Related papers: Catalytic Embeddings of Quantum Circuits
Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…
Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we…
Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision $\varepsilon$.…
We develop the first constructive algorithms for compiling single-qubit unitary gates into circuits over the universal $V$ basis. The $V$ basis is an alternative universal basis to the more commonly studied $\{H,T\}$ basis. We propose two…
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…
Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
Quantum circuit synthesis describes the process of converting arbitrary unitary operations into a gate sequence of a fixed universal gate set, usually defined by the operations native to a given hardware platform. Most current synthesis…
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear…
Current and imminent quantum hardware lacks reliability and applicability due to noise and limited qubit counts. Quantum circuit cutting -- a technique dividing large quantum circuits into smaller subcircuits with sizes appropriate for the…
The native gate set is fundamental to the performance of quantum devices, as it governs the accuracy of basic quantum operations and dictates the complexity of implementing quantum algorithms. Traditional approaches to extending gate sets…
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…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
We study ancilla-free approximation of single-qubit unitaries $U\in {\rm SU}(2)$ by gate sequences over Clifford+$G$, where $G\in\{T,V\}$ or their generalization. Let $p$ denote the characteristic factor of the gate set (e.g., $p=2$ for…
In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly…
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…
Quantum gate set tomography (GST) has emerged as a promising method for the full characterization of quantum logic gates. In contrast to quantum process tomography (QPT), GST self-consistently and correctly accounts for state preparation…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…