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We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
In quantum control theory, a question of fundamental and practical interest is how an arbitrary unitary transformation can be decomposed into minimum number of elementary rotations for implementation, subject to various physical…
In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which…
A breadth-first search method for determining optimal 3-line circuits composed of quantum NOT, CNOT, controlled-V and controlled-V+ (NCV) gates is introduced. Results are presented for simple gate count and for technology motivated cost…
Many quantum states arising in algorithms and physical systems occupy only a small, structured subset of the exponentially large Hilbert space, yet standard quantum state tomography fails to exploit this structure. We present an efficient…
We give a sound and complete equational theory for 3-qubit quantum circuits over the Toffoli-Hadamard gate set { X, CX, CCX, H }. That is, we introduce a collection of true equations among Toffoli-Hadamard circuits on three qubits that is…
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…
Proton transfer reactions are fundamental to many chemical and biological systems, where quantum effects such as tunneling, delocalization, and zero-point motion play key kinetic control roles. However, classical methods capable of…
In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four correlations. The resulting four-dimensional convex body of…
A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter…
Protocols for quantum measurement are an essential part of quantum computing. Measurements are no longer confined to the final step of computation but are increasingly embedded within quantum circuits as integral components of…
We propose a co-designed variant of ADAPT-VQE (Co-ADAPT-VQE) where the quantum hardware is taken into account in the construction of the ansatz. This framework can be readily used to optimize state preparation circuits for any device,…
Developing methods to solve nuclear many-body problems with quantum computers is an imperative pursuit within the nuclear physics community. Here, we introduce a quantum algorithm to accurately and precisely compute the ground state of…
We describe a practical method of constructing quantum combinational logic circuits with basic quantum logic gates such as NOT and general $n$-bit Toffoli gates. This method is useful to find the quantum circuits for evaluating logic…
Quantum computing has shown tremendous promise in addressing complex computational problems, yet its practical realization is hindered by the limited availability of qubits for computation. Recent advancements in quantum hardware have…
We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and…
Equivalence checking of quantum circuits is an essential element in quantum program compilation, in which a quantum program can be synthesized into different quantum circuits that may vary in the number of qubits, initialization…
We propose a scheme for implementing the CNOT gate over qubits encoded in a pair of electron spins in a double quantum dot. The scheme is based on exchange and spin orbit interactions and on local gradients in Zeeman fields. We find that…
Nielsen \cite{Nielsen05} recently asked the following question: "What is the minimal size quantum circuit required to exactly implement a specified $% \mathit{n}$-qubit unitary operation $U$, without the use of ancilla qubits?" Nielsen was…
Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction,…