IBM proposes a new superconducting quantum bit system
When it comes to superconducting quantum processors, the most commonly used quantum bit is transmon: it has a low sensitivity to noise; recently, IBM demonstrated a system with 127 transmon quantum bits. Despite these achievements, transmon has some operational problems that may prevent systems containing more quantum bits.
01transmon faces challenges, urgent need to reduce "frequency collisions"
In order for quantum computers to achieve a significant advantage over classical computers, they need to run error-correcting codes and have a sufficient number of quanta. A leading architecture for achieving such a general-purpose quantum computer is a lattice of quantum bits based on Josephson junctions, but the key to achieving such an architecture is to use highly coherent quantum bits that are easy to fabricate and characterize, and high-fidelity dual quantum bit gates that are fast and easy to tune: the two leading candidates that meet these requirements are single Josephson junction (JJ) transmon quantum bits and cross-resonant gates.
transmon circuit. (a) the fixed frequency transistor consists of a single Josephson junction; (b) the extensively tunable transistor consists of a symmetric dc-SQUID; (c) an asymmetric dc-SQUID can be formed using an external flux Φx threaded through the SQUID ring. in the asymmetric case, a large JJ area ratio allows for less tunability and sensitivity to flux noise. Significantly thicker oxides are required to produce EJ2, EJ1 during fabrication, thus potentially limiting the lifetime of the quantum bits.
However, despite these properties favoring the implementation of small quantum processors: including dozens of single JJ-transmon and cross-resonance gates, deploying such qubits and gates in large quantum processors is quite challenging. The difficulty arises from the fact that the fixed frequency fq of the quantum bit is mainly determined by the JJ energy, and that the standard deviation σf of its random scattering is comparable to the upper limit of the desired detuning degree (set by the anharmonicity of the quantum bit) due to the uncontrolled parameters in the fabrication process. Since transmon quantum bits operate at a fixed frequency, this means that in circuits containing a large number of transmon, the overlapping excitation energies of the quanta may trigger gate errors.
This imprecision greatly increases the likelihood of frequency collisions between neighboring quantum bits and reduces the yield of collision-free chips. Having neighboring quantum bits that operate at slightly different frequencies can solve this problem. However, the previous tunable transmon is highly susceptible to noise, such as flux noise, which can lead to fast de-phasing and gate errors in transmon.
02New weakly tunable quantum bits with improved relaxation time
Therefore, Abdo and his colleagues created a disorder-independent, tunable frequency quantum bit to solve this problem. The team implemented a superconducting quantum bit, the weakly tunable quantum bit (WTQ), which retains the desirable properties of JJ-transmon in a multi-qubit architecture: the WTQ works using Josephson junctions, but it contains three junctions instead of one; each junction has slightly different properties. The team used these properties to tune the frequency of each quantum bit to a few tenths of a degree: this tunability is large enough to avoid frequency collisions and small enough to limit its sensitivity to noise.
The frequency of the WTQ is tuned weakly with the applied magnetic flux. This limited tunability can solve the problem of frequency collisions in multiple quantum structures while maintaining high coherence; it can also improve the relaxation time of quantum bits by avoiding two-energy level systems (TLS) in frequency space.
Detailed WTQ circuit diagram. It has three Josephson junctions with inductances LJ1, LJ2, and LJ3 and capacitances CJ1, CJ2, and CJ3, respectively. Lc is the inductance of the coil that generates the magnetic field of the SQUID loop. Two partial inductors L1 and L2 are introduced to simulate the linear inductance of the SQUID loop, and they are inductively coupled to the coil with mutual inductance M1 and M2, respectively. Such a fine WTQ circuit structure avoids inconsistencies in the calculation of the decoherence rate.
03Engineering implementation: two seven-qubit chips
The experimental team then implemented and measured two seven-qubit chips (called A and B) with a design similar to that of the past single JJ-transmon: each chip consists of six WTQs and a single JJ-transmon quantum bit. Each quantum bit is capacitively coupled to a readout resonator, which in turn is capacitively coupled to a readout port. The resonator bus for all coupled quantum bits is disabled by shortening its end to ground.
The research team implemented the WTQ in two configurations, P-type and U-type, which differ in the shape of the gap capacitor electrodes that shunt the JJ. In the P-type configuration, the three capacitive electrodes are parallel to each other, while in the U-type configuration, an external electrode is wrapped around the three sides of the middle electrode of the quantum bit. The motivation for designing WTQ using these two possible configurations was to test experimentally whether these two configurations have any coherence advantage.
(a)Photograph of one of the two 7-qubit chips measured in this work. The chip consists of six WTQs and a single JJ-transmon (Q4). the WTQs are implemented using the two gap-capacitance geometries shown in (b) and (c). (b) P-type WTQ (Q2, Q3, Q7), where the capacitors are parallel. (c) U-shaped WTQ (Q1, Q5, Q6), where one capacitor is bent. (d) Equivalent WTQ circuit. c'1 and c'2 represent the total capacitance of the shunt JJ (including the self-capacitance of the JJ). the small junction of the SQUID is comparable to the single JJ-transmon's junction EJ2 Ì EJ1 Ì EJ, while the other JJ of the SQUID is slightly larger. The rounded corners used in the electrodes are to minimize E-field concentration and are not specific to the WTQ design.
Left: coherence measurement of chip A; Right: coherence measurement of chip B. From top to bottom, the quantum bit frequencies fq (blue circles), T1 (black star), T2E, T2R (red circles and magenta squares, respectively), and Tj (blue circles) are shown as a function of the applied coil bias current IB.
As shown above, WTQ exhibits coherence times, T1 and Tj, comparable to those of a single JJ-transmon quantum bit fabricated on the same chip. These times are consistent with the loss and fading mechanisms typically seen in single-junction transmon (see the solid blue curve in the fourth row of the figure). It is worth noting that no significant advantage of the P-type/U-type WTQ design in terms of measured relaxation times T1 for the various quantum bits in both chips was observed in the experiments (or at least in the 50-100 microsecond range measured in the experiments).
04Breakthrough experiments that promise to replace transmon quantum bits
This time, the IBM team introduced weakly tunable superconducting quantum bits whose frequency can be tuned by external magnetic flux; developed a theoretical model that captures the device physics and its coupling to the flux bias circuit; in addition, the experimental team fabricated and tested two superconducting chips containing several variations of these WTQ quantum bits.
The results show that the new superconducting chip can achieve a frequency tunability range down to 43-287 MHz with only a small asymmetry in its SQUID JJ size (αJ = 2-3.5): this is considerably lower than what is possible with highly asymmetric DC SQUID transistors (about 350 MHz tunability with an asymmetry factor of 15).
The use of such weak flux-tunable quantum bits should allow us to solve the most common frequency collision problems in multi-quantum structures while minimizing the sensitivity to flux noise; another important advantage of WTQs is that they are coupled together like transmon and, therefore, are equally expected to support other two-quantum bit gates such as cross-resonance gates.
Reference links：
[1]https://physics.aps.org/articles/v15/s130
[2]https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.18.034057
[3]https://arxiv.org/abs/2203.04164
