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Physical Review B

Quantum speeding-up of computation demonstrated in a superconducting two-qubit processor

Andreas Dewes, Romain Lauro, Florian R. Ong, Vivien Schmitt, P. Milman, Patrice Bertet, D. Vion, Daniel Esteve

Published Apr 5, 2012• 33 citations
Publisher

Abstract

We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with nondestructive single-shot readout of the two qubits. With this processor, we run the Grover search algorithm among four objects and find that the correct answer is retrieved after a single run with a success probability between $0.52$ and $0.67$, which is significantly larger than the $0.25$ achieved with a classical algorithm. This constitutes a proof of concept for the quantum speed-up of electrical quantum processors.

DOI
10.1103/physrevb.85.140503

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We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with nondestructive single-shot readout of the two qubits. With this processor, we run the Grover search algorithm among four objects and find that the correct answer is retrieved after a single run with a success probability between 0.520.520.52 and 0.670.670.67, which is significantly larger than the 0.250.250.25 achieved with a classical algorithm. This constitutes a proof of concept for the quantum speed-up of electrical quantum processors.
We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover search algorithm among four objects and find that the correct answer is retrieved after a single run with a success probability between 0.52 and 0.67, significantly larger than the 0.25 achieved with a classical algorithm. This constitutes a proof-of-concept for the quantum speed-up of electrical quantum processors.
We present the experimental implementation of two-qubit quantum algorithms in a superconducting circuit. Our processor incorporates local and fast flux biasing of two transmon qubits within a circuit QED architecture. An off-resonant cavity bus shields the qubits from the external environment and couples them to each other via virtual photon exchange. Meanwhile, integrated short-circuited coplanar waveguides proximal to each qubit allow nanosecond control of their frequencies. We demonstrate flux-controlled single-qubit z rotations and a qubit-qubit conditional phase (c-phase) interaction with a coupling strength tunable by two orders of magnitude. These operations are combined with frequency-multiplexed x and y rotations to form a set of gates universal for quantum computation. Dispersive frequency shifts of the cavity bus allow tomography of the two-qubit state, and accurate determination of state purity, fidelity and entanglement. The processor is first programmed to generate and detect entanglement on demand using sequences of five single-qubit operations and one c-phase. The four Bell states are generated with fidelities better than 90%, corresponding to a concurrence of 0.85 or an entanglement of formation of 0.8. Next, the Grover search algorithm is implemented by concatenating eight single-qubit and two c-phases operations. The fidelity of the algorithm output states to the theoretical ideal is ~ 80%, consistent with the observed T1 times ~ 1 us and the total duration ~ 130 ns of the algorithm sequence. We also program and execute the Deutsch-Jozsa algorithm, finding similar performance. Prospects for scaling the processor beyond two qubits will be discussed. Research supported by NSF, NSA and ARO.
Processing quantum information using quantum three-level systems or qutrits as the fundamental unit is an alternative to contemporary qubit-based architectures with the potential to provide significant computational advantages. We demonstrate a fully programmable two-qutrit quantum processor by utilizing the third energy eigenstates of two transmons. We develop a parametric coupler to achieve excellent connectivity in the nine-dimensional Hilbert space enabling efficient implementations of two-qutrit gates. We characterize our processor by realizing several algorithms like Deutsch-Jozsa, Bernstein-Vazirani, and Grover's search. Our hardware-efficient protocols allow us to show that two stages of Grover's amplification can improve the success rates of an unstructured search with quantum advantage. Our results pave the way for building fully programmable ternary quantum processors using transmons as building blocks for a universal quantum computer.
We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own nondestructive single-shot readout. The fixed capacitive coupling yields the sqrt[iSWAP] two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%.
Processing quantum information using quantum three-level systems or qutrits as the fundamental unit is an alternative to contemporary qubit-based architectures with the potential to provide significant computational advantages. We demonstrate a fully programmable two-qutrit quantum processor by utilizing the third energy eigenstates of two transmons. We develop a parametric coupler to achieve excellent connectivity in the nine-dimensional Hilbert space enabling efficient implementations of two-qutrit gates. We characterize our processor by realizing several algorithms like Deutsch-Jozsa, Bernstein-Vazirani, and Grover's search. Our efficient ancilla-free protocols allow us to show that two stages of Grover's amplification can improve the success rates of an unstructured search with quantum advantage. Our results pave the way for building fully programmable ternary quantum processors using transmons as building blocks for a universal quantum computer.
Grover's quantum search algorithm provides a proven quadratic speedup over classical linear search for unstructured databases. While its theoretical advantage is well established, experimental validation on real noisy intermediate-scale quantum (NISQ) hardware remains limited by noise, decoherence, and hardware constraints. In this work, we present an experimental comparison between classical linear search and Grover's quantum search algorithm executed on IBM Quantum real superconducting hardware using Qiskit Runtime. A four-qubit implementation corresponding to a 16-element search space is evaluated across multiple experimental runs. The results demonstrate consistent amplitude amplification, achieving an average success probability of 54.25% and an amplification factor of 8.68× over random guessing. Although classical execution remains faster in wall-clock time due to quantum hardware overhead, the experiment empirically validates the algorithmic advantage of Grover's search and quantifies the performance gap between ideal and real quantum processors in the NISQ era.