The universal quantum computer is a device capable of simulating any physicalsystem and represents a major goal for the field of quantum informationscience. Algorithms performed on such a device are predicted to offersignificant gains for some important computational tasks. In the context ofquantum information, "universal" refers to the ability to perform arbitraryunitary transformations in the system's computational space. The combination ofarbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate isa gate set capable of achieving universal control of any number of qubits,provided that these gates can be performed repeatedly and between arbitrarypairs of qubits. Although gate sets have been demonstrated in severaltechnologies, they have as yet been tailored toward specific tasks, forming asmall subset of all unitary operators. Here we demonstrate a programmablequantum processor that realises arbitrary unitary transformations on twoqubits, which are stored in trapped atomic ions. Using quantum state andprocess tomography, we characterise the fidelity of our implementation for 160randomly chosen operations. This universal control is equivalent to simulatingany pairwise interaction between spin-1/2 systems. A programmable multi-qubitregister could form a core component of a large-scale quantum processor, andthe methods used here are suitable for such a device.
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