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Related papers: Optimising quantum circuits is generally hard

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Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be…

NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…

Quantum Physics · Physics 2024-01-15 Yagnik Chatterjee , Eric Bourreau , Marko J. Rančić

Arbitrarily accurate fault-tolerant (FT) universal quantum computation can be carried out using the Clifford gates Z, S, CNOT plus the non-Clifford T gate. Moreover, a recent improvement of the Solovay-Kitaev theorem by Kuperberg implies…

Quantum Physics · Physics 2024-07-02 H. F. Chau

A physical limitation in quantum circuit design is the fact that gates in a quantum system can only act on qubits that are physically adjacent in the architecture. To overcome this problem, SWAP gates need to be inserted to make the circuit…

Optimization and Control · Mathematics 2025-08-28 Frank de Meijer , Dion Gijswijt , Renata Sotirov

Progress in quantum hardware design is progressing toward machines of sufficient size to begin realizing quantum algorithms in disciplines such as encryption and physics. Quantum circuits for addition are crucial to realize many quantum…

Quantum Physics · Physics 2021-06-10 Himanshu Thapliyal , Edgard Muñoz-Coreas , Vladislav Khalus

Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…

Quantum Physics · Physics 2025-02-07 Yifan Zhang , Yuxuan Zhang

Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…

Quantum Physics · Physics 2021-12-13 Yasuhiro Kondo , Ryuhei Mori , Ramis Movassagh

We study optimal synthesis of Clifford circuits, and apply the results to peep-hole optimization of quantum circuits. We report optimal circuits for all Clifford operations with up to four inputs. We perform peep-hole optimization of…

Quantum Physics · Physics 2013-11-12 Vadym Kliuchnikov , Dmitri Maslov

Quantum addition circuits are considered being of two types: 1) Toffolli-adder circuits which use only classical reversible gates (CNOT and Toffoli), and 2) QFT-adder circuits based on the quantum Fourier transformation. We present the…

Quantum Physics · Physics 2022-11-09 Alexandru Paler

Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…

Quantum Physics · Physics 2025-06-04 Joe Gibbs , Lukasz Cincio

In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence…

Quantum Physics · Physics 2009-11-10 Farrokh Vatan , Colin Williams

A quantum circuit may be strongly classically simulated with the aid of ZX-calculus by decomposing its $t$ T-gates into a sum of $2^{\alpha t}$ classically computable stabiliser terms. In this paper, we introduce a general procedure to find…

Quantum Physics · Physics 2024-08-13 Matthew Sutcliffe , Aleks Kissinger

We present an implementation of multi-controlled quantum gates which provides significant reductions of cost compared to state-of-the-art methods. The operator applied on the target qubit is a unitary, special unitary, or the Pauli X…

Quantum Physics · Physics 2025-03-19 Ben Zindorf , Sougato Bose

We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…

Quantum Physics · Physics 2012-02-20 M. Van den Nest

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…

Quantum Physics · Physics 2026-01-28 Daniele Lizzio Bosco , Lukasz Cincio , Giuseppe Serra , M. Cerezo

In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…

Quantum Physics · Physics 2011-03-07 Martin Plesch , Časlav Brukner

We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that…

Quantum Physics · Physics 2023-05-10 Nikita A. Nemkov , Evgeniy O. Kiktenko , Ilia A. Luchnikov , Aleksey K. Fedorov

We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a…

Quantum Physics · Physics 2010-03-12 M. B. Plenio , S. Virmani

Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…

Quantum Physics · Physics 2021-05-25 Jacob Biamonte

Resource consumption is an important issue in quantum information processing, particularly during the present NISQ era. In this paper, we investigate resource optimization of implementing multiple controlled operations, which are…

Quantum Physics · Physics 2024-02-08 Junhong Nie , Wei Zi , Xiaoming Sun