Dwave Systems publishes an eight page paper Experimental Investigation of an Eight Qubit Unit Cell in a Superconducting Optimization Processor Dwave Systems has previously announced their 128 qubit adiabatic quantum computer system. There is controversy over the quantumness of the system. Critics question if the computing system is actually in a quantum state and able to take advantage of quantum effects. This is important because a system that can actually leverage quantum effects can be far faster than a classical computer.
Dwave feels the results allow them to claim that they have demonstrated Quantum Annealing but not Adiabiatic Quantum computing. Quantum Annealing can still result in a speedup of up to one million times for some problems over classical non-quantum computers.
Given the limited bandwidth of our external bias lines, we were unable to elicit a substantial change in population statistics. Thus, we were restricted to studying the regime in which the thermalization times were much shorter than the annealing time. Consequently, we can only claim to have demonstrated QA, not AQO.
A superconducting chip containing a regular array of flux qubits, tunable interqubit inductive couplers, an XY-addressable readout system, on-chip programmable magnetic memory, and a sparse network of analog control lines has been studied. The architecture of the chip and the infrastructure used to control it were designed to facilitate the implementation of an adiabatic quantum optimization algorithm. The performance of an eight-qubit unit cell on this chip has been characterized by measuring its success in solving a large set of random Ising spin glass problems as a function of processor temperature. The experimental data are consistent with the predictions of a quantum mechanical model of an eight-qubit system coupled to an environment in thermal equilibrium. These results highlight many of the key practical challenges that we have overcome and those that lie ahead in the quest to realize a functional large scale adiabatic quantum information processor.
The purpose of this article is threefold:
1. address some of the practical questions regarding how to design a scalable superconducting AQO information processor. The answers to these questions will then serve as a motivation for the architecture of the device that we have fabricated.
2. present experimental results from a unit cell on one such chip consisting of eight flux qubits, sixteen in situ tunable inductive in-
terqubit couplers, an XY-addressable high fidelity readout architecture, an array of in situ programmable flux storage devices addressed by a single flux quantum demultiplexing circuit, and a sparse network of analog control lines. The data demonstrate that the unit cell can be used as a computer for solving small-scale Ising spin glass problems.
3. compare experimental data to the results of numerical simulations in order to highlight the fact that, when run very slowly with respect to the adiabatic limit, the performance of the unit cell is influenced by its tendency to thermalize to an environment in thermal equilibrium.
Our study has demonstrated that the most probable result from the hardware, when run slowly, is invariably the ground state. The remaining probability is distributed between low lying states that are roughly within an energy window O(kBT ) above the energy of the ground state at the point in the annealing process where the population statistics freeze. Depending upon the nature of the optimization problem, such low lying states may still constitute acceptable solutions. This observation suggests two possible modes of running a QA processor in practice:
• Run a given optimization problem a statistically large number of times. Take all |~si that are observed with probability greater than the read-
out resolution threshold and calculate E(~s) using Eq. (1). Take whatever |~si provides the lowest E as the solution.
• Run a given optimization problem once. Take the output |~si and calculate E(~s) using Eq. (1). If E is less than some user-defined threshold, then accept the solution. If not, then iterate.
Note that had our processor been operated in the first mode, then it would have returned the correct answer to all 6400 problem instances.
Still Open Questions
What happens when the CCJJ bias ramp time is reduced?
Given the limited bandwidth of our external bias lines, we were unable to elicit a substantial change in population statistics. Thus, we were restricted to studying the regime in which the thermalization times were much shorter than the annealing time. Consequently, we can only claim to have demonstrated QA, not AQO. Efforts are underway to build a new apparatus that will allow us to probe the regime in which thermalization times exceed the annealing time in an eight-qubit processor.
How does the performance scale with problem size?
The eight-qubit unit cell is too small to be used to address issues concerning scaling. The intention of this study was to provide a basic demonstration of what we believe to be a complete set of essential ingredients needed for building a scalable QA processor acting in concert. We will reserve a discussion of the operation of larger portions of a complete 128-qubit chip used in these experiments to a future publication.
How does one implement error correction in QA?
The work presented in this article is in much the same spirit as that of Ref. 53 – operate a small scale device that ‘looks’ like a basic quantum information processor and run it using the simplest algorithms known. We have made no attempts beyond statistical sampling to implement any form of error correction in these particular experiments. This is an active area of research at the moment.
How do the higher excited states of the CCJJ rf SQUIDs affect performance?
To our knowledge, this issue has not been addressed in the literature.
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