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The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
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…
Given oracle access to an unknown unitary C from the Clifford group and its conjugate, we give an exact algorithm for identifying C with O(n) queries, which we prove is optimal. We then extend this to all levels of the Gottesman-Chuang…
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes…
High-fidelity native multi-qubit operations are crucial to efficient quantum circuit compilation due to their ability of shortening circuit depth and enhence the performance. However, the design and implementation of these gates remain a…
We demonstrate the possibility to perform distributed quantum computing using only single photon sources (atom-cavity-like systems), linear optics and photon detectors. The qubits are encoded in stable ground states of the sources. To…
We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a 2D grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit's qubits in…
Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such…
We propose and analyze heralded quantum gates between qubits in optical cavities. They employ an auxiliary qubit to report if a successful gate occurred. In this manner, the errors, which would have corrupted a deterministic gate, are…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small…
We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…
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…
A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…
Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the 2-qubit CS (or CNOT) gate, we provide numerical evidence that the…
Quantum computing carries significant potential for addressing practical problems. However, currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits. Therefore, quantum…
Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as…
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient…
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group, one often resorts to $t$-designs. Unitary…