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International Journal of Quantum Chemistry

Decoherence of a Greenberger–Horne–Zeilinger state in a five‐qubit NMR quantum computer

Minaru Kawamura, Takuji Morimoto, Yoshiyuki Mori, Ryuichi Sawae, Kenichi Takarabe, Yoshinori Manmoto

Published Jan 1, 2006• 6 citations
Publisher

Abstract

Abstract This work provides a simple approximate method of creating a Greenberger–Horne–Zeilinger (GHZ) state with high fidelity, using nuclear magnetic resonance (NMR) techniques, and reports on the decoherence process for these GHZ states, which is observed with a pair of encoder and decoder quantum circuits. The prepared GHZ states are verified by measuring the quantum correlations, which are well known as GHZ correlations. The results of the decoherence experiments, show that the GHZ states decay faster than bipartite entangled states such as Bell states by a factor of 1.3, and it appears that two different decoherence processes exist. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

DOI
10.1002/qua.21172

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Abstract This work provides a simple approximate method of creating a Greenberger–Horne–Zeilinger (GHZ) state with high fidelity, using nuclear magnetic resonance (NMR) techniques, and reports on the decoherence process for these GHZ states, which is observed with a pair of encoder and decoder quantum circuits. The prepared GHZ states are verified by measuring the quantum correlations, which are well known as GHZ correlations. The results of the decoherence experiments, show that the GHZ states decay faster than bipartite entangled states such as Bell states by a factor of 1.3, and it appears that two different decoherence processes exist. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states, and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out classical local hidden variables. It nonetheless provides an unambiguous demonstration of the ``paradoxical'' GHZ correlations, and confirms the predictions of quantum mechanics.
Abstract Decoherence of the bipartite entangled mixed state in a five‐qubit system has been studied experimentally with liquid‐state nuclear magnetic resonance (NMR). The experimental results indicate that when only two qubits of the five qubits are partially initialized, the decoherence process of the bipartite entangled mixed state is not quantized, as the entanglability is weak. In contrast, when all five qubits are initialized, the decoherence process is quantized, which is understood to indicate that the entanglability is actually strong. From these results, it is conceivable that the entropy of the deviation density matrix is a crucial factor in measuring the entanglement in the liquid‐state NMR quantum computer. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
A scheme is proposed to implement microscopic analogs of the Greenberger-Horne-Zeilinger experiment, as described by Lloyd, on a nuclear magnetic resonance (NMR) quantum computer. This scheme includes how to prepare the effective pure spin state |0000〉 (a state with all the spins pointing along the direction of the magnetic field) from a state at thermal equilibrium, how to transform it into states of the form, e.g., $(|000〉\ensuremath{-}|111〉)|0〉$ (which comprises the first three spins in an entangled state and the fourth register-spin), and how to measure the eigenvalue of the operator product like ${\ensuremath{\sigma}}_{x}^{1}{\ensuremath{\sigma}}_{y}^{2}{\ensuremath{\sigma}}_{y}^{3}$ for such three-spin entangled states, where ${\ensuremath{\sigma}}^{i}$ is the Pauli matrix for the ithi\mathrm{th}ith spin, and store the result on the fourth spin. Also proposed is a general method to implement the controlled-not gate, an essential gate for any quantum algorithm, on n-qubit NMR quantum computers with n> 4.n>~4.n> 4.
Abstract Generating and detecting genuine multipartite entanglement (GME) of sizeable quantum states prepared on physical devices is an important benchmark for highlighting the progress of near-term quantum computers. A common approach to certify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure a GHZ fidelity of at least 0.5. We measure the fidelities using multiple quantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum ibmq_montreal device. Combinations of quantum readout error mitigation (QREM) and parity verification error detection are applied to the states. A fidelity of 0.546 ± 0.017 was recorded for a 27-qubit GHZ state when QREM was used, demonstrating GME across the full device with a confidence level of 98.6%. We benchmarked the effect of parity verification on GHZ fidelity for two GHZ state preparation embeddings on the heavy-hexagon architecture. The results show that the effect of parity verification, while relatively modest, led to a detectable improvement of GHZ fidelity.
Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schrödinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.