Abstract Quantum annealers require accurate control and optimized operation schemes to reduce noise levels, in order to eventually demonstrate a computational advantage over classical algorithms. We study a high coherence four-junction capacitively shunted flux qubit (CSFQ), using dispersive measurements to extract system parameters and model the device. Josephson junction asymmetry inherent to the device causes a deleterious nonlinear cross-talk when annealing the qubit. We implement a nonlinear annealing path to correct the asymmetry in situ, resulting in a substantial increase in the probability of the qubit being in the correct state given an applied flux bias. We also confirm the multi-level structure of our CSFQ circuit model by annealing it through small spectral gaps and observing quantum signatures of energy level crossings. Our results demonstrate an anneal-path correction scheme designed and implemented to improve control accuracy for high-coherence and high-control quantum annealers, which leads to an enhancement of success probability in annealing protocols.
Abstract Quantum annealers require accurate control and optimized operation schemes to reduce noise levels, in order to eventually demonstrate a computational advantage over classical algorithms. We study a high coherence four-junction capacitively shunted flux qubit (CSFQ), using dispersive measurements to extract system parameters and model the device. Josephson junction asymmetry inherent to the device causes a deleterious nonlinear cross-talk when annealing the qubit. We implement a nonlinear annealing path to correct the asymmetry in situ, resulting in a substantial increase in the probability of the qubit being in the correct state given an applied flux bias. We also confirm the multi-level structure of our CSFQ circuit model by annealing it through small spectral gaps and observing quantum signatures of energy level crossings. Our results demonstrate an anneal-path correction scheme designed and implemented to improve control accuracy for high-coherence and high-control quantum annealers, which leads to an enhancement of success probability in annealing protocols.
Abstract Quantum annealing (QA) provides us with a way to solve combinatorial optimization problems. In the previous demonstration of the QA, a superconducting flux qubit (FQ) was used. However, the FQs in these demonstrations have a short coherence time such as tens of nano seconds. For the purpose to utilize quantum properties, it is necessary to use another qubit with a better coherence time. Here, we propose to use a capacitive-shunted flux qubit (CSFQ) for the implementation of the QA. The CSFQ has a few order of magnitude better coherence time than the FQ used in the QA. We theoretically show that, although it is difficult to perform the conventional QA with the CSFQ due to the form and strength of the interaction between the CSFQs, a spin-lock based QA can be implemented with the CSFQ even with the current technology. Our results pave the way for the realization of the practical QA that exploits quantum advantage with long-lived qubits.
While quantum computation has the potential to revolutionize the scientific community, to date no architecture has been developed which offers the necessary combination of high coherence times and massive scalability. Superconducting flux qubits satisfy the second requirement well but to date useful devices are limited to coherence times of typically only a few &mus. In this dissertation we examine the possibilities of improving the coherence performance of the flux qubit to the levels required for fault-tolerant quantum computation. We find that coherence times for many devices are limited by photon-induced quasiparticles and mitigation of these quasiparticles increases coherence times by more than a factor of two. Beyond this, however, we find little improvement in flux qubit performance compared to prior results. Despite improved fabrication techniques and varied device designs we find flux qubit coherence times are still typically below 5 &mus. Furthermore, wide device-to-device variations are observed which prevent effective scaling of the flux qubit to quantum information circuits.Based on the proposal by You, et al. we develop of a capacitively-shunted version of the flux qubit called the C-shunt flux qubit. With the addition of a capacitive shunt across the small junction of the flux qubit we are able to reduce the amplitude sensitivity to both charge and flux noise by more than a factor of three. The result is a predicted ten-fold enhancement in the coherence times compared to the unshunted flux qubit. At the same time we preserve much of the anharmonicity of the flux qubit resulting in a device with coherence times comparable to modern transmons but with a factor of four better anharmonicity and more flexible coupling configurations.By using a high-quality MBE aluminum shunt process on an annealed sapphire substrate coupled with a more conventional electron-beam-evaporated aluminum Josephson junction process we fabricate hybrid C-shunt flux qubits. We also incorporate a new bridgeless junction technique which offers more robust and repeatable fabrication processing. This technique enables improved accuracy of the junction sizing, a trait which will become essential as we move to multi-qubit experiments. T1 and T2 times for these C-shunt devices reach in excess of 40 &mus at degeneracy, achieving the predicted ten-fold improvement based on the reduced noise sensitivity. At the same time we see decreased device-to-device variation with typical T1 times exceeding 20&ndash25 &mus at all bias points. Combined with the high anharmonicity and standard planar fabrication techniques these coherence times make the C-shunt flux qubit a competitive candidate for fault-tolerant quantum computation.
