Quantum Computing With Holograms

Arxiv – Quantum computing in a piece of glass (14 pages) The US Air Force is developing simple but reliable quantum computers that can be built with off-the-shelf components.

Quantum gates and simple quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photon’s linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of quantum computing within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate – the timeless nature of quantum computing. Second, photon entanglement can be encoded as a superposition state of a single photon in a higher-dimensional state space afforded by LM. Our theoretical and numerical results indicate that OptiGrate’s photo-thermal refractive (PTR) glass is an enabling technology. We will review our previous design of a quantum projection operator and give credence to this approach on a representative quantum gate grounded on coupled-mode theory and numerical simulations, all with parameters consistent with PTR glass. We discuss the strengths (high efficiencies, robustness to environment) and limitations (scalability, crosstalk) of this technology. While not scalable, the utility and robustness of such optical elements for broader quantum information processing applications can be substantial.

Volume holographic design of the 4-dimensional CNOT gate in PTR glass. The gate can be constructed by a stack of 4 LM gratings, or by a stack of two multiplexed gratings.

Technology Review – Quantum Computing With Holograms

In recent years, however, physicists have worked out how to make photons interact using interferometers and to carry out quantum computations using the output of one interferometer as the input for another.

The trouble is that interferometers are notoriously fickle. Sneeze and they need re-calibrating. So cascades of them tend to be hard to handle.

Today, Jonathan McDonald at the Air Force Research Laboratory in Rome New York, and a few pals reveal a way round this problem.

Their idea is to make holograms of interferometers so that their properties become ‘frozen’ in glass. This makes them much more stable.

The researchers then plan to stack the interferometers to perform simple quantum computations. “The approach here will “lock” these interferometers within a tempered piece of glass that is resistant to environmental factors,” they say.

MacDonald and co suggest using a commercial holographic material called OptiGrate to store these holograms and show how these devices could carry out simple tasks such as quantum teleportation and CNOT logic.

There are two serious limitations to this approach, however. First, these devices are not scalable. The reason is that a hologram requires a certain volume of space to carry out each computation with high fidelity. And since computations scale exponentially in quantum computers, so must the volume.

Second, these devices are not reprogrammable, at least not with today’s technology. The reason is that OptiGrate is a write-once material. Re-recordable holographic media are available but not currently with the fidelity that allows this kind of work though clearly that could change in future.

Given these limitations it’s easy to dismiss this idea as just another of a growing number of exotic forms of quantum computation that are gathering dust on (metaphorical) library shelves.

But there are a number of emerging applications for the kind of reliable but low-dimensional quantum computations that these devices could perform. These include quantum memory buses, quantum error correction circuits and quantum key distribution relays.

Constructing simple quantum algorithms and quantum gates in volume holograms provides substantially greater optical stability than the equivalent optical bench realization. For LOQC, this stability is the overarching advantage. Often quantum operators, e.g. the simple projection operator given by Eq. 3, require a cascade of interferometers where the output of one interferometer is used as the input of the next. Therefore, as the dimension of each state space increases, it becomes exceedingly hard to stabilize and is simply impractical beyond two qubits. Other approaches, such as crossed thin gratings lack the efficiency needed for QIP. The device proposed here can potentially achieve this in a single piece of glass without the problem of misalignment. The technology presented here can potentially replace “fi xed” optical components for a broad spectrum of classical and quantum photonics experiments.

The primary limitation of volume holographic QIP is that it is not scalable. Experience shows that multiplexing requires approximately 1mm per recording of the state space to achieve high delity, and in QIP applications this scales exponentially with the number of qubits. But then again, we are not aware of a realistic scalable quantum computer to date. Secondly, the holograms discussed here are write-once holograms and cannot be erased. Therefore the algorithm is “fi xed” into the holographic element. While there are re-recordable holographic media, none that we know of has the specifications to outperform PTR glass for the applications discussed in this manuscript. This is hardly a prescription for a quantum CPU; however, as mentioned in the paper, this technology might be integral to complete QIP systems where smaller d-partite operations are needed on a routine basis, e.g. a quantum memory bus, quantum error correction circuit, QKD relay system, etc…

While we have extensively analyzed volume holographic gates and algorithms using coupled-mode theory, paraxial wave equation simulations and nite-di erence time domain simulations, we have not analyzed the engineering particulars of this device. For example: (1) how many independent writes of orthogonal states into a holographic element can be made in the PTR glass before cross-talk or saturation between the modes becomes a limiting factor? (2) Is it difficult to stack the holograms due to the enhanced angular selectivity of the volume holograms? And (3) what is the maximum number of recordings in a multiplexed PTR hologram that can be reasonably be achieved? In this sense, we are well along in understanding these devices from a theoretical prospective; however, we are at the very beginning experimental

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