Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhase space simulation method for quantum computation with magic states on qubits
65
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides amplitude estimation. The simulation cost is then proportional to a robustness measure squared. For all quantum states, this robustness is smaller than or equal to robustness of magic.
rate research
Read More
We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation with magic states, the size of this state space only depends on the number of magic states used in the quantum computation, and not on the length of the gate and measurement sequence.
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. The 15-qubit Hamming code protects seven encoded qubits to distance three. We give fault-tolerant procedures for applying arbitrary Clifford operations on these encoded qubits, using only two extra qubits, 17 total. In particular, individual encoded qubits within the code block can be targeted. Fault-tolerant universal computation is possible with four extra qubits, 19 total. The procedures could enable testing more sophisticated protected circuits in small-scale quantum devices. Our main technique is to use gadgets to protect gates against correlated faults. We also take advantage of special code symmetries, and use pieceable fault tolerance.
We consider the task of secure multi-party distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our protocol requires an operational workspace of $n^2 + 4n$ qubits, as opposed to previously shown $Omegabig((n^3+n^2s^2)log nbig)$ qubits, where $s$ is a security parameter. Additionally, we reduce the communication complexity by a factor of $mathcal{O}(n^3log(n))$ qubits per node, as compared to existing protocols. To achieve universal computation, we develop a distributed procedure for verifying magic states, which allows us to apply distributed gate teleportation and which may be of independent interest. We showcase our protocol on a small example for a 7-node network.
Universal set of quantum gates are realized from the conduction-band electron spin qubits of quantum dots embedded in a microcavity via two-channel Raman interaction. All of the gate operations are independent of the cavity mode states, emph{i.e.}, insensitive to the thermal cavity field. Individual addressing and effective switch of the cavity mediated interaction are directly possible here. Meanwhile, gate operations also can be carried out in parallel. The simple realization of needed interaction for selective qubits makes current scenario more suitable for scalable quantum computation.
It is called blind quantum computation(BQC) that a client who has limited quantum technologies can delegate her quantum computing to a server who has fully-advanced quantum computers. But the privacy of the clients quantum inputs, algorithms and outputs is still a challenge. To realize a secure BQC, we mainly study how to hide quantum fourier transform (QFT) performed on Bell states. In this paper, three cases are considered as follows. For the first case, we design primary BQC protocols of QFT performed on qubits 12 of belonging to ${|phi^pmrangle_{12},$ $|psi^pmrangle_{12}}$ with relevant circuits. To strengthen security, we construct enhanced BQC protocols of QFT performed on qubits 13 of any two Bell states $|xirangle_{12}otimes|thetarangle_{34}$ with relevant quantum circuits. Featured the property of stronger security, we give generalized BQC protocols of QFT performed on qubits 13 and 24 of any two Bell states with relevant quantum circuits respectively. At last, we analyze and prove the blindness and correctness.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