Quantum annealing is a method to solve optimization problems that leverages quantum tunneling in a coupled qubit system. We present a detailed study of the coherence of a tunable capacitively-shunted flux qubit, designed for coherent quantum annealing applications. We find that for high qubit frequencies, thermal noise in the bias line makes a significant contribution to the relaxation, arising from the design choice to experimentally explore both fast annealing and high-frequency control. The measured dephasing rate is primarily due to intrinsic low-frequency flux noise in the two qubit loops, with additional contribution from the low-frequency noise of control electronics used for fast annealing. Our results characterize decoherence in a realistic setup for quantum annealing and are relevant for ongoing efforts toward building superconducting quantum annealers with increased coherence. Quantum annealers hold promise of outperforming classical computers in solving hard optimization problems, but one main challenge is understanding the role of noise in quantum annealing. Here, the authors characterize the relevant noise sources in a tunable flux qubit, a building block for quantum annealers, and provide a benchmark for future work on highly-coherent quantum annealers.
In a typical quantum annealing protocol, the system starts with a transverse field Hamiltonian that is gradually turned off and replaced by a longitudinal Ising Hamiltonian. The ground state of the Ising Hamiltonian encodes the solution to the computational problem of interest, and the state overlap with this ground state gives the success probability of the annealing protocol. The form of the annealing schedule can have a significant impact on the ground-state overlap at the end of the anneal, so precise control over these annealing schedules can be a powerful tool for increasing success probabilities of annealing protocols. Here we show how superconducting circuits, in particular capacitively shunted flux qubits, can be used to construct quantum annealing systems by providing tools for mapping circuit flux biases to Pauli coefficients. We use this mapping to find customized annealing schedules: appropriate circuit control biases that yield a desired annealing schedule, while accounting for the physical limitations of the circuitry. We then provide examples and proposals that utilize this capability to improve quantum annealing performance.
Superconducting devices as quantum bits (qubits) are one of the most promising candidates for implementing a practical quantum computer. Over the last decade, quantum coherence times of superconducting qubits have been continuously improved. Operating qubits in noise insensitive points, eliminating the participation of the lossy materials, and better isolation from environment increased the decoherence times from nanoseconds to tens of microseconds. One recent approach on the qubit design is to shunt the Josephson junctions with large capacitors to reduce the sensitivity to noise and to redistribute the stored electromagnetic energy in a well-engineered area. This approach was first applied on charge qubits and later adopted to other types of superconducting qubits. \n \nIn this thesis, we present the design and the characterization of a three-Josephson junction superconducting circuit with three large shunt capacitors. We present experiments on decoherence in the circuit used as a qubit. The qubit relaxation time T₁ is reaching as high as 47 μs and the spin-echo dephasing time T₂ = 9.4 μs. In addition, we present spectroscopy experiments and decoherence characterization in the qutrit subspace formed by the lowest three energy levels. The spectroscopy data is in excellent agreement with the complete circuit model based on the system capacitance matrix. At the flux symmetry point, the circuit has a large anharmonicity, defined as the difference between the 1-2 and 0-1 transition frequencies, approaching 2π × 3.7 GHz, which is enabling fast single qubit operations. We performed randomized benchmarking with the qubit gates with a duration of 1.62 ns and an average gate fidelity of 99.9%. \n \nMoreover, we present experiments with multi-level control in qutrit subspace, formed by the lowest three energy levels. We demonstrate a single step experimental implementation of a generalized Walsh-Hadamard gate. We use a decomposition of the quantum gate into two unitary operations, one implemented by an off-diagonal Hamiltonian and the other implemented by a diagonal Hamiltonian. The off-diagonal Hamiltonian is obtained by the simultaneous driving of the transitions between levels 0-1, 1-2, and 0-2, with the latter being a two-photon process. The diagonal Hamiltonian is effectively implemented by appropriately shifting the phases of adjacent pulses. The gate is characterized using tomography process and the average fidelity exceeds 90%, in good agreement with numerical simulations that take into account the multi-level structure of the system.
We demonstrate, for the first time, that a quantum flux parametron (QFP) is capable of acting as both isolator and amplifier in the readout circuit of a capacitively shunted flux qubit (CSFQ).By treating the QFP like a tunable coupler and biasing it such that the coupling is off, we show that T 1 of the CSFQ is not impacted by Purcell loss from its low-Q readout resonator (Q e = 760) despite being detuned by only 40 MHz.When annealed, the QFP amplifies the qubit's persistent current signal such that it generates a flux qubit-state-dependent frequency shift of 85 MHz in the readout resonator, which is over 9 times its linewidth.The device is shown to read out a flux qubit in the persistent current basis with fidelities surpassing 98.6% with only 80 ns integration, and reaches fidelities of 99.6% when integrated for 1 μs.This combination of speed and isolation is critical to the readout of high-coherence quantum annealers.