Related papers: Approximate encoded permutations and piecewise qua…

If a set $\mathbb{G}$ of quantum gates is countable, then the operators that can be exactly represented by a circuit over $\mathbb{G}$ form a strict subset of the collection of all unitary operators. When $\mathbb{G}$ is universal, one…

To overcome inherent limitations of analog signals in over-the-air computation (AirComp), this letter proposes a two's complement-based coding scheme for the AirComp implementation with compatible digital modulations. Specifically,…

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…

In [A.W. Harrow and R.A. Low, Commun. Math. Phys. 291, 257-302 (2009)], it was shown that a quantum circuit composed of random 2-qubit gates converges to an approximate quantum 2-design in polynomial time. We point out and correct a flaw in…

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 examine the fundamental problem of constructing depth-optimum circuits for binary addition. More precisely, as in literature, we consider the following problem: Given auxiliary inputs $t_0, \dotsc, t_{m-1}$, so-called generate and…

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a…

We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…

We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic…

Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components…

We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum…

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…

Targeting error-tolerant applications, approximate computing relaxes rigid functional equivalence to significantly improve power, performance, and area. Traditional approximate logic synthesis (ALS) relies on incremental rewriting, limiting…

Block-encodings of matrices have become an essential element of quantum algorithms derived from the quantum singular value transformation. This includes a variety of algorithms ranging from the quantum linear systems problem to quantum…

Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…

Quantum algorithms and protocols are often presented as quantum circuits for a better understanding. We give a list of equivalence rules which can help in the analysis and design of quantum circuits. As example applications we study quantum…

We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing's tket compiler. We present…

Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers…

Pure quantum states are often approximately encoded as classical bit strings such as those representing probability amplitudes and those describing circuits that generate the quantum states. The crucial quantity is the minimum length of…

Satisfiability Testing (SAT) techniques are well-established in classical computing where they are used to solve a broad variety of problems, e.g., in the design of classical circuits and systems. Analogous to the classical realm, quantum…