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The prevalent approach to executing quantum algorithms on quantum computers is to break-down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate…
Dynamic quantum simulation is a leading application for achieving quantum advantage. However, high circuit depths remain a limiting factor on near-term quantum hardware. We present a compilation algorithm based on Matrix Product Operators…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
In the noisy intermediate-scale quantum (NISQ) era, flexible quantum operations are essential for advancing large-scale quantum computing, as they enable shorter circuits that mitigate decoherence and reduce gate errors. However, the…
An efficient implementation of the Toffoli gate is of conceptual importance for running various quantum algorithms, including Grover's search and Shor's integer factorization. However, direct implementation of the Toffoli gate either…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
The multiplication of superpositions of numbers is a core operation in many quantum algorithms. The standard method for multiplication (both classical and quantum) has a runtime quadratic in the size of the inputs. Quantum circuits with…
In this paper, we present algorithms to solve matrix multiplication problems in the MPC model. In particular, we consider the problem under various processor/memory constraints in the MPC model and prove the following results. 1.…
Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized…
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
Trapped-ion quantum computing can utilize all motional modes of the ion-crystal, to entangle multiple qubits simultaneously, enabling universal computation with multi-qubit gates supplemented by single-qubit rotations. Using multiple tones…
We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting. We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log…
Three-qubit gates can be constructed using combinations of single-qubit and two-qubit gates, making their independent realization unnecessary. However, direct implementation of three-qubit gates reduces the depth of quantum circuits,…
We propose an effective realization of the universal set of elementary quantum gates in solid state quantum computer based on macroscopic (or mesoscopic) resonance systems - multi-atomic coherent ensembles, squids or quantum dots in quantum…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
Fault-tolerant quantum computing hinges on efficient logical compilation, in particular, translating high-level circuits into code-compatible implementations. Gate-by-gate compilation often yields deep circuits, requiring significant…
Quantum-dot cellular automata (QCA) shows promise as a post silicon CMOS, low power computational technology. Nevertheless, to generalize QCA for next-generation digital devices, the ability to implement conventional programmable circuits…
Rapid advancement in the domain of quantum technologies has opened up researchers to the real possibility of experimenting with quantum circuits and simulating small-scale quantum programs. Nevertheless, the quality of currently available…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
We consider the fundamental problem of constructing fast and small circuits for binary addition. We propose a new algorithm with running time $\mathcal O(n \log_2 n)$ for constructing linear-size $n$-bit adder circuits with a significantly…