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Scientific Reports

Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor

Shi‐Yao Hou, Yu‐Bo Sheng, Guanru Feng, Gui‐Lu Long

Published Oct 31, 2014• 26 citations
Publisher

Abstract

High quality single qubits are the building blocks in quantum information processing. But they are vulnerable to environmental noise. To overcome noise, purification techniques, which generate qubits with higher purities from qubits with lower purities, have been proposed. Purifications have attracted much interest and been widely studied. However, the full experimental demonstration of an optimal single qubit purification protocol proposed by Cirac, Ekert and Macchiavello [Phys. Rev. Lett. 82, 4344 (1999), the CEM protocol] more than one and half decades ago, still remains an experimental challenge, as it requires more complicated networks and a higher level of precision controls. In this work, we design an experiment scheme that realizes the CEM protocol with explicit symmetrization of the wave functions. The purification scheme was successfully implemented in a nuclear magnetic resonance quantum information processor. The experiment fully demonstrated the purification protocol, and showed that it is an effective way of protecting qubits against errors and decoherence.

DOI
10.1038/srep06857

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•Sep 12, 2014•0 citations
High quality single qubits are the building blocks in quantum information processing. But they are vulnerable to environmental noise. To overcome noise, purification techniques, which generate qubits with higher purities from qubits with lower purities, have been proposed. Purifications have attracted much interest and been widely studied. However, the full experimental demonstration of an optimal single qubit purification protocol proposed by Cirac, Ekert and Macchiavello [Phys. Rev. Lett. 82, 4344 (1999), the CEM protocol] more than one and half decades ago, still remains an experimental challenge, as it requires more complicated networks and a higher level of precision controls. In this work, we design an experiment scheme that realizes the CEM protocol with explicit symmetrization of the wave functions. The purification scheme was successfully implemented in a nuclear magnetic resonance quantum information processor. The experiment fully demonstrated the purification protocol, and showed that it is an effective way of protecting qubits against errors and decoherence.
Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (2008 Phys. Rev. A 77 012307). We report an error per randomized π/2 pulse of 1.3±0.1 × 10 −4 with a single-qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one- and two-qubit gates of 4.7±0.3 × 10 −3 for a three-qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.
Abstract We report on the first experimental realization of the single qubits purification protocol [J. I. Cirac, A. K. Ekert, and C. Macchiavello, Phys. Rev. Lett. 82, 4344 (1999)] for two copies of a qubit sent through a depolarizing channel. The purification of the polarization‐encoded photonic qubits is achieved with passive linear optical elements. Our experimental results suggest that the present approach may represent a viable alternative to quantum error correction or entanglement distillation.
Nuclear Magnetic Resonance (NMR) forms a natural test-bed to perform quantum information processing (QIP) and has so far proven to be one of the most successful quantum information processors. The nuclear spins in a molecule treated as quantum bits or qubits which are the basic building blocks of a quantum computer. The development of NMR over half a century puts it in a platform where we can utilize its excellent control techniques over an ensemble of spin systems and perform quantum computation in a highly controlled way. Apart from a successful quantum information processor, NMR is also a highly powerful quantum platform where many of the potentially challenging quantum mechanical experiments can be performed.
Quantum information processing devices promise to solve some problems more efficiently than their classical counterparts. The source of the speedup is the structure of quantum theory itself. In that sense, the physical units that are the building blocks of such devices are its power. The quest then is to find or manufacture a system that behaves according to quantum theory, and yet is controllable in such a way that the desired algorithms can be implemented. Candidate systems are benchmarked against general criteria to evaluate their success. In this thesis, I advance a particular system and present the progress made towards each of these criteria. The system is a three-qubit 13C solid-state nuclear magnetic resonance (NMR) based quantum processor. I report results concerning system characterization and control, pseudopure state preparation, and quantum error correction. I also report on using the system to test a central question in the foundation of quantum mechanics.
Quantum information processing has been the subject of countless discoveries since the early 1990's. It is believed to be the way of the future for computation: using quantum systems permits one to perform computation exponentially faster than on a regular classical computer. Unfortunately, quantum systems that not isolated do not behave well. They tend to lose their quantum nature due to the presence of the environment. If key information is known about the noise present in the system, methods such as quantum error correction have been developed in order to reduce the errors introduced by the environment during a given quantum computation. In order to harness the quantum world and implement the theoretical ideas of quantum information processing and quantum error correction, it is imperative to understand and quantify the noise present in the quantum processor and benchmark the quality of the control over the qubits. Usual techniques to estimate the noise or the control are based on quantum process tomography (QPT), which, unfortunately, demands an exponential amount of resources. \n \nThis thesis presents work towards the characterization of noisy processes in an efficient manner. The protocols are developed from a purely abstract setting with no system-dependent variables. To circumvent the exponential nature of quantum process tomography, three different efficient protocols are proposed and experimentally verified. The first protocol uses the idea of quantum error correction to extract relevant parameters about a given noise model, namely the correlation between the dephasing of two qubits. Following that is a protocol using randomization and symmetrization to extract the probability that a given number of qubits are simultaneously corrupted in a quantum memory, regardless of the specifics of the error and which qubits are affected. Finally, a last protocol, still using randomization ideas, is developed to estimate the average fidelity per computational gates for single and multi qubit systems. \n \nEven though liquid state NMR is argued to be unsuitable for scalable quantum information processing, it remains the best test-bed system to experimentally implement, verify and develop protocols aimed at increasing the control over general quantum information processors. For this reason, all the protocols described in this thesis have been implemented in liquid state NMR, which then led to further development of control and analysis techniques.
Quantum computers exploit quantum mechanical phenomena as resources to process information.They are therefore far more vulnerable to errors than their classical counterparts.The main obstacle to the practical realization of a working large-scale quantum computer is decoherence, i.e., the process by which a quantum system decays to a classical state through interaction with the environment.We herein discuss two techniques to implement robust quantum information processing, and report on their implementation in a liquid state NMR Quantum Computing experiment.We describe a method to implement a two-qubit gate between spins 2 and 3 of a three-spin linear chain molecule by applying a soft pulse to spin 1, with appropriate choices of the rf-field amplitude ω 1 and duration τ [1].The Bloch-Siegert effect for such a soft pulse is negligible in general, which makes NMR pulse programming and quantum gates design much simpler than with conventional hard π-pulses; it also makes this method suitable for use with both homo-and heteronuclear molecules.We then discuss a simple Operator Quantum Error Correction (OQEC) scheme with three qubits [2].This scheme provides the simplest possible Noiseless Subsystem, in terms of the number of CNOT gates, that is robust against (restricted) fully correlated noise.We demonstrated our OQEC scheme experimentally using a three-qubit NMR Quantum Computer, in which the ancillae are in the maximally mixed state.In this experiment, we made practical use of the soft pulse technique [1] to implement the two-qubit gates in the pulse sequences realizing encoding and decoding operations.