Quantum simulations of many-body systems in materials science and chemistry are promising application areas for quantum computers. However, the limited scale and coherence of near-term quantum processors pose a significant obstacle to realizing this potential. Here, we theoretically outline how a single-mode circuit quantum electrodynamics device, consisting of a transmon qubit coupled to a long-lived cavity mode, can be used to simulate the ground state of a highly entangled quantum many-body spin chain. We exploit recently developed methods for implementing quantum operations to sequentially build up a matrix product state (MPS) representation of a many-body state. This approach reuses the transmon qubit to read out the state of each spin in the chain and exploits the large state space of the cavity as a quantum memory encoding intersite correlations and entanglement. We show, through simulation, that analog (pulse-level) control schemes can accurately prepare a known MPS representation of a quantum critical spin chain in significantly less time than digital (gate-based) methods, thereby reducing the exposure to decoherence. We then explore this analog-control approach for the variational preparation of an unknown ground state. We demonstrate that the large state space of the cavity can be used to replace multiple qubits in a qubit-only architecture, and could therefore simplify the design of quantum processors for materials simulation. We explore the practical limitations of realistic noise and decoherence and discuss avenues for scaling this approach to more complex problems that challenge classical computational methods.
Quantum simulations of many-body systems in materials science and chemistry are promising application areas for quantum computers. However, the limited scale and coherence of near-term quantum processors pose a significant obstacle to realizing this potential. Here, we theoretically outline how a single-mode circuit quantum electrodynamics device, consisting of a transmon qubit coupled to a long-lived cavity mode, can be used to simulate the ground state of a highly entangled quantum many-body spin chain. We exploit recently developed methods for implementing quantum operations to sequentially build up a matrix product state (MPS) representation of a many-body state. This approach reuses the transmon qubit to read out the state of each spin in the chain and exploits the large state space of the cavity as a quantum memory encoding intersite correlations and entanglement. We show, through simulation, that analog (pulse-level) control schemes can accurately prepare a known MPS representation of a quantum critical spin chain in significantly less time than digital (gate-based) methods, thereby reducing the exposure to decoherence. We then explore this analog-control approach for the variational preparation of an unknown ground state. We demonstrate that the large state space of the cavity can be used to replace multiple qubits in a qubit-only architecture, and could therefore simplify the design of quantum processors for materials simulation. We explore the practical limitations of realistic noise and decoherence and discuss avenues for scaling this approach to more complex problems that challenge classical computational methods.
Superconducting circuit quantum electrodynamics is the main architecture for implementation of quantum processors. This work presents a proposal to miniaturize quantum memory devices by combining the quantum memory qubits encoded directly in the first two Fock states ${|0\ensuremath{\rangle},|1\ensuremath{\rangle}}$ and the bus channel in the same specially designed multimode cavity. One key feature of the resonant modes used for quantum memory is that the microwave current is localized, which facilitates the storage and retrieval of information in superconducting qubits while preventing crosstalk from other resonant modes. Frequency design and distinct coupling strengths in this kind of device are analyzed with electromagnetic simulations and numerical calculations. The quantum memory properties, e.g., storage speed, fidelity, and stability, are examined in four cases: (1) memory operation of single-qubit state, (2) disturbing effects, (3) coupling operation, and (4) entangled states storage. Decoherence time of the quantum processor can be extended to more than one order of magnitude longer than that without the memory. By integrating transmons with optimally designed coplanar waveguide multimode quantum memories, the present study could provide an optimistic perspective for the development of large-scale superconducting quantum processors.
In this thesis, we examine an extension of circuit quantum electrodynamics (QED), cavity QED using superconducting circuits, that utilizes multimode cavities as a resource for quantum information processing. We focus on the issue of qubit connectivity in the processors, with an ideal processor having random access -- the ability of arbitrary qubit pairs to interact directly. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-qubit memory, with a Josephson junction transmon circuit serving as the central processor. The quantum memory is a multimode cavity, using the eigenmodes of a linear array of coupled superconducting resonators. We selectively stimulate vacuum Rabi oscillations between the transmon and individual eigenmodes through parametric flux modulation of the transmon frequency. Utilizing these oscillations, we perform a universal set of quantum gates on 38 arbitrary pairs of modes and prepare multimode entangled states, all using only two control lines. We thus achieve hardware-efficient random access multi-qubit control. We also explore a novel design for creating long-lived 3D cavity memories compatible with this processor. Dubbed the ``quantum flute'', this design is monolithic, avoiding the loss suffered by cavities with a seam between multiple parts. We demonstrate the ability to manipulate the spectrum of a multimode cavity and also measure photon lifetimes of 0.5-1.3 ms for 21 modes. The combination of long-lived quantum memories with random access makes for a promising architecture for quantum computing moving forward.
Matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an N-qubit MPS with large N and large entanglement on a quantum platform is extremely challenging, since it requires high-level qudits or multi-body gates of two-level qubits to carry the entanglement. In this work, an efficient method that accurately encodes a given MPS into a quantum circuit with only one- and two-qubit gates is proposed. The idea is to construct the unitary matrix product operators that optimally disentangle the MPS to a product state. These matrix product operators form the quantum circuit that evolves a product state to the targeted MPS with a high fidelity. Our benchmark on the ground-state MPS's of the strongly-correlated spin models show that the constructed quantum circuits can encode the MPS's with much fewer qubits than the sizes of the MPS's themselves. This method paves a feasible and efficient path to realizing quantum many-body states and other MPS-based models as quantum circuits on the near-term quantum platforms.
Quantum processors based on superconducting circuitry have reached the scale of hundreds of qubits and demonstrated computational capabilities that challenge state-of-the-art classical methods for carefully designed problems. Despite these advances, fundamental questions persist over how to best improve and scale the computational power of this emerging technology. Most transmon-based quantum processors encode information in two-level systems, or qubits, leaving the rich multilevel structure of the transmon largely unexploited. In this thesis, we demonstrate how the capabilities of these devices can be meaningfully extended by harnessing this intrinsic multilevel structure to encode qudits — d-level quantum systems that access a larger and more connected Hilbert space than their qubit counterparts. We begin by demonstrating universal single-qudit operation before turning to microwave-activated entanglement to realize scalable two-qudit gates. We present a high-fidelity, fully entangling two-qutrit CZ gate based on a novel tunable cross-Kerr mechanism. We further explore two-qudit gates that selectively entangle subspaces of the full Hilbert space via two-photon multipartite Raman transitions, employing these operations to generate large entangled states across a transmon array. To address the noisy nature of near-term qudit computation, we introduce and characterize error suppression techniques for qudit circuits, including dynamical decoupling and quantum error mitigation. We then synthesize these directions by exploring simulations of quantum systems that have innate multilevel interactions and are therefore well tailored to qudit operation. First we investigate digital quantum simulations of collective neutrino oscillations and the spin-1 truncated Abelian Higgs model, finding error mitigation methods critical for improving circuit performance. Finally, out of equilibrium --- or Floquet --- spin-1 systems are realized using an array of 15 superconducting qutrits to probe a novel Z3 discrete time crystalline (DTC) phase of matter with intrinsically chiral interactions. This DTC result demonstrates that native qudit hardware provides powerful access to non-equilibrium phases rooted in higher discrete symmetries, opening a route to a broader landscape of dynamical orders beyond the Z2 Ising paradigm.
Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.
The matrix product state (MPS) belongs to the most important models in, for example, quantum information sciences and condensed-matter physics. However, realizing an N-qubit MPS with large N and large entanglement on a quantum platform is extremely challenging, since it requires high-level qudits or n-qubit gates with $n\ensuremath{\gg}2$ to carry or produce the entanglement. In this work, an efficient method that accurately encodes a given MPS into a quantum circuit with only one- and two-qubit gates is proposed. Essentially different from the existing compiling methods, our idea is to construct the unitary matrix product operators that optimally disentangle the MPS to a product state. These matrix product operators form the quantum circuit that evolves a product state to the targeted MPS with a high fidelity. Our benchmark on the ground-state MPSs of the strongly correlated spin models show that the constructed quantum circuits can simulate the MPSs with much fewer qubits than the sizes of the MPSs themselves. This method paves a feasible and efficient path to realizing useful and/or exotic quantum states and MPS-based models as quantum circuits on near-term quantum platforms.