Our work described in the thesis, the experimental studies of waveguide QED in the platform of superconducting circuits, provides a unique ground for studying quantum many-body physics and quantum computation with long-range photon- mediated interactions between qubits. Below I will enumerate a few interesting potential directions beyond the work described in the thesis.
8.1 Opportunities for studying many-body physics
Compared to traditional atom-based systems, superconducting qubits are read- ily equipped with full individual local qubit control (XY and Z), quantum non- demolition measurement, and real-time feedback operation. Without need for trap- ping atoms, experiments with superconducting qubits can be performed at ultra-high repetition rates (up to ∼ 1 MHz with active qubit reset [302–305]), offering new possibilities to study higher-order many-body effects that are often obscured by statistical fluctuations. Utilizing the advanced control and calibration techniques developed for building up practical quantum computers [76, 306], a novel set of tools for controlling and measuring quantum many-body systems could be envi- sioned. In the following, I outline few research directions for exploring quantum many-body physics with our quantum processor.
Extended Bose-Hubbard model
The Bose-Hubbard model [307, 308] describes the physics of interacting bosons subjected to a shallow lattice potential and was at the heart of pioneering quan- tum simulation experiments with cold atoms in optical lattice [87–89, 309–311].
Superconducting transmon qubits [190] are also often described as sites of the Bose-Hubbard model for photons due to their weak anharmonicity [101, 312, 313].
While most of the studies to date considered cases with inter-particle interactions on the same site and the range of hopping limited to only nearest-neighbor sites, investigating extended versions of the Bose-Hubbard model with longer-range in- teraction and hopping processes are expected to bring in new opportunities to study strongly-correlated quantum phases of matter [314, 315]. For example, inclusion of long-range interactions between particles is shown to enrich the phase diagram,
inducing Haldane insulator and density wave phases 1D [316] and supersolid phase with both superfluid and crystalline order in 2D [317]. Also, extended range of hop- ping is known to amplify long-range and higher-order quantum correlations e.g., by creating correlated triplon-hole-hole pairs in Mott insulators [318] and greatly influencing the phase boundary of Mott insulator-to-superfluid transition [319].
Our superconducting metamaterial quantum processor induces tunable long-range coupling between transmon qubits, naturally realizing an extended Bose-Hubbard model for photons. We envision experimental exploration of the canonical model in a new regime with an unprecedented level of control and with new methods for dissipative stabilizing quantum many-body states [101, 277].
Quantum information scrambling
Quantum information scrambling [320–323] refers to a general phenomenon where initially localized quantum information is spread across many-body quantum de- grees of freedom, resulting in a complex entanglement structure which prohibits the recovery of originally encoded information with local measurements. This topic has been a subject of extensive theoretical studies [324–327] in the last few years. While there has been pioneering experimental efforts to measure out-of- time-ordered correlators [328, 329] and to probe quantum information scrambling [330, 331] in state-of-the-art quantum platforms, scrambling effects arising from a more generic scenario of thermalization in quantum many-body systems remain yet to be observed. Also, an interesting question here is whether we can retrieve the scrambled quantum information buried in multipartite quantum correlations by utilizing high level of local control over a closed quantum system. We are currently working on developing hybrid quantum-classical protocols to decode the scrambled quantum information from chaotic quantum many-body evolution by measurement and feed-forward. Our rapid high-fidelity multiplexed readout and the ability to perform low-latency (< 1𝜇s) feedback operations based on measurement outcomes of a subsystem will play a crucial role in realizing this scheme.
Measurement-induced phase transition
There has been recent theoretical studies of competition between the growth of entanglement in a quantum many-body system and local projective measurements [292–295]. It was shown that if the rate of randomly interspersed local projective measurement exceeds a certain threshold, the entanglement growth of the quantum many-body system is restricted to follow the area-law. Such transition from the
entangling phase (volume law) to the disentangling phase (area law) is called the measurement-induced phase transition. Experimentally probing the measurement- induced phase transition has been a formidable task as it requires ability to perform random mid-circuit readout of arbitrary subsets of qubits without fully collapsing the many-body wavefunction. A pioneering experiment conducted in a trapped ion quantum simulator overcame this challenge by exploiting entangling gates between system and ancilla qubits to defer the measurement until the end of the circuit [296].
However, this method limits the total number of measurements to the number of ancillae and therefore is only applicable to short time evolution and small system size.
In superconducting circuits, it is known that the effect of measurement of one qubit on other unmeasured qubits is mild, only adding parasitic dephasing rates on the order of ¯Γ/2𝜋 ∼ 102kHz [287] during the on-time of readout pulses (𝜏𝑝 ∼102ns), and in principle can be avoided by careful design of feedlines and Purcell filters [184, 285, 287, 332] for readout resonators [231]. Employing the superconducting metamaterial waveguide as an efficient Purcell filter for readout, we look forward to probing full regimes of the measurement-induced phase transition including its criticality.
8.2 New directions for scaling up quantum processors
Scaling up quantum processors for conducting large-scale quantum computation and simulation experiments entails significant technical challenges. On one hand, realizing a large system often requires transition to a new scalable technology for constructing hardware and extensive engineering of electronics. On the other hand, achieving good systematic control over the large system involves serious efforts in software development. The state-of-the-art large-scale quantum experiments are being performed with∼ 60 qubits in superconducting circuits [76, 297, 298, 333],
∼ 50 qubits in trapped ions [14, 69], and ∼ 200 qubits in neutral atom quantum simulators [15, 16], all of which are expected to grow further in size over the next few years.
In Chapter 7, we have successfully developed hardware and software to systemati- cally control ten superconducting qubits with full individual addressing and long- range coupling. With established and new methods for cryogenics [159], microwave packaging of device [152], and calibration [306], we expect to be able to run exper- iments on the scale of∼ 100 qubits in the near future. Specifically, leveraging the inherent 1D-scalability and long-range connectivity of the metamaterial quantum processor will be a key goal in this direction.