Los Alamos National Laboratory (LANL) established the Quantum Cloud Access Project (QCAP) with the New Mexico Consortium (NMC) in order to provide a direct conduit for LANL researchers to experiment on commercial quantum systems. The first couple of years of the project have primarily focused on analog quantum systems, including D-Wave's Advantage2 platform, and QuEra's Aquila quantum computer. We are now vigorously moving into fault-tolerant, error-corrected, digital systems. Concurrently, the NMC's mission is built on education and community outreach across New Mexico. In this talk, we will cover three platforms available to you, the QCSS students: D-Wave's Advantage2, QuEra's Aquila, and Quantinuum's System Model H1. For each platform, we will cover the underlying architecture, how to gain access, and some toy model problems. (Other vendors are available but will not be covered.) Time permitting, we will then go through a sketch proof of the Kitaev-Feynman clock construction establishing polynomial equivalence between the adiabatic model and the standard circuit model of quantum computation.
- $A(s)$ represents the transverse, or tunneling, energy
- $B(s)$ is the energy applied to the problem Hamiltonian
- $s$ is the ratio between the current time during the anneal and the total annealing time and has a value between 0 and 1
- An excited atom prevents neighboring atoms from being excited, facilitating entanglement and gate operations
- The blockade also allows simulating ordered phases of matter by positioning atoms in different lattice structures
Physical Interpretation:
- Single-Qubit Terms: Internal energy of qubits
- Phonon Modes: Quantized motion of the ion chain
- Spin-Phonon Coupling: Drives entanglement via shared motional modes
- In the Feynman-Kitaev construction, each step of the circuit is enforced by a three-local Hamiltonian term $H_\ell'$ that checks
if the system transitions correctly from time step $t=\ell-1$ to $t=\ell$ under the intended unitary gate $U_\ell$
- Action on:
- The clock register to ensure the transition is between $|\ell - 1\rangle |\ell - 1\rangle$ and $|\ell\rangle |\ell\rangle$
- The computation register to apply $U_\ell$
- The coherence between timesteps, i.e. to penalize inconsistent evolution
- These local consistency-checks ensure the proper sequence of transitions (i.e., the valid history) yields the lowest energy with probability proportional to $1/L$
Kitaev-Feynman history state:
- Each blue circle represents the system's state at a discrete clock time, i.e., $|\psi_t\rangle |\psi_t\rangle$
- The grey arrows denote valid transitions: unitary steps of the original quantum circuit
- The dashed arc evokes the idea of coherent superposition across time—hinting that the actual history state is not a traversal, but a weighted sum over all these snapshots
Geometric and energetic structure:
- The orange path is the valid 1D history subspace—each point is a legal computational step $|\psi_t\rangle |\psi_t\rangle$
- The gold band represents the low-energy subspace preserved by the clock Hamiltonian
- The grey bands above and below are high-energy regions: any deviation from the valid history (marked with red Xs) is penalized
- The spectral gap between the ground state manifold and excited states is indicated explicitly, emphasizing that small deviations incur a non-negligible energy cost
- This gap is crucial—it ensures that the history state remains the unique ground state and that small perturbations don’t destabilize the encoded computation