Related papers: Conditions for optimal construction of two-qubit n…
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal…
In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence…
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…
We consider the implementation of two-qubit unitary transformations by means of CNOT gates and single-qubit unitary gates. We show, by means of an explicit quantum circuit, that together with local gates three CNOT gates are necessary and…
The information obtained from the operation of a quantum gate on only two complementary sets of input states is sufficient to estimate the quantum process fidelity of the gate. In the case of entangling gates, these conditions can be used…
The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a…
We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact…
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations…
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only…
While the question ``how many CNOT gates are needed to simulate an arbitrary two-qubit operator'' has been conclusively answered -- three are necessary and sufficient -- previous work on this topic assumes that one wants to simulate a given…
We construct optimized implementations of the CNOT and other universal two-qubit gates that, unlike many of the previously proposed protocols, are carried out in a single step. The new protocols require tunable inter-qubit couplings but, in…
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…
A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the…
We numerically study protocols consisting of repeated applications of two qubit gates used for generating random pure states. A necessary number of steps needed in order to generate states displaying bipartite entanglement typical of random…
The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two…
We present numerical results which show how two-bit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a…
A six-qubit quantum network consisting of conditional unitary gates is presented which is capable of implementing a large class of covariant two-qubit quantum operations. Optimal covariant NOT operations for one and two-qubit systems are…
We consider a general unitary operator acting on two qubits in a product state. We find the conditions such that the state of the qubits after the action is as entangled as possible. We also consider the possibility of using ancilla qubits…