Related papers: Exact Quantum Circuit Optimization is co-NQP-hard
Equational reasoning is central to quantum circuit optimisation and verification: one replaces subcircuits by provably equivalent ones using a fixed set of rewrite rules viewed as equations. A finite rule set is most informative when it…
A combinatorial optimization problem becomes very difficult in situations where the energy landscape is rugged, and the global minimum locates in a narrow region of the configuration space. When using the quantum approximate optimization…
Quantum computers are expected to scale in size to close the gap that currently exists between quantum algorithms and quantum hardware. To this end, quantum compilation techniques must scale along with the hardware constraints, shifting the…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
Quantum computing carries significant potential for addressing practical problems. However, currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits. Therefore, quantum…
This paper introduces an algorithm designed to approximate quantum transformation matrix with a restricted number of gates by using the block decomposition technique. Addressing challenges posed by numerous gates in handling large qubit…
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…
We study the quantum complexity class QNC^0_f of quantum operations implementable exactly by constant-depth polynomial-size quantum circuits with unbounded fan-out gates (called QNC^0_f circuits). Our main result is that the quantum OR…
Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [Quantum Inf. Comput., 4(2):134--145], Terhal and DiVincenzo have shown that these…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
In the noisy intermediate-scale quantum (NISQ) era, two-qubit gates in quantum circuits are more susceptible to noise than single-qubit gates. Therefore, reducing the number of two-qubit gates is crucial for improving circuit efficiency and…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
Quantum circuits must run on quantum computers with tight limits on qubit and gate counts. To generate circuits respecting both limits, a promising opportunity is exploiting uncomputation to trade qubits for gates. We present Reqomp, a…
Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum…
Reducing the circuit depth of quantum circuits is a crucial bottleneck to enabling quantum technology. This depth is inversely proportional to the number of available quantum gates that have been synthesised. Moreover, quantum gate…
Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into…
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and…
Currently available quantum computers, so called Noisy Intermediate-Scale Quantum (NISQ) devices, are characterized by relatively low number of qubits and moderate gate fidelities. In such scenario, the implementation of quantum error…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…