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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…
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum…
Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multi-scale entanglement…
In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…
We provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of…
We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific…
Quantum circuits of many qubits are extremely difficult to realize; thus, the number of qubits is an important metric in a quantum circuit design. Further, scalable and reliable quantum circuits are based on Clifford + T gates. An efficient…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
Pebble games are popular models for analyzing time-space trade-offs. In particular, the reversible pebble game is often applied in quantum algorithms like Grover's search to efficiently simulate classical computation on inputs in…
Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of…
We provide accurate upper bounds on the Boolean circuit complexity of the standard and the Karatsuba methods of integer multiplication
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
We present quantum circuits for comparison and increment operations that achieve an asymptotically optimal gate count of $\Theta(n)$ and depth of $\Theta(\log n)$ over the Clifford+Toffoli gate set, while using a provably minimal number of…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
We develop a method for approximate synthesis of single--qubit rotations of the form $e^{-i f(\phi_1,\ldots,\phi_k)X}$ that is based on the Repeat-Until-Success (RUS) framework for quantum circuit synthesis. We demonstrate how smooth…
Solving random subset sum instances plays an important role in constructing cryptographic systems. For the random subset sum problem, in 2013 Bernstein et al. proposed a quantum algorithm with heuristic time complexity…
In the noisy intermediate-scale quantum era, mid-circuit measurement and reset operations facilitate novel circuit optimization strategies by reducing a circuit's qubit count in a method called resizing. This paper introduces two such…
Shor's algorithm, which given appropriate hardware can factorise an integer $N$ in a time polynomial in its binary length $L$, has arguable spurred the race to build a practical quantum computer. Several different quantum circuits…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal…