2,047 research outputs found
Classical Rules in Quantum Games
We consider two aspects of quantum game theory: the extent to which the
quantum solution solves the original classical game, and to what extent the new
solution can be obtained in a classical model.Comment: The previous title, "Quantum games are no fun (yet)", was too
whimsical for Physical Review. This is a comment on most, but not all, papers
on quantum game theor
Restrictions on Transversal Encoded Quantum Gate Sets
Transversal gates play an important role in the theory of fault-tolerant
quantum computation due to their simplicity and robustness to noise. By
definition, transversal operators do not couple physical subsystems within the
same code block. Consequently, such operators do not spread errors within code
blocks and are, therefore, fault tolerant. Nonetheless, other methods of
ensuring fault tolerance are required, as it is invariably the case that some
encoded gates cannot be implemented transversally. This observation has led to
a long-standing conjecture that transversal encoded gate sets cannot be
universal. Here we show that the ability of a quantum code to detect an
arbitrary error on any single physical subsystem is incompatible with the
existence of a universal, transversal encoded gate set for the code.Comment: 4 pages, v2: minor change
Quantum Error Correction and Orthogonal Geometry
A group theoretic framework is introduced that simplifies the description of
known quantum error-correcting codes and greatly facilitates the construction
of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1
error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors,
and 1 to 29 qubits correcting 5 errors.Comment: RevTex, 4 pages, no figures, submitted to Phys. Rev. Letters. We have
changed the statement of Theorem 2 to correct it -- we now get worse rates
than we previously claimed for our quantum codes. Minor changes have been
made to the rest of the pape
Quantum Error Correction via Codes over GF(4)
The problem of finding quantum error-correcting codes is transformed into the
problem of finding additive codes over the field GF(4) which are
self-orthogonal with respect to a certain trace inner product. Many new codes
and new bounds are presented, as well as a table of upper and lower bounds on
such codes of length up to 30 qubits.Comment: Latex, 46 pages. To appear in IEEE Transactions on Information
Theory. Replaced Sept. 24, 1996, to correct a number of minor errors.
Replaced Sept. 10, 1997. The second section has been completely rewritten,
and should hopefully be much clearer. We have also added a new section
discussing the developments of the past year. Finally, we again corrected a
number of minor error
Magnetic qubits as hardware for quantum computers
We propose two potential realisations for quantum bits based on nanometre
scale magnetic particles of large spin S and high anisotropy molecular
clusters. In case (1) the bit-value basis states |0> and |1> are the ground and
first excited spin states Sz = S and S-1, separated by an energy gap given by
the ferromagnetic resonance (FMR) frequency. In case (2), when there is
significant tunnelling through the anisotropy barrier, the qubit states
correspond to the symmetric, |0>, and antisymmetric, |1>, combinations of the
two-fold degenerate ground state Sz = +- S. In each case the temperature of
operation must be low compared to the energy gap, \Delta, between the states
|0> and |1>. The gap \Delta in case (2) can be controlled with an external
magnetic field perpendicular to the easy axis of the molecular cluster. The
states of different molecular clusters and magnetic particles may be entangled
by connecting them by superconducting lines with Josephson switches, leading to
the potential for quantum computing hardware.Comment: 17 pages, 3 figure
Unified derivations of measurement-based schemes for quantum computation
We present unified, systematic derivations of schemes in the two known
measurement-based models of quantum computation. The first model (introduced by
Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed
entangled state, adaptive measurements on single qubits, and feedforward of the
measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308,
96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)])
uses adaptive two-qubit measurements that can be applied to arbitrary pairs of
qubits, and feedforward of the measurement results. The underlying principle of
our derivations is a variant of teleportation introduced by Zhou, Leung, and
Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two
measurement-based models of quantum computation and provide significantly
simpler schemes.Comment: 14 page
Quantum Communication With Zero-Capacity Channels
Communication over a noisy quantum channel introduces errors in the
transmission that must be corrected. A fundamental bound on quantum error
correction is the quantum capacity, which quantifies the amount of quantum data
that can be protected. We show theoretically that two quantum channels, each
with a transmission capacity of zero, can have a nonzero capacity when used
together. This unveils a rich structure in the theory of quantum
communications, implying that the quantum capacity does not uniquely specify a
channel's ability for transmitting quantum information.Comment: Final submitted versio
A Study on the Noise Threshold of Fault-tolerant Quantum Error Correction
Quantum circuits implementing fault-tolerant quantum error correction (QEC)
for the three qubit bit-flip code and five-qubit code are studied. To describe
the effect of noise, we apply a model based on a generalized effective
Hamiltonian where the system-environment interactions are taken into account by
including stochastic fluctuating terms in the system Hamiltonian. This noise
model enables us to investigate the effect of noise in quantum circuits under
realistic device conditions and avoid strong assumptions such as maximal
parallelism and weak storage errors. Noise thresholds of the QEC codes are
calculated. In addition, the effects of imprecision in projective measurements,
collective bath, fault-tolerant repetition protocols, and level of parallelism
in circuit constructions on the threshold values are also studied with emphasis
on determining the optimal design for the fault-tolerant QEC circuit. These
results provide insights into the fault-tolerant QEC process as well as useful
information for designing the optimal fault-tolerant QEC circuit for particular
physical implementation of quantum computer.Comment: 9 pages, 9 figures; to be submitted to Phys. Rev.
Time complexity and gate complexity
We formulate and investigate the simplest version of time-optimal quantum
computation theory (t-QCT), where the computation time is defined by the
physical one and the Hamiltonian contains only one- and two-qubit interactions.
This version of t-QCT is also considered as optimality by sub-Riemannian
geodesic length. The work has two aims: one is to develop a t-QCT itself based
on physically natural concept of time, and the other is to pursue the
possibility of using t-QCT as a tool to estimate the complexity in conventional
gate-optimal quantum computation theory (g-QCT). In particular, we investigate
to what extent is true the statement: time complexity is polynomial in the
number of qubits if and only if so is gate complexity. In the analysis, we
relate t-QCT and optimal control theory (OCT) through fidelity-optimal
computation theory (f-QCT); f-QCT is equivalent to t-QCT in the limit of unit
optimal fidelity, while it is formally similar to OCT. We then develop an
efficient numerical scheme for f-QCT by modifying Krotov's method in OCT, which
has monotonic convergence property. We implemented the scheme and obtained
solutions of f-QCT and of t-QCT for the quantum Fourier transform and a unitary
operator that does not have an apparent symmetry. The former has a polynomial
gate complexity and the latter is expected to have exponential one because a
series of generic unitary operators has a exponential gate complexity. The time
complexity for the former is found to be linear in the number of qubits, which
is understood naturally by the existence of an upper bound. The time complexity
for the latter is exponential. Thus the both targets are examples satisfyng the
statement above. The typical characteristics of the optimal Hamiltonians are
symmetry under time-reversal and constancy of one-qubit operation, which are
mathematically shown to hold in fairly general situations.Comment: 11 pages, 6 figure
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