Nonclassical states are essential resources for quantum computing that cannot be described by classical probability theory. In this thesis, we engineer nonclassical states in two separate systems: finite-dimensional high-spin nuclei, and infinite-dimensional bosonic cavity modes. In the finite-dimensional case, we study a spin−7/2 antimony (123Sb) donor in silicon, forming a D = 8 qudit. The required non-linearity for nonclassicality is provided by the quadratic quadrupole interaction. We fully characterize the 3 × 3 quadrupole with nuclear magnetic resonance (NMR) spectroscopy in a rotating magnetic field. Inspired by this model, we improve the QND readout of the 123Sb nucleus by developing an adaptive readout protocol. In the ancilla-mediated nuclear spin readout, we induce unwanted spin-flip transitions. The adaptive protocol minimizes errors by relying on negative-resultmeasurements, achieving an increase in readout fidelity from 98.93(7) % to 99.61(4) %. We proceed by improving the coherence of the qudit by applying qudit dynamical decoupling (DD). We show that implicit noise biases can simplify lengthy pulse sequences. By cyclically permuting the spin eigenstates, we decouple all dephasing noise and gain a factor 5-10 increase in the coherence time of various nonclassical states. We additionally protect logical spin cat qubit states. By applying a continuous spin-locking drive tailored to the noise bias, we achieve an order-of-magnitude improvement. We then directly address one of the main questions of this thesis by certifying the quantumness of nonclassical states in the 123Sb qudit through a uniform precession protocol. We provide a first experimental demonstration of nonclassicality in the dynamics of a spin. The quantum protocol score exceeds the classical bound by 18 standard deviations, ruling out any classical explanation for the observed set of measurements. We complement the finite-dimensional results by creating nonclassical bosonic (D = ∞) squeezed states with a frequency-tunable kinetic inductance parametric amplifier (KIPA). With a squeezed-state-receiver setup, we demonstrate 7.8(2) dBs of intercavity squeezing. These high levels of squeezing stay robust against the exposure of high magnetic fields over 1 T and elevated temperatures above 1 K. Lastly, we provide a future outlook by developing methods to scale spin qubits, industrially fabricated on 300mm wafers, aimed at improving the scalability of spin qubits
Nonclassical states are essential resources for quantum computing that cannot be described by classical probability theory. In this thesis, we engineer nonclassical states in two separate systems: finite-dimensional high-spin nuclei, and infinite-dimensional bosonic cavity modes. In the finite-dimensional case, we study a spin−7/2 antimony (123Sb) donor in silicon, forming a D = 8 qudit. The required non-linearity for nonclassicality is provided by the quadratic quadrupole interaction. We fully characterize the 3 × 3 quadrupole with nuclear magnetic resonance (NMR) spectroscopy in a rotating magnetic field. Inspired by this model, we improve the QND readout of the 123Sb nucleus by developing an adaptive readout protocol. In the ancilla-mediated nuclear spin readout, we induce unwanted spin-flip transitions. The adaptive protocol minimizes errors by relying on negative-resultmeasurements, achieving an increase in readout fidelity from 98.93(7) % to 99.61(4) %. We proceed by improving the coherence of the qudit by applying qudit dynamical decoupling (DD). We show that implicit noise biases can simplify lengthy pulse sequences. By cyclically permuting the spin eigenstates, we decouple all dephasing noise and gain a factor 5-10 increase in the coherence time of various nonclassical states. We additionally protect logical spin cat qubit states. By applying a continuous spin-locking drive tailored to the noise bias, we achieve an order-of-magnitude improvement. We then directly address one of the main questions of this thesis by certifying the quantumness of nonclassical states in the 123Sb qudit through a uniform precession protocol. We provide a first experimental demonstration of nonclassicality in the dynamics of a spin. The quantum protocol score exceeds the classical bound by 18 standard deviations, ruling out any classical explanation for the observed set of measurements. We complement the finite-dimensional results by creating nonclassical bosonic (D = ∞) squeezed states with a frequency-tunable kinetic inductance parametric amplifier (KIPA). With a squeezed-state-receiver setup, we demonstrate 7.8(2) dBs of intercavity squeezing. These high levels of squeezing stay robust against the exposure of high magnetic fields over 1 T and elevated temperatures above 1 K. Lastly, we provide a future outlook by developing methods to scale spin qubits, industrially fabricated on 300mm wafers, aimed at improving the scalability of spin qubits
Encoding quantum information in d-dimensional systems (qudits) with d>2 offers appealing new directions for resource-efficient quantum computing. However, protecting the coherence of nonclassical qudit resource states remains an open challenge. Dynamical decoupling (DD) is a well-established technique for extending coherence, but its application to qudits is hindered by the quadratic scaling of the decoupling sequence overhead with the dimension d. As a result, demonstrations of qudit DD have so far been limited to low-dimensional qudits. Here, we show that noise-biased qudits enable a nontrivial reduction of this overhead, for example, from quadratic to linear. We perform qudit DD on a model d=8 qudit, the nuclear spin of an antimony donor in silicon. We benchmark DD performance on highly nonclassical states such as uniform superpositions, cat states, and Haar random states and measure coherence improvements up to a factor 5 to 10. For a spin-cat error correction code, continuous DD extends the coherence time of the logical superposition ∣+⟩L to 225~ms, compared to 19~ms under free evolution and 85~ms with a Hahn echo. This improvement shows that DD sequences tailored to a system's noise bias can significantly enhance the lifetime of encoded logical qubits.
The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a sweet spot near a clock transition in the spectrum of quadrupolar nuclei (having spin I≥1) to achieve a suppression of charge and magnetic noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a Z2-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states for sufficiently high asymmetry parameters. For nuclei in highly asymmetric electric-field gradients, the nuclear spin could therefore be initialized in the spin-Kerr-cat subspace using SU(2) rotations and measurement rather than full SU(2I+1) control. We calculate the dephasing time of the spin Kerr-cat qubit under a model of 1/f noise, as well as relaxation of the qubit due to breaking of the Z2 symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (123Sb) donors in silicon, we estimate that second-scale T2∗ times could be achieved with this encoding, with bitflips and leakage occurring on significantly longer timescales. We propose a two-qubit gate acting on spin Kerr-cat qubits and electron-spin qubits, enabled by adiabatically moving an electron on and off the donor potential. Based on numerical simulations, we estimate that with an enhancement of measured quadrupolar couplings by a factor of ≈2, a gate fidelity exceeding 99% could be achieved for spin Kerr cats encoded in 123Sb, with a gate time under 100 ns. By entangling the nuclear spin with an electron spin in this way, the spin Kerr-cat qubit could then be measured using a Pauli spin blockade readout of the electron.
Ultra-cold atoms are highly sensitive to both inertial effects and electromagnetic fields, making atom interferometers excellent candidates for a variety of precision sensing applications. Furthermore, highly tunable atomic interactions combined with well established experimental techniques for trapping, cooling and manipulating ensembles of ultra-cold atoms, make them well suited to quantum enhancement. For these reasons, ensembles of ultra-cold atoms are excellent candidates for quantum-enhanced measurement devices. Broadly, this thesis presents a number of theoretical results which share the aim of progressing the proof-of-principle regime of current experiments to genuinely useful, ultra-precise quantum enhanced sensors.In Chapter 4 we explore the challenge of devising a useful, quantum-enhanced inertial measurement - to date no such experiment has been performed. Specifically, we present a model of a spin-squeezed rotation sensor utilising the Sagnac effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input states for the interferometer are seeded using Raman pulses with Laguerre-Gauss beams and are amplified by the bosonic enhancement of spin-exchange collisions, resulting in spin-squeezing and potential quantum enhancement in the interferometry. The ring geometry has an advantage over separated beam path atomic rotation sensors due to the uniform condensate density. We model the interferometer both analytically and numerically for realistic experimental parameters and find that significant quantum enhancement is possible. However, this enhancement is partially degraded when working in a regime with strong atomic interactions, indicating that perhaps interaction-based squeezing is not the best route to a quantum-enhanced inertial measurement.Continuing the theme of practical spin-squeezing with atomic interactions, in Chapter 5 we explore methods to combat detection noise, which is currently one of the most significant experimental limitations for quantum-enhanced atom interferometers. A useful quantum-enhanced interferometer requires nonclassical states with a high particle number and the (close to) optimal exploitation of the states' quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cram´er-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. “Interaction-based readout” protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. We prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily-accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.Macroscopic superposition states (known as spin-cat states in atomic ensembles) achieve the ultimate quantum precision limit. In Chapters 6 and 7 we turn our attention to studying decoherence that arises in creating and manipulating these states. In its simplest form, decoherence occurs when a quantum state is entangled with a second state, but the results of measurements made on the second state are not accessible. As the second state has effectively ``measured the first, in Chapter 6 we argue that the quantum Fisher information is the relevant metric for predicting and quantifying this kind of decoherence. In particular we apply this analysis to studying decoherence imparted on spin-cat states via atom-light interactions, which are an essential process in atom interferometry. We find that, compared to classical atomic states, spin-cat states are highly susceptible to this kind of decoherence. We investigate the required optical field occupation, such that this decoherence is negligible.Finally, in Chapter 7 we explore the deleterious effects of spatial and phase dynamics during the creation of spin-cat states via one-axis twisting in a two-component Bose-Einstein condensate. We simulate the breathing dynamics in 1 spatial dimension, employing the method of Sinatra and Castin, whereby the state is expanded into the Fock basis, with each basis state evolving within the Hartree-Fock approximation. This method is able to capture both multi-mode effects and quantum correlations, which allows us to calculate the quantum Fisher information. We find that so long as the time taken for the condensate to reach a spin-cat state is an integer multiple of the breathing period, it is sometimes possible to realise something extremely close to a spin-cat state, despite significant dynamics. These results indicate that large non-linearities, and the associated speed-up in entangling dynamics, are not fundamentally incompatible with the production of fragile, highly entangled states such as spin-cat states.
