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We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically…
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…
In the near term, programming quantum computers will remain severely limited by low quantum volumes. Therefore, it is desirable to implement quantum circuits with the fewest resources possible. For the common Clifford+T circuits, most…
Quantum circuits of arithmetic operations such as addition are needed to implement quantum algorithms in hardware. Quantum circuits based on Clifford+T gates are used as they can be made tolerant to noise. The tradeoff of gaining fault…
Fault-tolerant quantum computation enables reliable quantum computation but incurs a significant overhead from both time and resource perspectives. To reduce computation time, Austin G. Fowler proposed time-optimal quantum computation by…
We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…
We introduce a measure for evaluating the efficiency of finite universal quantum gate sets $\mathcal{S}$, called the Quantum Circuit Overhead (QCO), and the related notion of $T$-Quantum Circuit Overhead ($T$-QCO). QCO compares the circuit…
In fault-tolerant quantum computing systems, realising (approximately) universal quantum computation is usually described in terms of realising Clifford+T operations, which is to say a circuit of CNOT, Hadamard, and $\pi/2$-phase rotations,…
We formulate and investigate the simplest version of time-optimal quantum computation theory (t-QCT), where the computation time is defined by the physical one and the Hamiltonian contains only one- and two-qubit interactions. This version…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
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 consider the problem of approximating arbitrary single-qubit z-rotations by ancilla-free Clifford+T circuits, up to given epsilon. We present a fast new probabilistic algorithm for solving this problem optimally, i.e., for finding the…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
We present new optimal and heuristic algorithms for exact synthesis of multi-qubit unitaries and isometries. For example, our algorithms find Clifford and T circuits for unitaries with entries in $\mathbb{Z}[i,1/\sqrt{2}]$. The optimal…
Clifford gates play a role in the optimisation of Clifford+T circuits. Reducing the count and the depth of Clifford gates, as well as the optimal scheduling of T gates, influence the hardware and the time costs of executing quantum…
The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer. Here we revisit this theorem and extend it to quantum circuits composed of Clifford and T gates,…
We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford+T circuit with T-count $O(2^{4n/3} n^{2/3})$. This improves upon the previous best known upper bound of $O(2^{3n/2} n)$, while the best…
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…
In this work, we introduce a new circuit optimization technique to reduce the number of T gates in Clifford+T circuits by treating T gates conjugated by Clifford gates as $\frac{\pi}{4}$-rotations around Pauli operators. The tested…