DS-2026-02: Folkertsma, Marten (2026) Empowering Quantum Computation with: Measurements, Catalysts, and Guiding States. Doctoral thesis, Universiteit van Amsterdam.
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Abstract
Over the past decade, there has been significant progress in the development of physical quantum computational devices. As of this year (2025), we are beginning to see the first implementations of quantum devices with active error correction. Nevertheless, many milestones remain before fully error-corrected quantum computation becomes available. A natural question is whether additional resources might aid in the development of these devices. In this thesis, we identify three stages in the progression of quantum devices and propose three corresponding resources that can enhance their computational capabilities. While these resources are motivated by specific stages of device development, their applicability extends beyond these regimes.
In Part one, we study the pre–error-correction regime, where computations are performed directly on physical qubits without error correction. As errors accumulate with circuit depth, this regime is effectively restricted to constant-depth circuits, severely limiting computational power (e.g., long-range entanglement generation). To mitigate this, we introduce the model of Local Alternating Quantum–Classical Computations (LAQCC), which augments constant-depth quantum circuits with intermediate measurements and fast intermediate classical computations. We show that LAQCC substantially extends the range of feasible computations beyond that of bare constant-depth circuits.
In Part two, we consider the early fault-tolerance regime, where computations are constrained by the number of available logical qubits rather than runtime. Motivated by the classical catalytic space model, we define a quantum analogue in which a space-bounded quantum machine is given access to an auxiliary catalytic register, initialized in an arbitrary quantum state, which can be altered during the computation, as long as it is restored at the end of the computation. We show that this catalytic resource extends the computational power of quantum space-bounded machines.
In Part three, we study the problem of estimating the ground-state energy of a Local Hamiltonian, a central task in quantum chemistry. A common approach is to first generate a guiding state—a state with nontrivial overlap with the ground space—via a classical heuristic, and then apply Quantum Phase Estimation to approximate the smallest eigenvalue. The second step of this procedure, estimating the ground state energy given a guiding state, has been formalized as the Guided Local Hamiltonian problem, which is known to be BQP-hard for certain parameter regimes. We extend this result by showing that hardness persists over a broader range of parameters. Then we study an alternative version of this problem, the Guidable Local Hamiltonian problem, in which one is not given a guiding state, but instead only promised that it exists. We use this to give complexity-theoretic evidence that classical heuristics for generating guiding states are, in this setting, as powerful as quantum heuristics. Furthermore, we use this problem to give restrictions on possible gap-amplification procedures, required for proving the quantum PCP (probabilistically checkable proofs) conjecture.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Report Nr: | DS-2026-02 |
| Series Name: | ILLC Dissertation (DS) Series |
| Year: | 2026 |
| Subjects: | Computation Logic |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 02 Dec 2025 22:13 |
| Last Modified: | 29 Jan 2026 15:51 |
| URI: | https://eprints.illc.uva.nl/id/eprint/2400 |
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