Superconducting Circuits and Quantum Computation

The notion of a quantum computer was first put forth by Richard Feynman in 1982. He suggested that the only way to effectively simulate a quantum system was with another quantum system. The question of whether quantum computation could be more powerful than classical computation in general was first pioneered by David Deutsch in the mid-1980’s. He developed the notion of a universal quantum computer as well as the first quantum algorithm, as opposed to a simulation. It was not until 1994, when Peter Shor published an algorithm that could factorize large numbers into prime numbers exponentially faster than ever before, that the field of quantum computation really began to flourish.

The reason Shor’s factoring algorithm is so responsible for the burgeoning of the field of quantum computation is security. The most popular encryption schemes for digital information, i.e., the encryption used to prevent people from stealing your credit card information when you buy something on the internet, are safe because people cannot factor a large number into two primes in any amount of reasonable time. Shor’s algorithm, if we had a quantum computer, could solve this problem in an instant. Though still not known for sure, many people speculate that a quantum computer could solve an entire class of problems that today’s computers find impossible to solve.

Besides the enormous computational power a quantum computer seems to offer, the systems that could make up quantum computers also present fascinating physics and engineering challenges. The fundamental unit of information in today’s computers is the bit. In a quantum computer these bits would be replaced by their quantum cousins, qubits. An accurately manipulated and well-behaved single qubit is the most fundamental component of a quantum computer, and it is an extremely interesting and challenging problem. For a quantum computer you would also need to couple lots of qubits together, which is another fascinating challenge. And of course all these sensitive qubits must be shielded from all the microscopic noise that constantly surrounds us but doesn’t bother us, but which would ruin all hope of computing with the qubits.

The goal of our group is to implement a quantum computer with superconducting qubits. There exist many quantum systems that could be used as part of a quantum computer, but the class of superconducting qubits based on Josephson junction circuits is one of the most promising. One advantage of these qubits is the ability to precisely engineer the Hamiltonian of the system, which includes single qubit design, multiple qubit design, and measurement design. The superconducting circuit we study is the Persistent-Current Qubit (PC Qubit).

A fully functional single qubit is the first step towards a quantum computer. This is why single qubit characterization and the demonstration of single qubit control is our top priority. One of the hallmarks of a quantum system is its discrete energy levels, and so characterization always includes a study of the qubit energy spectra via spectroscopy. Single qubit control is studied by applying radiation to the qubit and using nanosecond-scale resolution measurements to watch population transfer between eigenstates.

Just as important as a fully functional qubit is a good way to measure the qubit. The conventional way of measuring flux qubits is by ramping the bias current of a DC SQUID magnetometer until a voltage is seen across the DC SQUID. The qubit state is then inferred from the current at which the switch to finite voltage takes place. However, strong qubit decoherence can result due to this readout process. To address this we have experimentally implemented a resonant readout technique that only requires the readout SQUID to be biased at low currents along the supercurrent branch. The low current bias tends to maintain the first-order noise isolation, helping to minimize the level of decoherence of the qubit. Since the SQUID does not switch to the voltage state, the number of quasi-particles is also drastically reduced. In addition, the resonant readout approach utilizes a narrow-band filter that shields the qubit from broadband noise.

The greatest applications of a quantum computer require thousands of qubits coherently coupled. To avoid having enormous amounts of room temperature electronics, as well as the noise they contribute, it would be extremely advantageous to integrate qubit and control electronics monolithically. Modern superconducting foundries, such as the one at MIT Lincoln Laboratory, have the capability of manufacturing classical digital and analog electronics alongside quantum bits in the same integrated circuit process. We have recently studied a single Josephson junction coupled inductively to the PC Qubit. When sufficient dc current is provided, the device acts as a current controlled oscillator. Utilizing radiation sources directly integrated with qubits permits individual control radiation for many different qubits with a modest overhead in room-temperature electronic complexity. The eventual need for very large-scale control circuitry to control timing and order of operations on different qubits also has us investigating Rapid Single Flux Quantum (RSFQ). RSFQ is capable of shuttling fundamental quanta of magnetic flux throughout a microprocessor at clock speeds of 10’s of GHz. These magnetic quanta are used as digital data bits, and can also be used to stimulate the state of the qubit.

A thorough understanding of the nature of the decoherence present in our system is another extremely important step towards a quantum computer. Probing decoherence with Electromagnetically Induced Transparency is a technique we have mapped from the atomic world to the PC Qubit. The basic idea is that you utilize three states of the qubit, two meta-stable states 1 and 2, and a third, shorter-lived state 3, that may spontaneously decay (to other unmentioned states) at a relatively fast rate R3. A strong “control” microwave source couples the 2-3 transition, and a weak “probe” microwave source couples the 1-3 transition. Individually, the microwaves from the probe and control sources are readily absorbed by the qubit and thus the transmittance of the radiation through the PC Qubit is quite low. However, when the control and probe sources are applied simultaneously, destructive quantum interference between the qubit states involved in the two driven transitions causes the qubit to become "transparent" to both the probe and control radiation. Thus, the fields pass through with virtually no absorption. This can serve as a sensitive probe of decoherence since even the smallest deviations from perfect destructive interference between the qubit states results in a loss of transparency.

With the daunting tasks involved with building a large quantum computer, the ability to do near-term quantum computation is quite attractive. This is why we have designed schemes to implement the Factorized Quantum Lattice-Gas Algorithm (FQLGA) for fluid dynamics simulation, as well as a scheme to run our quantum computer as an Adiabatic Quantum Computer. The FQLGA is the quantum version of classical lattice-gases. By replacing bits with qubits you gain an exponential decrease in required memory and the ability to simulate arbitrarily small viscosities. These advantages are seen with only modest numbers of qubits, making the implementation foreseeable in the not so far future. We have demonstrated multiple schemes to implement this algorithm with the PC Qubit. Adiabatic quantum computation, while mathematically equivalent to conventional quantum computation, runs by exploiting the ability of coherent quantum systems to adiabatically follow the ground state of a slowly changing Hamiltonian. This has great practical interest because encoding a quantum computation in a single eigenstate, the ground state, offers intrinsic protection against dephasing and dissipation. We have demonstrated a scalable superconducting architecture for adiabatic quantum computation that can handle any class NP problem without requiring interqubit couplings that vary during the course of the computation. The proposal we have given requires neither interqubit couplings to extend beyond nearest neighbors nor qubit measurements to be highly efficient.