Related papers: Quantum Circuit Synthesis Using an Exact T Library
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…
Exact synthesis provides unconditional optimality and canonical structure, but is often limited to small, carefully scoped regimes. We present an exact synthesis framework for two-qubit circuits over the Clifford+$T$ gate set that optimizes…
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 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…
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…
Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…
Quantum error correction is essential for achieving practical quantum computing but has a significant computational overhead. Among fault-tolerant (FT) gate operations, non-Clifford gates, such as $T$, are particularly expensive due to…
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…
Clifford circuit optimization is an important step in the quantum compilation pipeline. Major compilers employ heuristic approaches. While they are fast, their results are often suboptimal. Minimization of noisy gates, like 2-qubit CNOT…
Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean…
For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
Efficient synthesis of arbitrary quantum states and unitaries from a universal fault-tolerant gate-set e.g. Clifford+T is a key subroutine in quantum computation. As large quantum algorithms feature many qubits that encode coherent quantum…
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model…
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…
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
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…
The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates. For CSS codes that can implement Clifford gates transversally it suffices to provide one additional non-Clifford gate, such…