Quantum measurement theory describes the dynamics of a quantum system when it transfers information to an observer. Within the framework of continuous measurement, this outflow of information and resultant back-action occur at a finite rate. Continuously measured systems do not instantaneously collapse to eigenstates, but rather undergo stochastic evolution highly correlated with the observer’s received information. When the measurement rate is on the same timescale as the processing speed of classical control electronics, we can perform feedback on a quantum system during its collapse process. We experimentally realize such a protocol by using an adaptively controlled quantum amplifier to implement a canonical phase measurement on a flying photon. Continuous measurements can also be used as a tool in quantum error correction. Error correction typically requires discrete rounds of measurement, often using entangling gates and ancilla qubits. In contrast, continuous error correction is implemented via always-on measurements of parity syndromes. Using direct parity measurements of pairs of qubits in a three qubit system along with a custom classical controller, we implement the first continuous quantum error correction code.

In harnessing quantum advantages for computation, there is a need for developing high fidelity operations on qubits. An algorithm can be broken down into single qubit operations and multi-qubit entangling gates. However, as the leading quantum processors today are limited to 50-100 qubits and each qubit is sensitive to decoherence noise (often referred to as NISQ era devices), running algorithms with long gate depth is difficult. Understanding the errors that plague existing gates and also expanding the dictionary of available gates is an important part of building a quantum computer. In this thesis we demonstrate two multiqubit gate experiments.

In the first experiment we demonstrate a multiqubit entangling gate for superconducting qubits on an all-to-all connected processor that draws upon the advantages of Rabi driven qubits. We also take inspiration from the ion qubit community by using a Mølmer-Sørensen-like interaction through the use of a shared coplanar waveguide (CPW) resonator driven superconducting qubits. We perform sensitivity analysis to understand the parameters that limit our gate fidelities.

In the second experiment we introduce and demonstrate a technique for scalable RB of many universal and continuously parameterized gate sets, using a class of circuits called randomized mirror circuits. The technique can be applied to a gate set containing an entangling Clifford gate and the set of arbitrary single-qubit gates, as well as gate sets containing controlled rotations about the Pauli axes. We use our technique to benchmark universal gate sets on four qubits, including a gate set containing a controlled-S gate and its inverse, and we investigate how the observed error rate is impacted by the inclusion of non-Clifford gates. We also show that our technique scales to many qubits with experiments on a 27-qubit IBM Q processor. We use our technique to quantify the impact of crosstalk on this 27-qubit device, and we find that it contributes approximately 2/3 of the total error per gate in random many-qubit circuit layers.

As the cutting edge of science and technology pushes towards smaller length scales, sensing technologies with nanoscale precision become increasingly important. In this thesis I will discuss the optimization and application of a 3D nanobridge SQUID magnetometer for studying solid state spin systems, in particular for sensing impurity spins in diamond. Solid state spins have proposed applications in memory and computation for both classical and quantum computing. Isolated spins typically have longer coherence times, making them attractive qubit candidates, but necessitating the development of very sensitive detectors for readout.

This 3D nanobridge SQUID combines the exquisite spatial sensitivity of a traditional nanoSQUID with a large non-linearity on par with a tunnel junction SQUID. This allows us to build a highly sensitive magnetometer which can act as both an efficient flux transducer as well as a nearly quantum limited lumped Josephson Parametric Amplifier. We show that the device has a minimum flux noise of 17 ± 0.9 nΦ₀/Hz^1/2 with only a factor of ∼2.5 increase in flux noise up to 61 mT. A second generation device with a smaller capacitor achieves field tolerance up to 75 mT. The maximal bandwidth values range from 25-40 MHz in the parametric amplification regime to 70 MHz in the linear regime. This combination of large bandwidth, low flux noise, large flux coupling and field tolerance make this sensor a promising candidate for near-single-spin dynamics measurements.

In the last part of this thesis we begin to demonstrate the utility of a nanobridge SQUID magnetometer for characterizing spin systems in the solid state. We use the magnetometer to measure the decay characteristics of P1 centers in diamond. We find that the spin-lattice relaxation time varies with temperature, with an order of magnitude decrease in the decay time between 25 mK and 370 mK.

Superconducting quantum circuits are a leading technology in the quest toward building a quantum computer, which promises to outperform conventional, or “classical” computers, in solving a variety of tasks. To be useful for computation, a quantum processing unit (QPU) architecture must be scalable and have low error rates. Microwave activated entangling interactions, while often being slower than interactions that use flux-tunable components, are a scalable approach to realizing entanglement in that they are compatible with a minimally complex QPU design: single-junction transmon qubits with fixed qubit-qubit coupling. A prominent microwave-activated gate in this architecture, the cross resonance (CR) gate, is experimentally investigated, including mitigation of leakage errors, and budgeting of coherent and incoherent errors. Importantly, the fidelity of the CR gate is limited in general by the static cross-Kerr, or ZZ, interaction between the qubits. A novel cross-Kerr entangling interaction that commutes with the static cross-Kerr interaction is presented, based on simultaneous off-resonant drives. This cross-Kerr interaction is tunable, enabling the complete cancellation or enhancement of qubit-qubit coupling, a first for this fixed-frequency, fixed-coupling architecture. We show the tunability of the sign of the interaction, and use it to implement a two qubit controlled-phase (CZ) gate. This gate is observed to have lower coherent error than the CR gate. Designing a QPU with this as the native entangling inter- action could enable faster microwave-activated gates, improving overall performance while maintaining minimal hardware complexity.

