Related papers: CNOT-count optimized quantum circuit of the Shor's…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…
Exchange-only quantum computation is a version of spin-based quantum computation that entirely avoids the difficulty of controlling individual spins by a magnetic field and instead functions by sequences of exchange pulses. The challenge…
Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary…
Current experimental quantum computing devices are limited by noise, mainly originating from entangling gates. If an efficient gate sequence for an operation is unknown, one often employs layered parameterized quantum circuits, especially…
In this paper, we study the close relationship between Reed-Muller codes and single-qubit phase gates from the perspective of $T$-count optimization. We prove that minimizing the number of $T$ gates in an $n$-qubit quantum circuit over CNOT…
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum…
In this note we present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-S (CS) and controlled-X (CX) gates, using the generating set of quantum gates [X, T, CX, CS]. We…
The optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. By harnessing higher-dimensional Hilbert spaces, we reduce the cost of a…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…
In the past years, research on Shor's algorithm for solving elliptic curves for discrete logarithm problems (Shor's ECDLP), the basis for cracking elliptic curve-based cryptosystems (ECC), has started to garner more significant interest. To…
As the field of quantum computing grows, novel algorithms which take advantage of quantum phenomena need to be developed. As we are currently in the NISQ (noisy intermediate scale quantum) era, quantum algorithm researchers cannot reliably…
Quantum circuits currently constitute a dominant model for quantum computation. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We…
We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…
We present a genetic algorithm for finding a set of pulse sequences, or rotations, for a given quantum logic gate, as implemented by NMR. We demonstrate the utility of the method by showing that shorter sequences than have been previously…
We present a theoretical result, which is based on the linear algebra theory (similar operators). The obtained theoretical results optimize the experimental technique to construct quantum computer e.g., reduces the number of steps to…
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. I propose a method for constructing the ME operators that relies upon the…
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…
We present QEst, a procedure to systematically generate approximations for quantum circuits to reduce their CNOT gate count. Our approach employs circuit partitioning for scalability with procedures to 1) reduce circuit length using…
Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access…