Related papers: Matchgates and classical simulation of quantum cir…
Learning an unknown quantum process is a central task for validation of the functioning of near-term devices. The task is generally hard, requiring exponentially many measurements if no prior assumptions are made on the process. However, an…
The Clifford hierarchy, introduced by Gottesman and Chuang in 1999, is an increasing sequence of sets of quantum gates crucial to the gate teleportation model for fault-tolerant quantum computation. Gates in the hierarchy can be…
Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…
Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near-term. In this…
In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…
We construct a completely analog framework that emulates universal quantum gates and quantum algorithms. It is based on electronic circuits made of operational amplifiers, resistors and capacitors. In these circuits, input and output lines…
We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.…
We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely…
We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…
We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…
We introduce a new family of quantum circuits for which the scrambling of a subspace of non-local operators is classically simulable. We call these circuits `super-Clifford circuits', since the Heisenberg time evolution of these operators…
We present a low-depth randomised algorithm for the estimation of entanglement fidelity between an $n$-qubit matchgate circuit $\mathcal{U}$ and its noisy implementation $\mathcal{E}$. Our procedure makes use of a modified Pauli-Liouville…
The Clifford group plays a central role in quantum randomized benchmarking, quantum tomography, and error correction protocols. Here we study the structural properties of this group. We show that any Clifford operator can be uniquely…
Magic states are essential for universal quantum computation and are widely viewed as a key source of quantum advantage, yet in realistic devices they are inevitably noisy. In this work, we characterize how noise on injected magic resources…
We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are…
We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
Shortened abstract: In this thesis, I study two restricted models of quantum computing related to free identical particles. Free fermions correspond to a set of two-qubit gates known as matchgates. Matchgates are classically simulable when…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in…