Controlling arbitrary quantum operations using additional degrees of freedom. (a) Logic circuit in which quantum operation O is implemented on a register of qubits (target register), conditional on the logical state of a single control qubit. (b) Our approach to implementing the circuit in (a). The target information carriers are four dimensional systems with logical states |0right fence,|1right fence,|2right fence and |3right fence. Initially and finally, only the bottom two ‘qubit’ levels (|0right fence and |1right fence) are populated. Controlled-Xa gates (equations 1 and 2) swap information between the qubit levels and the upper levels (|2right fence and |3right fence), on which O does not act. In this way, conditional on the state of the control qubit, the entire quantum state of the target register is temporarily moved into an effective quantum memory on which O does not act.
Dr Xiao-Qi Zhou and colleagues at the University of Bristol’s Centre for Quantum Photonics and the University of Queensland, Australia, have shown that controlled operations — ones that are implemented on the condition that a “control bit” is in the state 1 — can be dramatically simplified compared to the standard approach. The researchers believe their technique will find applications across quantum information technologies, including precision measurement, simulation of complex systems, and ultimately a quantum computer — a powerful type of computer that uses quantum bits (qubits) rather than the conventional bits used in today’s computers.
Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology. The technique, which is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. Here, we demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity.
Experimental setup for realizing CU gates. A 60 mW continuous-wave (CW) laser beam with a central wavelength of 404 nm is focused onto a BiBO crystal to create photon pairs. Both the horizontal (modes 1r and 2r) and vertical (modes 1b and 2b) photon pairs are collected. Before collection into polarization-maintaining fibres (PMF), the photons are spectrally filtered by narrow-band filters (ΔλFWHW=3.2 nm). A1, B1, A2 and B2 are four single-qubit gates. By post-selecting the case the two photons exit at ports 1 and 2, one would effectively realize a two-qubit quantum gate (A1 A2+B1 B2). The phase between the two components is stabilized by monitoring the coincidence count rates between detectors 1′ and 2
A major obstacle for realizing a quantum computer is the complexity of the quantum circuits required. As with conventional computers, quantum algorithms are constructed from a small number of elementary logic operations. Controlled operations are at the heart of the majority of important quantum algorithms. The traditional method to realize controlled operations is to decompose them into the elementary logic gate set. However, this decomposition is very complex and prohibits the realization of even small-scale quantum circuits.
The researchers now show a completely new way to approach this problem. “By using an extra degree of freedom of quantum particles, we can realize the control operation in a novel way. We have constructed several controlled operations using this method,” said Dr Xiao-Qi Zhou, research fellow working on this project, “This will significantly reduce the complexity of the circuits for quantum computing.”
“The new approach we report here could be the most important development in quantum information science over the coming years,” said Professor Jeremy O’Brien, director of the Centre for Quantum Photonics, “It provides a dramatic reduction in quantum circuit complexity — the major barrier to the development of more sophisticated quantum algorithms — just at the time that the first quantum algorithms are being demonstrated.”
The team now plans to apply this technique to implement some important quantum algorithms, such as the phase estimation algorithm and Shor’s factoring algorithm.