Related papers: Reducing T Gates with Unitary Synthesis
We present two deterministic algorithms to approximate single-qutrit gates. These algorithms utilize the Clifford + $\mathbf{R}$ group to find the best approximation of diagonal rotations. The first algorithm exhaustively searches over the…
In fault-tolerant quantum computing, errors in unitary gate synthesis is comparable with noise inherent in the gates themselves. While mixed synthesis can suppress such coherent errors quadratically, there is no clear understanding on its…
In this paper we study the potential of using reinforcement learning (RL) in order to synthesize quantum circuits, while optimizing the T-count and CS-count, of unitaries that are exactly implementable by the Clifford+T and Clifford+CS gate…
Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
State-of-the-art quantum circuit optimization (QCO) algorithms for T-count reduction often lead to a substantial increase in two-qubit gate count (2Q-count) -- a drawback that existing 2Q-count optimization techniques struggle to address…
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…
For a number of useful quantum circuits, qudit constructions have been found which reduce resource requirements compared to the best known or best possible qubit construction. However, many of the necessary qutrit gates in these…
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…
Recently, it was shown that Repeat-Until-Success (RUS) circuits can achieve a $2.5$ times reduction in expected $T$-count over ancilla-free techniques for single-qubit unitary decomposition. However, the previously best known algorithm to…
Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set. These approximation algorithms find asymptotically optimal approximations in probabilistic…
We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+$T$ basis, that minimize the number of phase-rotation gates in the synthesized approximation circuit.…
We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely…
Efficient constructions for quantum logic are essential since quantum computation is experimentally challenging. This thesis develops quantum logic synthesis as a paradigm for reducing the resource overhead in fault-tolerant quantum…
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the…
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…
Many quantum algorithms can be written as a composition of unitaries, some of which can be exactly synthesized by a universal fault-tolerant gate set, while others can be approximately synthesized. A quantum compiler synthesizes each…
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…
The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of…
The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit…