Related papers: Transversal non-Clifford gates on almost-good quan…
Fault-tolerant quantum computing hinges on efficient logical compilation, in particular, translating high-level circuits into code-compatible implementations. Gate-by-gate compilation often yields deep circuits, requiring significant…
We provide a recursively defined sequence of flag circuits which will detect logical errors induced by non-fault-tolerant $R_{\overline{Z}}(\frac{\pi}{2^l})$ gates on CSS codes with a fault distance of two. As applications, we give a family…
We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment,…
We derive two families of EA-QC quantum LDPC (EA-QC-QLDPC) codes by tiling permutation matrices of prime and composite orders. The unassisted portion of the Tanner graphs corresponding to these codes, constructed from two distinct classical…
Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [Quantum Inf. Comput., 4(2):134--145], Terhal and DiVincenzo have shown that these…
Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the…
A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons…
Quantum low-density parity-check (QLDPC) codes offer a promising path to low-overhead fault-tolerant quantum computation but lack systematic strategies for exploration. In this Letter, we establish a topological framework for studying the…
We construct toric codes on various high-dimensional manifolds. Assuming a conjecture in geometry we find families of quantum CSS stabilizer codes on $N$ qubits with logarithmic weight stabilizers and distance $N^{1-\epsilon}$ for any…
We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit…
Controlled operations are fundamental building blocks of quantum algorithms. Decomposing $n$-control-NOT gates ($C^n(X)$) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces $C^n(X)$ circuits…
Semiconductor quantum dots offer a promising platform for controlling spin qubits and realizing quantum logic gates, essential for scalable quantum computing. In this work, we utilize a variational quantum compiling algorithm to design…
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group, one often resorts to $t$-designs. Unitary…
In order for quantum computations to be done as efficiently as possible it is important to optimise the number of gates used in the underlying quantum circuits. In this paper we find that many gate optimisation problems for approximately…
A quantum error correcting code protects encoded logical information against errors. Transversal gates are a naturally fault-tolerant way to manipulate logical qubits but cannot be universal themselves. Protocols such as magic state…
The increasing scale of near-term quantum hardware motivates the need for efficient noise characterization methods, since qubit and gate level techniques cannot capture crosstalk and correlated noise in many qubit systems. While scalable…
We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation (Gottesman…
Here we study the unitary groups that can be constructed using elements from the qubit Clifford Hierarchy. We first provide a necessary and sufficient canonical form that semi-Clifford and generalized semi-Clifford elements must satisfy to…
In this paper, we introduce the gauge-fixed QLDPC surgery scheme, an improved logical measurement scheme based on the construction of Cohen et al. (Sci. Adv. 8, eabn1717). Our scheme leverages expansion properties of the Tanner graph to…
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal…