Universal Quantum Gates
نویسنده
چکیده
For classical circuits, both {AND, NOT} and the single-gate set {NAND} are universal. To nd universal sets of quantum gates, we use the quantum circuit model, in which each gate is represented by a 2 by 2 unitary matrix. Composition of gates is done by multiplying these matrices. The space of operations generated by a set of gates is a subgroup of the unitary group U (2) (or SU (2), ignoring global phase) as long as we can generate g−1 for each g ∈ G. Since the space of quantum gates is continuous rather than discrete, to exactly perform any operation requires an uncountably in nite set of gates; we call a set that can do this exactly universal. Otherwise, we use a weaker de nition in which the gates approximate an operation to arbitrary precision:
منابع مشابه
Learning robust pulses for generating universal quantum gates
Constructing a set of universal quantum gates is a fundamental task for quantum computation. The existence of noises, disturbances and fluctuations is unavoidable during the process of implementing quantum gates for most practical quantum systems. This paper employs a sampling-based learning method to find robust control pulses for generating a set of universal quantum gates. Numerical results ...
متن کاملA Simple Proof that Toffoli and Hadamard are Quantum Universal
Recently Shi [15] proved that Toffoli and Hadamard are universal for quantum computation. This is perhaps the simplest universal set of gates that one can hope for, conceptually; It shows that one only needs to add the Hadamard gate to make a ’classical’ set of gates quantum universal. In this note we give a few lines proof of this fact relying on Kitaev’s universal set of gates [11], and discu...
متن کاملAlgebras and universal quantum computations with higher dimensional systems
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford algebras, and dis...
متن کاملUniversal Sets of Quantum Gates for Detected Jump-Error Correcting Quantum Codes
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into statistically independent reservoirs. The proposed universal quantum gates are constructed with the help of Heisenbergand Ising-type Hamiltonians acting on these phys...
متن کاملUniversal Fault-Tolerant Gates on Concatenated Stabilizer Codes
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of nontransversal, yet still fault-tolerant, gates that work directly on sma...
متن کامل