Related papers: Clifford Gate Optimisation and T Gate Scheduling: …
In this paper we study the Clifford+Toffoli universal fault-tolerant gate set. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the Toffoli-count of arbitrary…
In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…
We show how to efficiently simulate continuous-time quantum query algorithms that run in time T in a manner that preserves the query complexity (within a polylogarithmic factor) while also incurring a small overhead cost in the total number…
We investigate Clifford+$T$ quantum circuits with a small number of $T$-gates. Using the sparsification lemma, we identify time complexity lower bounds in terms of $T$-gate count below which a strong simulator would improve on the…
Quantum circuits are the preferred formalism for expressing quantum information processing tasks. Quantum circuit design automation methods mostly use a waterfall approach and consider that high level circuit descriptions are hardware…
To approximate arbitrary unitary transformations on one or more qubits, one must perform transformations which are outside of the Clifford group. The gate most commonly considered for this purpose is the T = diag(1, exp(i \pi/4)) gate. As T…
We propose hardware-efficient schemes for implementing logical H and S gates transversally on rotated surface codes with reconfigurable neutral atom arrays. For logical H gates, we develop a simple strategy to rotate code patches…
Many quantum systems are being investigated in the hope of building a large-scale quantum computer. All of these systems suffer from decoherence, resulting in errors during the execution of quantum gates. Quantum error correction enables…
We present a method for optimizing quantum circuit compilation by automating the allocation of auxiliary qubits for multi-qubit gate decompositions. This approach is implemented and evaluated within the high-level quantum programming…
Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…
While mapping a quantum circuit to the physical layer one has to consider the numerous constraints imposed by the underlying hardware architecture. Connectivity of the physical qubits is one such constraint that restricts two-qubit…
We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the…
A major challenge in developing quantum computing technologies is to accomplish high precision tasks by utilizing multiplex optimization approaches, on both the physical system and algorithm levels. Loss functions assessing the overall…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…
We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities. Our method is based on the framework of spacetime codes, and is particularly suited to near-term hardware since it…
Circuit optimization is a fundamental task for practical applications of near-term quantum computers. In this work we address this challenge through the powerful lenses of tensor network theory. Our approach involves the full…
Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…
Topological subsystem color codes add to the advantages of topological codes an important feature: error tracking only involves measuring 2-local operators in a two dimensional setting. Unfortunately, known methods to compute with them were…