This dissertation presents a theoretical analysis of protocols relevant for quantum information processing with superconducting qubits. The purpose of these protocols is decoherence suppression and quantum information transfer. Our analysis makes use of the standard density matrix formalism and Kraus operator (operator-sum) representation of quantum operations. We also use the mathematical trick of unravelling continuous evolution into discrete scenarios with corresponding probabilities.We show that decoherence due to zero-temperature energy relaxation can be almost completely suppressed, probabilistically, by weak measurement reversal (also known as quantum uncollapsing). To protect a qubit, a weak (partial) quantum measurement moves it towards the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength.We also analyze several simple quantum error correction (QEC) and quantum error detection (QED) protocols, relevant to superconducting qubits. We show that for energy relaxation the repetitive N-qubit quantum codes cannot be used for QEC, but can be used for QED (also known as probabilistic error correction). Moreover, the repetitive code with only two qubits is sufficient for QED. We also present several other two-qubit algorithms realizable with the current technology of superconducting phase qubits; these algorithms can demonstrate QEC for intentional errors and QED for real decoherence.We also analyze a procedure designed to transfer the state of a microwave qubit from one superconducting resonator to another resonator via a transmission line; the emission and capture of the microwave energy is achieved using tunable couplers. The procedure is shown to be robust against experimental imperfections of required pulse shapes. Our results also indicate that a successful state transfer requires nearly equal resonator frequencies for the entire duration of the procedure.
This dissertation presents a theoretical analysis of protocols relevant for quantum information processing with superconducting qubits. The purpose of these protocols is decoherence suppression and quantum information transfer. Our analysis makes use of the standard density matrix formalism and Kraus operator (operator-sum) representation of quantum operations. We also use the mathematical trick of unravelling continuous evolution into discrete scenarios with corresponding probabilities.We show that decoherence due to zero-temperature energy relaxation can be almost completely suppressed, probabilistically, by weak measurement reversal (also known as quantum uncollapsing). To protect a qubit, a weak (partial) quantum measurement moves it towards the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength.We also analyze several simple quantum error correction (QEC) and quantum error detection (QED) protocols, relevant to superconducting qubits. We show that for energy relaxation the repetitive N-qubit quantum codes cannot be used for QEC, but can be used for QED (also known as probabilistic error correction). Moreover, the repetitive code with only two qubits is sufficient for QED. We also present several other two-qubit algorithms realizable with the current technology of superconducting phase qubits; these algorithms can demonstrate QEC for intentional errors and QED for real decoherence.We also analyze a procedure designed to transfer the state of a microwave qubit from one superconducting resonator to another resonator via a transmission line; the emission and capture of the microwave energy is achieved using tunable couplers. The procedure is shown to be robust against experimental imperfections of required pulse shapes. Our results also indicate that a successful state transfer requires nearly equal resonator frequencies for the entire duration of the procedure.
We show that qubit decoherence due to zero-temperature energy relaxation can be almost completely suppressed by using the quantum uncollapsing (measurement reversal) procedure. To protect a qubit state, a partial quantum measurement moves it toward the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength. The experiment can be realized in a straightforward way using the superconducting phase qubit.
We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive N-qubit codes cannot be used for quantum error correction, but can be used for quantum error detection. In the latter case it is sufficient to use only two qubits for the encoding. In the analysis we demonstrate a useful technique of unraveling the qubit energy relaxation into ``relaxation'' and ``no relaxation'' scenarios. Also, we propose and numerically analyze several two-qubit algorithms for quantum error detection and correction, which can be readily realized at the present-day level of the phase qubit technology.
We demonstrate a protocol, that combines quantum uncollapsing and dynamical decoupling, to protect the quantum state stored in a qubit against decoherence errors. The protocol can simultaneously suppress the two kinds of decoherence processes: the energy relaxation and the low-frequency noise induced dephasing. We present the analytical derivation and numerical simulations in detail. We also provide a preliminary experimental test in superconducting phase qubits, using the process fidelity to calibrate the performance of the protocol. Our results suggest that the protocol can be effective against errors due to both energy relaxation and the low-frequency dephasing noise, except at a reduced probability of success.
The potential of superconducting qubits as the medium for a scalable quantum computer has motivated the pursuit of improved interactions within this system. Two challenges for the field of superconducting qubits are measurement fidelity, to accurately determine the state of the qubit, and the efficient transfer of quantum states. In measurement, the current state-of-the-art method employs dispersive readout, by coupling the qubit to a cavity and reading the resulting shift in cavity frequency to infer the qubit's state; however, this is vulnerable to Purcell relaxation, as well as being modeled off a simplified two-level abstraction of the qubit. In state transfer, the existing proposal for moving quantum states is mostly untested against non-idealities that will likely be present in an experiment. In this dissertation, we examine three problems within these two areas.We first describe a new scheme for fast and high-fidelity dispersive measurement specifically designed to circumvent the Purcell Effect. To do this, the qubit-resonator interaction is turned on only when the resonator is decoupled from the environment; then, after the resonator state has shifted enough to infer the qubit state, the qubit-resonator interaction is turned off before the resonator and environment are recoupled. We also show that the effectiveness of this ``Catch-Disperse-Release'' procedure partly originates from quadrature squeezing of the resonator state induced by the Jaynes-Cummings nonlinearity.The Catch-Disperse-Release measurement scheme treats the qubit as a two-level system, which is a common simplification used in theoretical works. However, the most promising physical candidate for a superconducting qubit, the transmon, is a multi-level system. In the second work, we examine the effects of including the higher energy levels of the transmon. Specifically, we expand the eigenstate picture developed in the first work to encompass multiple qubit levels, and examine the resulting changes to the system. In particular, we analyze the population of the non-target eigenstates as a result of this expanded model, and provide an analytical form for these deviations from the simpler model in Catch-Disperse-Release (i.e., the dressed state approximation).Lastly, we assess the robustness of the existing quantum state transfer protocol, testing its performance under typical experimental deviations from the ideal case. We show that the procedure is resilient to almost all non-idealities, except frequency mismatch between the two cavities. We also demonstrate a method to compensate for one such error in frequency-matching.
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.
Quantum computing holds the promise of solving problems that are intractable for classical computers, with applications ranging from optimization and materials simulation to cryptography. It achieves this by leveraging the exponentially scaling dimensionality of the space encoding quantum information and by executing algorithms on quantum registers in superposition states – a feature often referred to as quantum parallelism. However, while encoding information in computational units capable of exploring a continuous set of quantum states enables exponential scaling of computational power with system size, quantum systems are also more susceptible to errors than their classical counterparts. These errors take the form of both control errors, where miscalibration of the control pulses causes coherent errors on the qubit states, as well as incoherent errors due to energy relaxation and dephasing. Scaling quantum systems to run useful algorithms involving hundreds or thousands of logical qubits will require quantum error correction. In this approach, quantum information is redundantly encoded across an entangled state of many physical qubits. This has enabled experimental demonstrations across various platforms – including ion traps, superconducting circuits, and neutral atoms – showing that encoded quantum states can be preserved beyond the coherence times of the constituting physical qubits. However, quantum state preservation is only one component needed for scalable quantum computing. To execute algorithms, it is also necessary to implement quantum gates on and between encoded qubits, in a way that maintains fault tolerance by preserving the ability to correct errors as they occur during the computation. In the first part of this thesis, we demonstrate the implementation of an error-corrected quantum operation that entangles two logical qubits. This is achieved by performing lattice surgery on a distance-three surface code qubit, resulting in a logical Bell state encoded in distance-three repetition codes, which enable the correction of single bit-flip errors. We further introduce techniques to benchmark and characterize the performance of logical operations, including applying the protocol to arbitrary logical input states and performing logical quantum process tomography. Together, these results constitute one of the first realizations of error-corrected lattice surgery in superconducting circuits. While quantum error correction can correct errors provided they occur with sufficiently low frequency, it may fail when many qubits experience errors simultaneously. In the second part of this thesis, we therefore shift focus to a specific error mechanism known to cause correlated errors in superconducting circuits – quasiparticle-induced decoherence. In this case, various forms of energy deposition on the quantum device can break Cooper pairs into quasiparticles, which may subsequently diffuse to the tunnel junction and interact with the qubit state, thereby causing decoherence. In this thesis, we investigate the impact of quasiparticle tunneling on qubit performance, with a focus on infrared-induced quasiparticles. We compare the sensitivity of niobium-based qubits to those made from tantalum – a material that has gained interest in recent years following demonstrations of qubits with improved coherence times based on this material. Using a thermal radiator source, we show that the performance of tantalum qubits may be limited by infrared-induced quasiparticles in typical superconducting circuit experimental setups. By employing both ambient and in-line infrared filters, we investigate the effectiveness of different filtering strategies and develop best practices for engineering cryogenic environments for superconducting quantum processors. The results presented in this thesis contribute to the advancement of quantum computing based on superconducting circuits by implementing and characterizing quantum error-corrected operations, and by investigating quasiparticles as a source of decoherence, along with strategies to improve infrared filtering and signal conditioning in cryogenic environments for future fault-tolerant quantum computing.