Related papers: Crystalline Quantum Circuits
In this paper we continue to explore "hybrid" quantum circuit models in one-dimension with both unitary and measurement gates, focussing on the entanglement properties of wavefunction trajectories at long times, in the steady state. We…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact…
We demonstrate that $k$-Markov sequences of unitary gates provide low-cost handles to manipulate the rate and structure of information spreading compared to traditional random, 0-Markov, circuits. For SWAP gates and brickwork circuits, we…
Path sums are a convenient symbolic formalism for quantum operations with applications to the simulation, optimization, and verification of quantum protocols. Unlike quantum circuits, path sums are not limited to unitary operations, but can…
We explore a roughening phase transition that occurs in the entanglement dynamics of certain quantum circuits. Viewing entanglement as the free energy of a membrane in a circuit-defined random environment, there is a competition between…
Quantum Supremacy is a demonstration of a computation by a quantum computer that can not be performed by the best classical computer in a reasonable time. A well-studied approach to demonstrating this on near-term quantum computers is to…
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a…
Controlling the waveform of light is the key for a versatile light source in classical and quantum electronics. Although pulse shaping of classical light is a mature technique and has been used in various fields, more advanced applications…
As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be…
We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment,…
We present an entirely 2D transversal realization of phase gates at any level of the Clifford hierarchy, and beyond, using non-Abelian surface codes. Our construction encodes a logical qubit in the quantum double $D(G)$ of a non-Abelian…
In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finite sequences of elementary quantum gates and establish their…
One of the key challenges in quantum information is coherently manipulating the quantum state. However, it is an outstanding question whether control can be realized with low error. Only gates from the Clifford group -- containing $\pi$,…
We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a…
Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of non-iterative energy corrections, based on the method of…