A space-efficient quantum computer simulator suitable for high-speed FPGA implementation

Conventional vector-based simulators for quantum computers are quite limited in the size of the quantum circuits they can handle, due to the worst-case exponential growth of even sparse representations of the full quantum state vector as a function of the number of quantum operations applied. However, this exponential-space requirement can be avoided by using general space-time tradeoffs long known to complexity theorists, which can be appropriately optimized for this particular problem in a way that also illustrates some interesting reformulations of quantum mechanics. In this paper, we describe the design and empirical space-time complexity measurements of a working software prototype of a quantum computer simulator that avoids excessive space requirements. Due to its space-efficiency, this design is well-suited to embedding in single-chip environments, permitting especially fast execution that avoids access latencies to main memory. We plan to prototype our design on a standard FPGA development board.Comment: 12 pages, 6 figures, presented at Quantum Information and Computation VII, Orlando, April 2009. Author reprint of final submitted manuscrip

On-chip SQUID measurements in the presence of high magnetic fields

We report a low temperature measurement technique and magnetization data of a quantum molecular spin, by implementing an on-chip SQUID technique. This technique enables the SQUID magnetometery in high magnetic fields, up to 7 Tesla. The main challenges and the calibration process are detailed. The measurement protocol is used to observe quantum tunneling jumps of the S=10 molecular magnet, Mn12-tBuAc. The effect of transverse field on the tunneling splitting for this molecular system is addressed as well.Comment: 7 pages, 3 figure

Space-Efficient Simulation of Quantum Computers

Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale platform with only a few gigabytes of main memory. However, more memory-efficient simulations are possible, requiring only polynomial or even linear space in the size of the quantum circuit being simulated. In this paper, we describe one such technique, which was recently implemented at FSU in the form of a C++ program called SEQCSim, which we releasing publicly. We also discuss the potential benefits of this simulation in quantum computing research and education, and outline some possible directions for further progress.Comment: 6 pages, 3 figures, author reprint of final submitted manuscrip

Strong coupling of a Gd3+^{3+} multilevel spin system to an on-chip superconducting resonator

International audienceWe report the realization of a strong coupling between a Gd$^{3+}$ spin ensemble hosted in a scheelite (CaWO$_4$) single crystal and the resonant mode of a coplanar stripline superconducting cavity leading to a large separation of spin-photon states of 146 MHz. The interaction is well described by the Dicke model and the crystal-field Hamiltonian of the multilevel spin system. We observe a change of the crystal-field parameters due to the presence of photons in the cavity that generates a significant perturbation of the crystal ground state. Using finite-element calculations, we numerically estimate the cavity sensing volume as well as the average spin-photon coupling strength of $g_0\approx$ 620 Hz. Lastly, the dynamics of the spin-cavity states are explored via pulsed measurements by recording the cavity ring-down signal as a function of pulse length and amplitude. The results indicate a potential method to initialize this multilevel system in its ground state via an active cooling process

Sustaining Rabi oscillations by using a phase-tunable image drive

Abstract: Recent electron spin resonance experiments on CaWO4:Gd3 + and other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance, together with another microwave field (image drive) with a frequency smaller than the Larmor frequency. These observations are confirmed by the new experimental results reported in this paper. We use numerical and analytical techniques to study the interplay between the microwave drives and three different mechanisms of relaxation. The first model describes a magnetic moment subject to microwave fields, interacting with a bath of two-level systems which acts as a source of decoherence and dissipation. The second model describes identical, interacting magnetic moments, subject to the same microwave fields. The decay of the Rabi oscillations is now due to the interactions. Third, we study Rabi oscillation decay due to the inhomogeneity of the microwave radiation. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that are not readily accessible experimentally. Graphic abstract: [Figure not available: see fulltext.

Sustaining Rabi oscillations by using a phase-tunable image drive

International audienceRecent electron spin resonance experiments on CaWO4:Gd 3+ and other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance, together with another microwave field (image drive) with a frequency smaller than the Larmor frequency. These observations are confirmed by the new experimental results reported in this paper. We use numerical and analytical techniques to study the interplay between the microwave drives and three different mechanisms of relaxation. The first model describes a magnetic moment subject to microwave fields, interacting with a bath of two-level systems which acts as a source of decoherence and dissipation. The second model describes identical, interacting magnetic moments, subject to the same microwave fields. The decay of the Rabi oscillations is now due to the interactions. Third, we study Rabi oscillation decay due to the inhomogeneity of the microwave radiation. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that are not readily accessible experimentally