Related papers: Quantum Lower Bounds for Fanout
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…
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 introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…
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…
Variational algorithm using Quantum Approximate Optimization Algorithm (QAOA) can solve the prime factorization problem in near-term noisy quantum computers. Conventional Variational Quantum Factoring (VQF) requires a large number of…
Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of…
We show that the $T$-depth of any single-qubit $z$-rotation can be reduced to $3$ if a certain catalyst state is available. To achieve an $\epsilon$-approximation, it suffices to have a catalyst state of size polynomial in…
Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly-interacting systems and black holes. The…
The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information…
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…
The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a…
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a…
The impressive progress in quantum hardware in the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can…
We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 is…
An important aspect that strongly impacts the experimental feasibility of quantum circuits is the ratio of gate times and typical error time scales. Algorithms with circuit depths that significantly exceed the error time scales will result…
We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
Rigorously establishing that the error in an experimental quantum operation is beneath the threshold for fault-tolerant quantum computation currently requires considering the worst-case error, which can be orders of magnitude smaller than…
Shannon proved that almost all Boolean functions require a circuit of size $\Theta(2^n/n)$. We prove a quantum analog of this classical result. Unlike in the classical case the number of quantum circuits of any fixed size that we allow is…
Structured variational quantum algorithms such as the Quantum Approximate Optimisation Algorithm (QAOA) have emerged as leading candidates for exploiting advantages of near-term quantum hardware. They interlace classical computation, in…