Superconducting quantum coherent circuits have opened up a novel area of fundamental low-temperature science since they could potentially be the element base for future quantum computers. Here we report a quasi-three-level coherent system, the so-called superconducting qutrit, which has some advantages over a two-level information cell (qubit) and is based on the qutrit readout circuit intended to measure individually the states of each qubit in a quantum computer. The designed and implemented radio-frequency superconducting qutrit detector (rf SQUTRID) with atomic-size ScS-type contact utilizes the coherent-state superposition in the three-well potential with energy splitting $\ensuremath{\Delta}{E}_{01}/{k}_{B}\ensuremath{\approx}1.5\phantom{\rule{0.16em}{0ex}}$K at the 30th quantized energy level with good isolation from the electromagnetic environment. The reason why large values of $\ensuremath{\Delta}{E}_{01}$ (and thus using atomic-size Nb-Nb contact) are required is to ensure an adiabatic limit for the quantum dynamics of magnetic flux in the rf SQUTRID.
Superconducting quantum coherent circuits have opened up a novel area of fundamental low-temperature science since they could potentially be the element base for future quantum computers. Here we report a quasi-three-level coherent system, the so-called superconducting qutrit, which has some advantages over a two-level information cell (qubit) and is based on the qutrit readout circuit intended to measure individually the states of each qubit in a quantum computer. The designed and implemented radio-frequency superconducting qutrit detector (rf SQUTRID) with atomic-size ScS-type contact utilizes the coherent-state superposition in the three-well potential with energy splitting \ensuremathΔE01/kB\ensuremath≈1.5K at the 30th quantized energy level with good isolation from the electromagnetic environment. The reason why large values of \ensuremathΔE01 (and thus using atomic-size Nb-Nb contact) are required is to ensure an adiabatic limit for the quantum dynamics of magnetic flux in the rf SQUTRID.
A quantum detector whose working principle is based on magnetic-field modulation of a circulating supercurrent in the quantum ground state of a macroscopic superconducting loop with a Josephson junction. Under the influence of an external magnetic flux equal to Φ0∕2 (or Φ0), two (or three) classical states are coupled to each other by quantum tunneling through a potential barrier, and therefore the detector is a two-level (or three-level) system. In the low-temperature region and under the condition of very weak damping, the mean value of the circulating supercurrent reflects the character of the variation of the quantum superposition of macroscopic states, which is sensitive to the symmetry of the potential. The variations of the current are amplified and detected in a measurement scheme similar to the signal registration in a nonhysteretic rf SQUID. It is shown by a numerical analysis that in comparison with a qubit detector based on an SIS junction, a detector with an ScS junction is faster and has much larger amplitudes of energy splitting at the same parameters. The results presented for double- and triple-well potentials clearly indicate that a qubit with an ScS junction can act as a detector with a sensitivity determined by the quantum noise of the amplifier.
As classical computers struggle to keep up with Moore's law, quantum computing may represent a big step in technology and yield significant improvement over classical computing for many important tasks. Building a quantum computer, however, is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possible, to reduce the amount of required control and operation time and thus improve the quantum state coherence. Here we propose a superconducting circuit for implementing a tunable spin chain consisting of a qutrit (three-level system analogous to spin-1) coupled to two qubits (spin-1/2). Our system can efficiently accomplish various quantum information tasks, including generation of entanglement of the two qubits and conditional three-qubit quantum gates, such as the Toffoli and Fredkin gates, which are universal for reversible classical computations. Furthermore, our system realizes a conditional geometric gate which may be used for holonomic (non-adiabatic) quantum computing. The efficiency, robustness and universality of our circuit makes it a promising candidate to serve as a building block for larger spin networks capable of performing involved quantum computational tasks.
Compared to a qubit, a qutrit (a three-level or three-state quantum system) possesses a larger Hilbert space to process and store quantum information. On the other hand, large-scale qutrit-based hybrid quantum computing usually requires performing hybrid multi-qutrit quantum gates with diverse qutrits, different in their nature or in their encoding format. In this work, we consider two types of qutrits, i.e., superconducting (SC) qutrits and cat-state qutrits. We propose to implement a hybrid controlled-SUM gate with one SC qutrit simultaneously controlling multiple-target cat-state qutrits. The gate is implemented in a circuit-QED system, which is composed of an SC ququart and multiple microwave cavities. The SC ququart here refers to a four-level quantum system, with the three lowest levels forming a qutrit and an auxiliary higher energy level utilized for the coherent state manipulation. The gate implementation does not require applying a classical pulse. Because the auxiliary higher energy level of the SC ququart is only virtually excited during the gate operation, decoherence from this level is greatly suppressed. The gate is deterministic, as it requires no measurement of the cavity or SC ququart states. Moreover, the gate operational time is independent of the number of qutrits, thus it does not increase with the number of qutrits. As an application of this gate, we further discuss the generation of a hybrid maximally entangled state of one SC qutrit and multiple cat-state qutrits. We also numerically analyze the experimental feasibility of creating the hybrid entangled state of one SC qutrit and two cat-state qutrits in a circuit QED system. This proposal may be extended to accomplish the same task in other physical systems, such as a four-level artificial atom (e.g., a quantum dot, an NV center, a magnon, etc.) coupled to multiple optical or microwave cavities.
Superconducting circuits containing Josephson junctions have previously been shown to exist in superpositions of states of electric charge and of superconducting phase. This superposition manifests itself in so-called Rabi oscillations between the two energy levels produced by the superposition. In his Perspective,
Clarke
highlights the report of
Chiorescu
et al. , who demonstrate that a superconducting ring containing three Josephson junctions also exhibits Rabi oscillations, and thus exists in a superposition of magnetic flux states. The experiments are elegant demonstrations of coherence in superconducting circuits, and are potentially of interest as quantum bits in a future computer.
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.
Superconducting qubits are fabricated "loss-free" electrical circuits on a chip with size features of tens of nanometers. If cooled to cryogenic temperatures below -273 °C they behave as quantum elements, similar to atoms and molecules. Such a qubit can be manipulated by fast-oscillating magnetic fields and its resulting quantum state can be measured using a proper magnetic detector. These qubits could be the basic elements for a quantum processor. To that order, multiple qubits have to controllably interact, and to that purpose very high quality resonators are fabricated on the same chip. Effectively the interaction results from the phase-coherent exchange of a single photon between qubit and resonator. In this way it is highly analogous to the so-called cavity QED in atomic physics where single atoms couple to a single trapped photon, all inside a cavity resonator. In this thesis, a superconducting flux qubit has been coupled to an LC resonator and coherent exchange of a single photon between qubit and resonator has been achieved. A striking option in these superconducting circuits, not attainable in "common" atomic cavity-QED, is that the interaction between qubit and photon can be made very large, up to the limit that one no longer can talk about the qubit and resonator as such. This limit requires a fully different description and it leads to novel effects, e.g. in the energy spectrum of the qubit-resonator composite. The Bloch-Siegert spectral shift is experimentally demonstrated in this thesis. As a small but critical technical aside a new type of control line filter has been developed, which allows strong suppression of excess electrical noise that forms a threat for qubit coherence. Having two modes of operation, it shorts all low-frequency noise if control is idle while being transparent if control is active, where short or open is determined by the control line signal level itself.