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Optoelectronics & Communications
Qubus: quantum computation via communication
William Munro, Kae Nemoto, and Timothy Spiller
A new approach to scalable quantum computing, the ‘qubus computer,’ exploits the interaction of quantum bits with a quantum communication bus mode.
20 February 2007, SPIE Newsroom. DOI: 10.1117/2.1200702.0558
Quantum computing has reached a very interesting stage. Numerous proposals have been made over the last decade for physically realizing qubits to store quantum information and for designing scalable quantum computers.^{1,2,3} Researchers have demonstrated the more mature proposals at the fewqubit level in the laboratory, including trapped ions, nuclear spins, cavity quantum electrodynamics, and photonic qubits.^{2} They have demonstrated twoqubit gates and smallscale quantum algorithms.^{3} However, two key issues urgently need to be addressed: How can we scale up these devices above the fewqubit level, and what tasks can we perform with them?
Let us concentrate on the first issue, scalability. In terms of the longterm prospects for scalable quantum computing, ‘solidstate’ qubits, based on the fabrication techniques and technologies used for conventional information technology, show considerable promise.^{4–7} At present, these solidstate approaches lag behind the more mature ones, and they are only just realizing controllable twoqubit interactions. It will be interesting to see which systems can deliver on their promised scalability over the next few years.
Techniques for measuring the state of a qubit and for avoiding decoherence due to interactions of qubits with their surroundings are both extremely important for solidstate qubits. The current demonstration qubit experiments raise the hope that these problems will be addressed enough to permit useful smallscale quantum processing.
Even if these problems can be solved, however, we need an implementation of twoqubit quantum gates that permits scalable addition of more qubits to a system. For twoqubit gates that rely on direct qubitqubit interaction, adding an extra qubit may change the properties of the existing qubits. More important, the qubits have to be so close together that individual addressing could be a significant problem.
Here we present a new approach to scalable quantum computing—a ‘qubus computer’—that realizes qubit measurement and quantum gates through qubits interacting with a continuousvariable, quantum communication bus mode. There is no requirement for direct interaction between the qubits. The key concept is that the qubit can conditionally change the state of the bus depending on its state.
To elaborate, consider a qubit in one of two basis states, 0> or 1>. If the qubit is in the 0> state, the controlled interaction with the bus mode rotates the phase of the bus mode by an angle θ. However, if the qubit is in the 1> state, it rotates the phase by an angle θ (see Figure 1). The rotation applied to the bus mode depends on the initial state of the qubit. This leads to an immediate benefit even before we consider twoqubit gates: by determining which direction the busmode phase has been rotated, we can infer the state of the qubit indirectly. We do not need to measure the qubit directly to determine its state. This is known as a quantum nondemolition (QND) measurement and forms one of the key components in our qubus approach.^{8}
Figure 1. The state of a qubit can be measured indirectly, based on the controlled phase rotation it imposes on a probe bus. The left sides shows the circuit diagram, while the right side shows the phasespace evolution of the bus amplitudes corresponding to the two states of the qubit. If the qubit is in the 0> (1>) state, the probe bus is rotated upwards (downwards). Measuring the rotation indicates whether the qubit was in the 0> or 1> state, without disturbing it.
Twoqubit gates and beyond
We now consider how to implement a gate with two qubits. This can be achieved using the QND measurement, but now we delay the measurement of the bus mode once it has interacted with the first qubit. We instead have the bus mode interact with the second qubit before the measurement (depicted in Figure 2). For our two qubits we have four basis states, 0>_{1} 0>_{2}, 0>_{1} 1>_{2}, 1>_{1} 0>_{2}, and 1>_{1}1>_{2}, where the subscripts 1 and 2 denote the first and second qubits.
Figure 2.The twoqubit parity gate is based on controlled rotations between the qubits and the probe bus, followed by bus number measurement. The left side shows the circuit diagram, and the right side the phasespace evolution of the bus amplitudes corresponding to the four qubit computational basis states.