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. However, qubits in the noisy intermediate-scale quantum (NISQ) era are short-lived and susceptible to a variety of errors and noise due to imperfect control signals and incomplete isolation from the surrounding environment. For example, systematic miscalibrations, unwanted entanglement, and crosstalk in the control of qubits can lead to a coherent form of error which has no classical analog. Coherent errors can severely limit the performance of quantum algorithms in an unpredictable manner on timescales shorter than the coherence times of qubits. In recent years, there has been growing interest in using methods which randomize the physical implementation of quantum gates to mitigate the impact of coherent errors, effectively tailoring them into a form of stochastic noise. In this thesis, we study one such method --- randomized compiling --- and show how gate errors under randomized compiling are accurately described by a stochastic Pauli noise model without coherent errors. We demonstrate significant performance gains under randomized compiling for various different quantum algorithms, such as the quantum Fourier transform. We further show that randomized compiling can improve the predictability of quantum algorithms, and enables unique forms of error mitigation for enhancing the performance of quantum computations in the NISQ era. Finally, we show that randomized compiling can reduce worst-case error rates by orders of magnitude, enabling the accurate characterization of quantum gates for fault tolerance. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day, noisy quantum processors, paving the way forward for scalable quantum computing and fault tolerant quantum error correction.

The laws of quantum mechanics imply the existence of an intrinsic uncertainty, or noise, in the electromagnetic field. These noise fluctuations are central to many processes in atomic physics and quantum optics, including spontaneous emission of radiation by an atomic system, backaction on an atomic system during non-demolition measurement by probe light, and intrinsic bounds on the noise performance of an ideal amplifier. While quantum noise cannot be eliminated, the noise of one observable quantity may be reduced provided that of the conjugate observable is increased in accord with the relevant Heisenberg uncertainty relation; this process is known as squeezing.

Recently, superconducting circuits have emerged as a powerful platform for studying the interaction of squeezed light and matter, leveraging the low-dimensionality of the circuit environment to efficiently couple atomic systems to squeezed radiation. Beyond enabling the verification of canonical predictions of quantum optics, these experiments explore the potential utility of squeezing for the state readout of quantum bits, or qubits, used for quantum information processing.

In this thesis, we present three experiments probing the interaction of a superconducting qubit with squeezed radiation. First, we observe how the fluorescence spectra emitted by a two-level atomic system are modified by squeezing of a resonant drive. The subnatural linewidths of the resulting spectra provide the first successful verification in any system of predictions from nearly three decades prior, and provide a tool for characterization of microwave squeezed states. Second, we combine injected squeezed noise with a stroboscopic measurement scheme to demonstrate the first improvement of the signal-to-noise ratio of qubit state readout due to input squeezing. This study includes a characterization of the effect of squeezing on measurement backaction, exhibiting the first use of squeezing to slow measurement-induced dephasing. Finally, we develop a circuit incorporating the qubit inside of a squeezed-microwave source and extensively study the measurement physics of this hybrid system. This device enables the transfer of quantum information from the qubit at $\sim$30 milliKelvin to a room temperature detector with a marked increase in steady-state efficiency.

Real-time monitoring of a quantum state provides powerful tools for studying the backaction of quantum measurement and performing quantum feedback. Historically, this monitoring capability has been the exclusive province of atomic and optical physics. This thesis describes the implementation of the first such high-fidelity readout scheme in a solid state circuit, a superconducting quantum bit (qubit) coupled to a microwave cavity in the circuit quantum electrodynamics (circuit QED) architecture. The qubit-state-dependent resonance frequency of the cavity is probed with a microwave drive tone, and the resulting signal amplified using a fast, ultralow-noise superconducting parametric amplifier. This arrangement enables the observation of quantum jumps between the qubit states in real time.

The ability to monitor the qubit continuously with high fidelity and resolve quantum jumps can be used to investigate the backaction of the measurement process on the qubit. This thesis examines the quantum Zeno effect--where strong measurement inhibits the evolution of a quantum system-- as well as the transition to non-ideal measurement with increasing measurement strength in the circuit QED architecture, a phenomenon shown to be due to the upconversion of low-frequency dephasing noise. These data allow probes of ``universal'' flux noise in previously inaccessible frequency ranges. The work presented here opens the door for quantum feedback and error correction in solid-state quantum systems using continuous weak measurement.

Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.