We show average-case lower bounds for explicit Boolean functions against bounded-depth thresh-old circuits with a superlinear number of wires. We show that for each integer d > 1, there isεd > 0 such that Parity has correlation at most 1/nΩ(1) with depth-d threshold circuits whichhave at most n1+εd wires, and the Generalized Andreev Function has correlation at most 1/2nwith ...

Attention is called to previous research on realization of an arbitrary switching function by a network of threshold gates (or threshold elements) and modulo 2 gates (or parity elements), establishment of greatest lower bounds on the number of gates needed, artifices that lead to further network reduction in special cases, and systematic minimization of the number of module 2 gates required. Al...

We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf ) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[q], and counting. Classically, we need logarithmic depth even if we can use unboun...

There are specific kinds of circuits for which lower bounds techniques were successfully developed. One is small-depth circuits, the other is monotone circuits. For constant-depth circuits with AND,OR,NOT gates, people proved that they cannot compute simple functions like PARITY [3, 1] or MAJORITY. For monotone circuits, Alexander A. Razborov proved that CLIQUE, an NP-complete problem, has expo...

We use a Ramsey-theoretic argument to obtain the first lower bounds for approximations over Zm by nonlinear polynomials: A degree-2 polynomial over Zm (m odd) must differ from the parity function on at least a 1=2 1=2(logn) (1) fraction of all points in the Boolean n-cube. A degree-O(1) polynomial over Zm (m odd) must differ from the parity function on at least a 1=2 o(1) fraction of all points...

I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced ...

Fault-tolerant quantum computation with depolarization error often requires demanding threshold and resource overhead. If the operations can maintain high noise bias---dominated by dephasing small bit-flip error---we achieve hardware-efficient fault-tolerant a more favorable threshold. Distinct from two-level physical systems, multilevel systems (such as harmonic oscillators) desirable set of b...

In this paper it is shown how a circuit, given as a net-list of gates, can be transformed into two diierent types of code-disjoint circuits. A new method for a joint design of the functional circuit, the output parity and the input parity is proposed. Carefully selected internal nodes of the functional circuit are utilized to reduce the necessary area overhead for the design of input and output...

Stabilized cat codes can provide a biased noise channel with set of bias-preserving (BP) gates, which significantly reduce the resource overhead for fault-tolerant quantum computing. All existing schemes BP however, require adiabatic evolution, performance limited by excitation loss and nonadiabatic errors during gates. In this paper, we apply derivative-based leakage-suppression technique to o...