Related papers: Lower T-count with faster algorithms
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…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and 'nearly diagonal' semi-Clifford gates are particularly important:…
For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…
We present an algorithm for building a circuit that approximates single qubit unitaries with precision {\epsilon} using O(log(1/{\epsilon})) Clifford and T gates and employing up to two ancillary qubits. The algorithm for computing our…
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…
Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…
We show that quantum circuits cannot be made fault-tolerant against a depolarizing noise level of approximately 45%, thereby improving on a previous bound of 50% (due to Razborov). Our precise quantum circuit model enables perfect gates…
Exploring low-cost applications is paramount to creating value in early fault-tolerant quantum computers. Here we optimize both gate and qubit counts of recent algorithms for simulating the Fermi-Hubbard model. We further devise and compile…
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
We present new optimal and heuristic algorithms for exact synthesis of multi-qubit unitaries and isometries. For example, our algorithms find Clifford and T circuits for unitaries with entries in $\mathbb{Z}[i,1/\sqrt{2}]$. The optimal…
As the size and complexity of a quantum computer increases, quantum bit (qubit) characterization and gate optimization become complex and time-consuming tasks. Current calibration techniques require complicated and verbose measurements to…
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…
Although many of works have been done in multivalued quantum logic synthesis, the question whether multivalued quantum circuits are more efficient than the conventional binary quantum circuits is still open. In this article we devote to the…
We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to…
In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. These bounds…
Compilation and optimization of quantum circuits are critical components in the execution of algorithms on quantum computers. These components must successfully balance two competing priorities: minimizing the number of expensive resources,…