We experimentally assess the suitability of transmon qubits with fixed frequencies and fixed interactions for the realization of analogue quantum simulations of spin systems. We test a set of necessary criteria for this goal on a commercial quantum processor using full quantum process tomography and more efficient Hamiltonian tomography. Significant single qubit errors at low amplitudes are identified as a limiting factor preventing the realization of analogue simulations on currently available devices. We additionally find spurious dynamics in the absence of drive pulses, which we identify with coherent coupling between the qubit and a low dimensional environment. With moderate improvements, analogue simulation of a rich family of time-dependent many-body spin Hamiltonians may be possible.
We experimentally assess the suitability of transmon qubits with fixed frequencies and fixed interactions for the realization of analogue quantum simulations of spin systems. We test a set of necessary criteria for this goal on a commercial quantum processor using full quantum process tomography and more efficient Hamiltonian tomography. Significant single qubit errors at low amplitudes are identified as a limiting factor preventing the realization of analogue simulations on currently available devices. We additionally find spurious dynamics in the absence of drive pulses, which we identify with coherent coupling between the qubit and a low dimensional environment. With moderate improvements, analogue simulation of a rich family of time-dependent many-body spin Hamiltonians may be possible.
Quantum information processing holds the promise of a paradigm shift in computational power for specific problem classes. While contemporary quantum processors operate in the Noisy Intermediate-Scale Quantum (NISQ) regime and remain highly susceptible to errors, ongoing experimental efforts on these near-term devices are crucial for advancing the underlying technology. Among the various hardware implementations, superconducting quantum circuits stand out as one of the most robust architectures for scalable quantum technologies. Nevertheless, the primary bottleneck in these systems is the fragility of quantum information: interactions with the environment inevitably perturb the quantum states, a phenomenon known as decoherence. This rapid loss of stored information imposes a fundamental limit on the time available to reliably execute computations on these devices. Within this context, this thesis focuses on the comprehensive experimental characterization of a planar chip featuring isolated, fixed-frequency superconducting transmon qubits. The measurements were conducted in a cryogenic environment, relying on a dilution refrigerator to maintain the device at millikelvin temperatures. To probe the quantum system under these conditions, custom measurement scripts were developed to operate state-of-the-art microwave control electronics (Keysight Quantum Control System), establishing full control over pulse generation, signal acquisition, and digital demodulation. The experimental workflow systematically mapped the physical properties of the device through a progressive series of characterization steps. Initial spectroscopic techniques probed the coupled resonator-qubit system, identifying its fundamental transition frequencies and relevant energy scales. Building upon these frequency-domain measurements, coherent control was achieved by calibrating resonant microwave pulses to drive single-qubit rotations, enabling the reliable preparation of the qubit in excited or coherent superposition states. Finally, specific time-domain protocols were implemented to evaluate the operational limits of the device. By executing standard pulse sequences, the characteristic decoherence metrics of the system, namely the longitudinal energy relaxation time (T1) and the inhomogeneous dephasing time (T2*), were successfully extracted, providing a quantitative assessment of the qubit's overall performance and establishing a baseline for future implementations of more advanced quantum control protocols.
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.
We develop a simulator for quantum computers composed of superconducting transmon qubits. The simulation model supports an arbitrary number of transmons and resonators. Quantum gates are implemented by time-dependent pulses. Nontrivial effects such as crosstalk, leakage to non-computational states, entanglement between transmons and resonators, and control errors due to the pulses are inherently included. The time evolution of the quantum computer is obtained by solving the time-dependent Schrödinger equation. The simulation algorithm shows excellent scalability on high-performance supercomputers. We present results for the simulation of up to 16 transmons and resonators. Additionally, the model can be used to simulate environments, and we demonstrate the transition from an isolated system to an open quantum system governed by a Lindblad master equation. We also describe a procedure to extract model parameters from electromagnetic simulations or experiments. We compare simulation results to experiments on several NISQ processors of the IBM Q Experience. We find nearly perfect agreement between simulation and experiment for quantum circuits designed to probe crosstalk in transmon systems. By studying common gate metrics such as the fidelity or the diamond distance, we find that they cannot reliably predict the performance of repeated gate applications or practical quantum algorithms. As an alternative, we find that the results from two-transmon gate set tomography have an exceptional predictive power. Finally, we test a protocol from the theory of quantum error correction and fault tolerance. We find that the protocol systematically improves the performance of transmon quantum computers in the presence of characteristic control and measurement errors.
Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.
When quantum particles interact, many-body phenomena that are hard to simulate classically emerge. Quantum analog simulation offers an alternative in which the target system's dynamics is directly realized in controllable quantum hardware. Here, we give a general protocol for simulating the Bose-Hubbard and anyon-Hubbard models using lattices of capacitively coupled flux-tunable transmons. By modulating the transmon frequencies in an alternating pattern, we resonantly drive multiple many-body transitions and can tune the on-site interaction and density-dependent hopping amplitudes for up to three bosons per site, with no additional restriction on the total particle number. By adding phases to the modulation, which renders the transition amplitudes complex-valued, we propose the first simulation protocol for the anyon-Hubbard model with transmons. Numerical simulations of the driven transmon arrays with experimentally realistic parameters reproduce the characteristic dynamics of the target models across a range of interaction strengths and statistical phases, including the interaction-dependent localization and the statistics-dependent asymmetry of the anyonic quantum walk.
Developments of quantum techniques have drastically improved the control ability of current quantum processors. Characterizing quantum simulations performed on these processors has become a vital topic in quantum information processing. Traditional characterizing techniques such as quantum process and state tomography fully characterize quantum simulations, but always with the exponentially increased resource cost, unfortunately. It may place their applications only in small-scale quantum systems. Meanwhile, many potential characterizing methods have been put forward in the past decades. In this work we experimentally test and compare different methods for characterizing quantum simulations of Ising Hamiltonians on the nuclear magnetic resonance (NMR) platform, including the recent quantum Hamiltonian tomography with polynomial complexity to estimate the generator of quantum simulations and nonrepetitive direct fidelity estimation with the Monte Carlo method to estimate the fidelity of dynamical states. We also experimentally estimate the parameters of Hamiltonian via full quantum process tomography and quantum state tomography for the comparison. These methods have merits and demerits in accuracy, the required resource, and prior knowledge. Our experiments test the performance of different methods while providing a beneficial reference for characterizing quantum simulations in the future.