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We show that Gottesman's (1998) semantics for Clifford circuits based on the Heisenberg representation gives rise to a lightweight Hoare-like logic for efficiently characterizing a common subset of quantum programs. Our applications include…
A new method for simulation of a binary homogeneous Markov process using a quantum computer was proposed. This new method allows using the distinguished properties of the quantum mechanical systems -- superposition, entanglement and…
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…
We demonstrate the use of optimal control to design two entropy-manipulating quantum gates which are more complex than the corresponding, commonly used, gates, such as CNOT and Toffoli (CCNOT): A 2-qubit gate called PE (polarization…
Basic logic gates and their operations in ternary quantum domain are involved in the synthesis of ternary quantum circuits. Only a few works define ternary algebra for ternary quantum logic realization. In this paper, a ternary logic…
We demonstrate a technique for optimizing quantum circuits that is analogous to classical windowing. Specifically, we show that small table lookups can allow control qubits to be iterated in groups instead of individually. We present…
Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this…
A common approach to quantum circuit transformation is to use the properties of a specific gate set to create an efficient representation of a given circuit's unitary, such as a parity matrix or stabiliser tableau, and then resynthesise an…
We consider quantum gates for trapped ions using state-selective displacement of the ions. We generalize earlier work in order to treat arbitrary separations between the traps. This requires the impact of anharmonicity arising from the…
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…
This paper presents a novel way to use the algebra of unit quaternions to express arbitrary roots or fractional powers of single-qubit gates, and to use such fractional powers as generators for algebras that combine these fractional input…
Controlled and multi-controlled quantum gates, whose action on a target qubit depends on the state of multiple control qubits, represent a fundamental logical building block for complex quantum algorithms. We propose a scheme for realizing…
Single-mode squeezing and Fourier transformation operations are two essential logical gates in continuous-variable quantum computation, which have been experimentally implemented by means of an optical four-mode cluster state. In this…
Quantum computation is conventionally performed using quantum operations acting on two-level quantum bits, or qubits. Qubits in modern quantum computers suffer from inevitable detrimental interactions with the environment that cause errors…
A Bernoulli factory is a randomness manipulation routine that takes as input a Bernoulli random variable, outputting another Bernoulli variable whose bias is a function of the input bias. Recently proposed quantum-to-quantum Bernoulli…
A matrix can be converted into a doubly stochastic matrix by using two diagonal matrices. And a doubly stochastic matrix can be written as a sum of permutation matrices. In this paper, we describe a method to write a given generic matrix in…
Current quantum computers are especially error prone and require high levels of optimization to reduce operation counts and maximize the probability the compiled program will succeed. These computers only support operations decomposed into…
We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to…
Reversible single-target gates are a generalization of Toffoli gates which are a helpful formal representation for the description of synthesis algorithms but are too general for an actual implementation based on some technology. There is…
How to implement multi-qubit gates is an important problem in quantum information processing. Based on cross phase modulation, we present an approach to realizing a family of multi-qubit gates that deterministically operate on single…