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We employed the techniques from [Phys. Rev. A \textbf{70}, 052328 (2004)/arXiv:0406196] to analytically study two set of quantum circuits containing one $T$ gate/magic $|T\rangle = \frac{|0\rangle+\sqrt{i}|1\rangle}{\sqrt{2}}$ state. These…
Rotation gates are widely used in various quantum algorithms. To implement fault-tolerant rotation gates, state distillation or gate synthesis is typically employed. However, the overhead of these schemes scales rapidly with increasing…
We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic…
Recent advances in quantum hardware are bringing fault-tolerant quantum computing (FTQC) closer to reality. In the early stage of FTQC, however, the numbers of available logical qubits and high-fidelity $T$ gates remain limited, making it…
Fast quantum gates are crucial not only for the contemporary era of noisy intermediate-scale quantum devices but also for the prospective development of practical fault-tolerant quantum computing. Leakage errors, which arise from data…
Superconducting qubits are a promising candidate for building a quantum computer. A continued challenge for fast yet accurate gates to minimize the effects of decoherence. Here we apply numerical methods to design fast entangling gates,…
This work augments the recently introduced Stabilizer Tensor Network (STN) protocol with magic state injection, reporting a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford…
Continuous variable measurement-based quantum computation on cluster states has in recent years shown great potential for scalable, universal, and fault-tolerant quantum computation when combined with the Gottesman-Kitaev-Preskill (GKP)…
Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…
We present a theorem that shows that all useful protocols for magic state distillation output states with a fidelity that is upper-bounded by those generated by a much smaller class of protocols. This reduced class consists of the protocols…
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…
Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and…
An important task required to build a scalable, fault-tolerant quantum computer is to efficiently represent an arbitrary single-qubit rotation by fault-tolerant quantum operations. Traditionally, the method for decomposing a single-qubit…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Quantum computing relies on quantum error correction for high-fidelity logical operations, but scaling to achieve near-term quantum utility is highly resource-intensive. High-rate quantum LDPC codes can reduce error correction overhead, yet…
Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford…