Related papers: Quantum circuit synthesis using Householder transf…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
In order to implement a quantum computing application, problem instances must be encoded into a quantum circuit and then compiled for a specific platform. The lengthy compilation process is a key bottleneck in this workflow, especially for…
The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms,…
During the noisy intermediate-scale quantum (NISQ) era, it is important to optimize the quantum circuits in circuit depth and gate count, especially entanglement gates, including the CNOT gate. Among all the unitary operators, diagonal…
In this note we construct a quantum Fourier transform circuit in a recursive way, by directly copying the 'divide and conquer' construction of the fast Fourier transform algorithm, rather than using the explicit formula that is given in…
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…
To evaluate a quantum circuit on a quantum processor, one must find a mapping from circuit qubits to processor qubits and plan the instruction execution while satisfying the processor's constraints. This is known as the qubit mapping and…
We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on…
Quantum signal processing (QSP) is a framework for implementing certain polynomial functions via quantum circuits. To construct a QSP circuit, one needs (i) a target polynomial $P(z)$, which must satisfy $\lvert P(z)\rvert\leq 1$ on the…
Quantum compiling means fast, device-aware implementation of quantum algorithms (i.e., quantum circuits, in the quantum circuit model of computation). In this paper, we present a strategy for compiling IBM Q -aware, low-depth quantum…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
We consider the task of breaking down a quantum computation given as an isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT gates small. Although several decompositions are known for general isometries, here we…
In this paper we develop a classical algorithm of complexity $O(K \, 2^n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits, where $K$ is the total number of one-qubit and two-qubit control gates. The algorithm is developed by…
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are…
Any potential application of quantum computing, once encoded as a quantum circuit, needs to be compiled in order to be executed on a quantum computer. Deciding which qubit technology, which device, which compiler, and which corresponding…
This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme…
The block canonical coset decomposition is developed as a universal algorithmic tool to synthesize n-qubit quantum gates out of experimentally realizable NMR elements. The two-, three-, and four-qubit quantum Fourier transformations are…
High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning…
Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this letter we demonstrate how to utilize it to compute the dynamical response functions of many-body quantum systems. Specifically, we design…