After the first qubit has interacted with the bus mode, the bus mode is rotated by θ for the 0>_{1} state and ? for the 1>_{1} state. Similarly, for the second qubit the bus mode is rotated by θ for the 0>_{2} state and θ for the 1>_{2} state. This means the bus mode can take one of three phase shifts: 2θ corresponding to the 0>_{1} 0>_{2} qubit state, 2θ corresponding to the 1>_{1} 1>_{2} qubit state, and 0 corresponding to the 0>_{1} 1>_{2} and 1>_{1} 0>_{2} qubit states. We then measure whether the bus mode has been phase shifted or not, without measuring the sign of the phase shift. This measurement will tell us whether we were in the evenparity subspace spanned by 0>_{1} 0>_{2} and 1>_{1}1>_{2} or the oddparity subspace spanned by 0>_{1} 1>_{2} and 1>_{1}0>_{2} (no phase shift). This sequence of operations, which we call a parity gate, is our primitive twoqubit gate.^{9,10}
Now consider starting with the product state in which each qubit is in the superposition 0>+1> instead of a pure basis state. After the bus interactions and measurements, the twoqubit state will either be 0>_{1} 0>_{2}+1>_{1}1>_{2} for the evenparity result or 0>_{1} 1>_{2}+1>_{1}0>_{2} for the oddparity result. Both of these states are maximally entangled, so our parity gate is an operation that can create entanglement. For this parity gate we can create all the required twoqubit operations necessary for universal quantum computation. We do not, however, need to restrict ourselves to parity. In fact, we can consider more complicated quantum circuits using the qubitbus interaction to implement a controlled NOT, without the need of the bus measurement.^{8,11}
The qubus technique we have described has a number of interesting applications. It can be used to implement a gate in quantum computation via either the standard gate model^{8,9} or the socalled cluster states.^{12–14} Our approach does not force a choice of computation scheme and processor architecture. Rather, it provides highly efficient and scalable building blocks which can be put together to suit the task at hand. Because of the efficiency of our approach and the fact that the qubits can be spatially separated, linked only by the bus, it could well have shortterm fewqubit applications—such as in quantum repeaters—before full quantum computation becomes possible. These repeaters are likely to distribute entanglement with rates above 100Hz over thousands of kilometers with near perfect fidelity.^{15} Such entanglement can then be used for quantum key distribution and distributed quantum information processing.
Conclusion
We have presented a new paradigm for quantum computing—a qubus computer—that brings together discrete qubits with quantum continuous variables in a single scheme. The qubits are used for computation, while the continuous variables are used for interqubit communication. More specifically, a universal twoqubit gate is realized through the interaction with a common bus mode. Our approach requires only modest resources, and it uses these very efficiently. Thus it promises to be extremely useful for the first quantum technologies, when resources are still scarce. Furthermore, in the longer term this approach provides both options and scalability for efficient manyqubit quantum computation.
William Munro Quantum Information Processing group, HewlettPackard Laboratories
Bristol, UK
Bill Munro is a principal researcher within HewlettPackard Laboratories' Quantum Information Processing group located in Bristol. His current interests are focused on practical implementation of optical and solidstate quantum hardware, generation of optical nonlinearities, characterization of quantum states and processes, novel quantum communication protocols, and quantum metrology. Finally, he also has a keen interest in the foundational tests of quantum theory.
Kae Nemoto, Timothy Spiller Quantum Information Sciences group, National Institute of Informatics
Tokyo, Japan
Kae Nemoto is an associate professor in the Quantum Information Sciences group at NII. Her research interests and efforts are currently focused on the requirements for true quantum computation as opposed to quantum processes that can be efficiently classically simulated, the generation of optical nonlinearities, schemes for quantum computation and information processing, quantum/atom optics and quantum nonlinear dynamics, and finally the foundations of quantum mechanics.
Tim Spiller carries the titles of distinguished scientist and director of HewlettPackard Laboratories' Quantum Information Processing group. His main QIPC research interest is quantum hardware theory, examples being superconducting circuits, magnetic and other solidstate systems and nonlinear devices such as Josephson and EIT (electromagnetically induced transparency) systems, and the transformation of quantum information science into actual technologies.
References:
15. P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, Y. Yamamoto, Hybrid quantum repeater using bright coherent light,
Phys. Rev. Lett. 96, pp. 240501, 2006.