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, which has been demonstrated using continuous-variable states in microwave cavities or the motional modes of trapped ions. For example, high-dimensional systems can be used to realise `Schrödinger cat' states, superpositions of widely displaced coherent states that can also be used to illustrate quantum effects at large scales. Recent proposals have suggested encoding qubits in high-spin atomic nuclei, finite-dimensional systems that can host hardware-efficient versions of continuous-variable codes. Here we demonstrate the creation and manipulation of Schrodinger cat states using the spin-7/2 nucleus of an antimony atom embedded in a silicon nanoelectronic device. We use a multi-frequency control scheme to produce spin rotations that preserve the symmetry of the qudit, and constitute logical Pauli operations for qubits encoded in the Schrodinger cat states. Our work demonstrates the ability to prepare and control nonclassical resource states, a prerequisite for applications in quantum information processing and quantum error correction using our scalable, manufacturable semiconductor platform.
Quantum error correction (QEC) requires non-invasive measurements for fault tolerant quantum computing. Deviations from ideal quantum non-demolition (QND) measurements can disturb the encoded information. To address this challenge, we develop a readout protocol for a D−dimensional system that, after a single positive outcome, switches to probing only the D−1 remaining subspace. This adaptive switching strategy minimizes measurement-induced errors by relying on negative-result measurement results that do not perturb the Hamiltonian. We apply the protocol on an 8-dimensional 123Sb nuclear qudit in silicon, and achieve an increase in the readout fidelity from (98.93±0.07)% to (99.61±0.04)%, while reducing threefold the overall readout time. To highlight the broader relevance of measurement-induced errors, we study a 10-dimensional 73Ge nuclear spin read out through Pauli spin blockade, revealing nuclear spin flips arising from hyperfine and quadrupole interactions. These results unveil the effect of non-ideal QND readout across diverse platforms, and introduce an efficient readout protocol that can be implemented with minimal FPGA logic on existing hardware.
Superconducting circuits provide an architecture upon which cavity quantum electrodynamics (QED) can be implemented at microwave frequencies in a highly tunable environment. Known as circuit QED, these systems can achieve larger nonlinearities, stronger coupling and greater controllability than can be achieved in cavity QED, all in a customisable, solid state device, making this technology an exciting test bed for both quantum optics and quantum information processing. These new parameter regimes open up new avenues for quantum technology, while also allowing older quantum optics results to finally be tested. In particular is is now possible to experimentally produce nonclassical states, such as squeezed and Schr\\"odinger cat states, relatively simply in these devices. Using open quantum systems methods, in this thesis we investigate four problems which involve the use of nonclassical states in circuit QED. First we investigate the effects of a Kerr nonlinearity on the ability to preserve transported squeezed states in a superconducting cavity, and whether this setup permits us to generate, and perform tomography, of a highly squeezed field using a qubit, with possible applications in the characterisation of sources of squeezed microwaves. Second, we present a novel scheme for the amplification of cat states using a coupled qubit and external microwave drives, inspired by the stimulated Raman adiabatic passage. This scheme differs from similar techniques in circuit QED in that it is deterministic and therefore compatible with a protocol for stabilising cat states without the need for complex dissipation engineering. Next we use solutions of Fokker-Planck equations to study the exact steady-state response of two nonlinear systems: a transmon qubit coupled to a readout resonator, where we find good agreement with experiments and see simultaneous bistability of the cavity and transmon; and a parametrically driven nonlinear resonator, where we compare the classical and quantum phases of the system and discuss applications in the generation of squeezed states and stabilisation of cat states. Finally, we investigate the use of two different types of superconducting qubits in a single experiment, seeing that this enables engineering of the self- and cross-Kerr effects in a line of cavities. This could provide a valuable means of entangling cavity states, in addition to a resource for quantum simulation.