Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor (0903.2030v2)

Abstract: By harnessing the superposition and entanglement of physical states, quantum computers could outperform their classical counterparts in solving problems of technological impact, such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Simultaneously meeting the conflicting requirements of long coherence, state preparation, universal gate operations, and qubit readout makes building quantum processors challenging. Few-qubit processors have already been shown in nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We employ a novel two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond time scales, which is mediated by a cavity bus in a circuit quantum electrodynamics (cQED) architecture. This interaction allows generation of highly-entangled states with concurrence up to 94%. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfill the promise of a scalable technology.

• The paper demonstrates high-fidelity execution of Grover and Deutsch–Jozsa algorithms on a superconducting processor with two transmon qubits.
• It employs a novel tunable two-qubit interaction via a cavity bus to generate entangled states with up to 94% concurrence.
• The study outlines a pathway for scaling quantum processors by addressing challenges in coherence times and gate fidelities.

Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor

This paper documents the advancement in implementing quantum algorithms using a superconducting quantum processor with two transmon qubits. The authors demonstrate the execution of the Grover search and Deutsch–Jozsa algorithms, utilizing a novel two-qubit interaction mediated by a cavity bus in a circuit quantum electrodynamics (cQED) configuration. The interaction mechanism in this architecture is notable for its tunable strength, adjustable by two orders of magnitude within nanosecond timescales, enabling the generation of highly entangled states with up to 94% concurrence.

Technological Context and Achievements

Over the past decade, significant strides have been made in superconducting circuits, specifically aimed at satisfying the requirements for an electrically-controlled, solid-state quantum computer. These include enhancing coherence times and improving gate fidelities. The paper reports coherence times extending to approximately 1s, single-qubit gates achieving error rates as low as 1%, and readout fidelities of roughly 90%. These advances, however, are challenged by integrating them into a single, cohesive device, where achieving an optimal coherence and gate performance remains a bottleneck.

Implementation in a Superconducting Quantum Processor

The experimental setup consists of two transmon qubits placed within a microwave cavity bus. The circuit design incorporates local flux-bias lines that control qubit frequencies. By pulsing the qubit frequencies to specific avoided crossings, a controlled-phase (c-Phase) gate is realized. The strong-dispersive regime operation of cQED allows efficient joint readout, which is critical for two-qubit state tomography.

Algorithm Execution and Quantum Entanglement

The paper provides demonstration on-demand generation and measurement of maximally entangled states, executing key quantum algorithms with significant fidelity. Grover's algorithm and the Deutsch–Jozsa algorithm benefit from the high-fidelity entanglement achieved, demonstrating the potential of the processor to solve quantum problems computationally demanding for classical systems. The entangled quantum states were prepared with a fidelity to the ideal Bell states exceeding 90%, and the Grover search algorithm achieved an 85% fidelity for the expected final state, suggesting potential parity with or exceeding classical processing even with existing systematic errors in measurement.

Future Implications

The successful implementation of two-qubit algorithms on a superconducting platform opens new avenues for expanding to more complex quantum algorithms with higher numbers of qubits. While the system's fidelity and coherence times are noteworthy, further improvements in these areas will be crucial for scaling the architecture to larger systems capable of tackling more challenging computational tasks. The results underscore a path forward for superconducting circuits potentially becoming a viable technology for full-scale quantum computing applications.

In conclusion, this work demonstrates significant progress towards the practical implementation of quantum algorithms using superconducting qubits and highlights the ongoing need for enhancements in coherence and gate performance. The capability to manipulate entanglement with high precision is foundational to future advances in quantum information processing.