by using local gates in the orthogonal group the group generated by $R_y(θandXgates). We also show that, up to local gates in the orthogonal group, every 3-qubit with real amplitudes can be written as[φ\rangle=λ_1 [000\rangle+λ_2 [011\rangle+λ_3[101\rangle+λ_4[110\rangle+λ_5[111\ranglewith theλ_i$ real numbers. An explanation of this result can be found in the youtube video \url{https://youtu.be/gDN20QHzsoQ}

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This paper contributes to the Quantum Circuit Design & Gate Engineering research area in the Quantum Articles archive.
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From the Schmidt representation we have that, up to local gates, every 2-qubit state can be written as [φrangle=λ1 [00rangle+λ2 [11rangle with λ1 and λ2 real numbers.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.14031 [2] arXiv https://arxiv.org/abs/2012.14031 [3] Publisher https://arxiv.org/abs/2012.14031

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