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arXiv:1806.05543 · Physical Review Letters

Witnessing Quantum Resource Conversion within Deterministic Quantum Computation Using One Pure Superconducting Qubit

Weishuai Wang, J. Han, Benjamin Yadin, Yuxin Ma, Jiajun Ma, Weizhou Cai, Yuan Xu, Ling Hu, Hanrui Wang, Yipu Song, Mile Gu, Luyan Sun

Published Nov 26, 2019• 20 citations
arXivHTMLPDF

Abstract

Deterministic quantum computation with one qubit (DQC1) is iconic in highlighting that exponential quantum speedup may be achieved with negligible entanglement. Its discovery catalyzed a heated study of general quantum resources, and various conjectures regarding their role in DQC1's performance advantage. Coherence and discord are prominent candidates, respectively, characterizing nonclassicality within localized and correlated systems. Here we realize DQC1 within a superconducting system, engineered such that the dynamics of coherence and discord can be tracked throughout its execution. We experimentally confirm that DQC1 acts as a resource converter, consuming coherence to generate discord during its operation. Our results highlight superconducting circuits as a promising platform for both realizing DQC1 and related algorithms, and experimentally characterizing resource dynamics within quantum protocols.

DOI
10.1103/physrevlett.123.220501

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Deterministic quantum computation with one qubit (DQC1) is iconic in highlighting that exponential quantum speedup may be achieved with negligible entanglement. Its discovery catalyzed a heated study of general quantum resources, and various conjectures regarding their role in DQC1's performance advantage. Coherence and discord are prominent candidates, respectively, characterizing nonclassicality within localized and correlated systems. Here we realize DQC1 within a superconducting system, engineered such that the dynamics of coherence and discord can be tracked throughout its execution. We experimentally confirm that DQC1 acts as a resource converter, consuming coherence to generate discord during its operation. Our results highlight superconducting circuits as a promising platform for both realizing DQC1 and related algorithms, and experimentally characterizing resource dynamics within quantum protocols.
Quantum discord has been proposed as a resource responsible for the exponential speedup in deterministic quantum computation with one pure qubit (DQC1). Investigation of the quantum discord generated in DQC1 is of significant importance from a fundamental perspective. However, in practical applications of DQC1, qubits generally interact with the environment. Thus, it is also important to investigate the discord when DQC1 is implemented in a noisy environment. We implement DQC1 on an electron spin resonance (ESR) architecture in such an environment and nonzero quantum discord is observed. Furthermore, we find that the values of discord correspond to the values of purity α and quantum Fisher information, which reflect the power of the algorithm. Our results provide further evidence for the role of discord as a resource in DQC1 and are beneficial for understanding the origin of the power of quantum algorithms.
Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.
We use quantum discord to characterize the correlations present in the model called deterministic quantum computation with one quantum bit (DQC1), introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)10.1103/PhysRevLett.81.5672]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. The initial state, operations, and measurements in the model all point to a natural bipartite split between the control qubit and the mixed ones. Although there is no entanglement between these two parts, we show that the quantum discord across this split is nonzero for typical instances of the DQC1 ciruit. Nonzero values of discord indicate the presence of nonclassical correlations. We propose quantum discord as figure of merit for characterizing the resources present in this computational model.
The power of one qubit deterministic quantum processor (DQC1) (Knill and Laflamme (1998)) generates a nonclassical correlation known as quantum discord. The DQC1 algorithm executes in an efficient way with a characteristic time given by τ=Tr[Un]/2n , where Un is an n qubit unitary gate. For pure states, quantum discord means entanglement while for mixed states such a quantity is more than entanglement. Quantum discord can be thought of as the mutual information between two systems. Within the quantum discord approach the role of time in an efficient evaluation of τ is discussed. It is found that the smaller the value of t/T is, where t is the time of execution of the DQC1 algorithm and T is the scale of time where the nonclassical correlations prevail, the more efficient the calculation of τ is. A Mösbauer nucleus might be a good processor of the DQC1 algorithm while a nuclear spin chain would not be efficient for the calculation of τ .
In this thesis, I look at the role of quantum entanglement in mixed-state quantum computation. The model we consider is the DQC1 or `power of one qubit' model. I show that there is minimal bipartite entanglement in a typical instance of the DQC1 circuit and even put an upper bound on the possible amount of entanglement. This limited amount of entanglement, however, does not imply that the system is classically simulatable. A matrix product state (MPS) algorithm for a typical instance of the DQC1 system requires exponential classical resources. This exposes a gap between the amount of entanglement and the amount of purely nonclassical correlations in a quantum system. This gap, I suggest, can be filled by quantum discord. I calculate it in a typical instance of the DQC1 circuit and find that the amount of discord is a constant fraction of the maximum possible discord for a system of that size. This allows an interpretation of quantum discord as the resource that drives mixed-state quantum computation. I also study quantum discord as a quantity of independent interest. Its role in the phenomenon of entanglement distribution is studied through an easily comprehensible example. This thesis also contains discussions on the relation between the complexity classes P, BQP and DQC1. Additional material is presented on the connections between the DQC1 model, Jones polynomials and statistical mechanics. The thesis concludes with a discussion of a few open problems related to the DQC1 model, the quantum discord and their scope in quantum information science.
The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work, we analyze the quantum correlations called entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model, only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit, taking it out from the totally mixed state and consequently promoting other quantum correlations between the qubits, such as entanglement and Bell's nonlocality. Through the optimization of the purification process, we conclude that even a small purification is enough to generate entanglement and Bell's nonlocality. We obtain, that by applying the purification process repeatedly an average of 12 times, the auxiliary qubit becomes 9999%99 pure. In this situation, almost maximally entangled states are achieved, which almost maximally violate Bell's inequality. This result suggests that with a simple modification, the DQC1 model can be promoted to a universal model of quantum computing.