Related papers: Multi-qubit circuit synthesis and Hermitian lattic…
Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical…
The solving of linear systems provides a rich area to investigate the use of nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for skewed linear systems for…
Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
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 error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum…
Path sums are a convenient symbolic formalism for quantum operations with applications to the simulation, optimization, and verification of quantum protocols. Unlike quantum circuits, path sums are not limited to unitary operations, but can…
We present a quantum synthesis algorithm designed to produce short circuits and to scale well in practice. The main contribution is a novel representation of circuits able to encode placement and topology using generic "gates", which allows…
We devise greedy heuristics tailored for synthesizing quantum circuits that implement a specified set of Pauli rotations. Our heuristics are designed to minimize either the count of entangling gates or the depth of entangling gates, and…
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
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…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
In this work, we introduce a new circuit optimization technique to reduce the number of T gates in Clifford+T circuits by treating T gates conjugated by Clifford gates as $\frac{\pi}{4}$-rotations around Pauli operators. The tested…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
Linear combination of unitaries (LCU for short) is one of the most important techniques in designing quantum algorithms. In this paper, we propose a new quantum algorithm in three different forms to achieve LCU. Different from previous…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
To run a quantum program in the real device, the compiler maps the logical qubits to physical qubits. This is the most crucial step of compiling a quantum circuit. Because the fidelity of a quantum circuit depends heavily on this mapping…
In this paper we study single qutrit circuits consisting of words over the Clifford$+D$ cyclotomic gate set, where $D=\text{diag}(\pm\xi^{a},\pm\xi^{b},\pm\xi^{c})$, $\xi$ is a primitive $9$-th root of unity and $a,b,c$ are integers. We…
Although many of works have been done in multivalued quantum logic synthesis, the question whether multivalued quantum circuits are more efficient than the conventional binary quantum circuits is still open. In this article we devote to the…
Prevailing proposals for the first generation of quantum computers make use of 2-level systems, or qubits, as the fundamental unit of quantum information. However, recent innovations in quantum error correction and magic state distillation…