Related papers: On the power quantum computation over real Hilbert…
We show that universal quantum computation can be achieved in the standard pure-state circuit model while, at any time, the entanglement entropy of all bipartitions is small---even tending to zero with growing system size. The result is…
Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational…
Realistic physical implementations of quantum computers can entail tradeoffs which depart from the ideal model of quantum computation. Although these tradeoffs have allowed successful demonstration of certain quantum algorithms, a crucial…
A conception of virtual quantum information bit - virtual qubit - is introduced. It is shown by means of virtual qubit representation that four states of a single quantum particle is enough for implementation of full set of the gates, which…
This paper considers the following problem. Two mixed-state quantum circuits Q and R are given, and the goal is to determine which of two possibilities holds: (i) Q and R act nearly identically on all possible quantum state inputs, or (ii)…
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
We study the computational difficulty of computing the ground state degeneracy and the density of states for local Hamiltonians. We show that the difficulty of both problems is exactly captured by a class which we call #BQP, which is the…
We show that the class QAM does not change even if the verifier's ability is restricted to only single-qubit measurements. To show the result, we use the idea of the measurement-based quantum computing: the verifier, who can do only…
Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic…
We consider quantum computing in the k-qubit model where the starting state of a quantum computer consists of k qubits in a pure state and n-k qubits in a maximally mixed state. We ask the following question: is there a general method for…
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach…
We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different…
By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for…
We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a…
An infinite dimensional system such as a quantum harmonic oscillator offers a potentially unbounded Hilbert space for computation, but accessing and manipulating the entire state space requires a physically unrealistic amount of energy.…
Establishing an advantage for (white-box) computations by a quantum computer against its classical counterpart is currently a key goal for the quantum computation community. A quantum advantage is achieved once a certain computational…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…