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We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity.…

We present some compact quantum circuits for a deterministic quantum computing on electron-spin qubits assisted by quantum dots inside single-side optical microcavities, including the CNOT, Toffoli, and Fredkin gates. They are constructed…

We present an explicit construction of a relativistic quantum computing architecture using a variational quantum circuit approach that is shown to allow for universal quantum computing. The variational quantum circuit consists of tunable…

Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity…

Matchgates are a restricted set of two-qubit gates known to be classically simulable under particular conditions. Specifically, if a circuit consists only of nearest-neighbour matchgates, an efficient classical simulation is possible if…

Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the…

Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical…

We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that non-trivial quantum encodings exist that…

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…

Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…

Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…

We consider procedures to realize an approximate universal NOT gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the…

A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system.…

Although the quality of quantum bits (qubits) and quantum gates has been steadily improving, the available quantity of qubits has increased quite slowly. To address this important issue in quantum computing, we have demonstrated arbitrary…

Yao (1993) proved that quantum Turing machines and uniformly generated quantum circuits are polynomially equivalent computational models: $t \geq n$ steps of a quantum Turing machine running on an input of length $n$ can be simulated by a…

In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…

Several physical architectures allow for measurement-based quantum computing using sequential preparation of cluster states by means of probabilistic quantum gates. In such an approach, the order in which partial resources are combined to…

We propose an experimentally feasible scheme to achieve quantum computation based on a pair of orthogonal cyclic states. In this scheme, quantum gates can be implemented based on the total phase accumulated in cyclic evolutions. In…

A universal programmable quantum processor uses program quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming…

Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…