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quant-ph9807022.txt \|@word unavoidable:1 allowed:1 consider:4 saying:1 rev:4 results:15 projected:1 leads:1 broader:1 consists:2 follow:2 causes:1 whose:5 maximally:14 sin2θ:2 concerned:2 technique:1 γk:4 present:2 under:5 must:17 worth:1 applied:1 g4:1 presently:1 orthogonal:31 springer:1 every:1 bringing:1 condition:4 generalised:7 level:3 turns:2 notes:1 solution:5 occurs:1 large:2 solved:1 vector:3 phase:1 annihilates:2 eigenvalues:7 anal:1 discriminates:2 degrading:1 direct:1 prevents:1 discriminated:4 zero:11 design:1 further:7 canonical:1 established:3 what:3 errors:3 giving:9 section:13 jaeger:7 brief:1 expressed:2 new:2 method:3 satisfy:2 simultaneously:1 respectively:1 never:3 here:7 met:1 explore:1 possibility:2 others:1 represented:3 70s:1 interpret:1 deduced:1 obtained:7 convert:2 study:2 larger:5 allows:1 contradiction:1 maximising:2 resulting:1 within:1 schumacher:1 action:1 proof:2 studies:1 involves:1 uniquely:1 examining:2 orthonormality:1 useful:3 namely:1 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quant-ph9807023.txt \|@word represent:1 consider:5 ceases:1 similarity:2 helstrom:1 results:1 leads:2 constants:1 equiprobable:1 whose:2 c0:4 γr:6 deterministic:1 γk:8 under:2 overlaps:1 applied:1 g4:1 orthogonal:9 far:1 springer:1 every:1 difference:1 exact:1 condition:5 arrange:1 generalised:1 obvious:1 immediately:1 guo:1 solution:4 solved:1 phase:1 small:1 eigenvalues:5 upper:2 discriminated:3 likely:1 further:3 crystallography:1 linear:4 aim:3 what:1 errors:3 section:3 jaeger:3 expressed:1 cell:1 experiment:1 ˆd:11 ˆe:1 ˆf:3 ˆh:1 new:3 increasing:3 ˆl:6 coefficient:1 led:1 notions:1 here:7 behaviour:2 desired:3 others:1 alone:1 consideration:1 appears:1 obtained:5 solid:2 until:1 vectors:2 allows:1 approaches:1 contradiction:1 example:1 prior:2 maximising:1 simultaneous:1 within:1 pˆh:2 spin:1 changes:1 technique:1 useful:3 ˆr:2 discontinuous:1 distributed:1 engineering:1 outcomes:2 brought:1 addressed:2 eiφk:1 summation:1 apply:2 total:1 manipulate:1 conventional:2 takes:1 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quant-ph9807024.txt \|@word monte:4 measurements:1 partial:1 consider:4 varying:3 results:1 illustrated:2 localized:1 excludes:1 calculate:5 tr:2 tn:2 γn:2 applied:1 random:1 very:1 frequencies:6 induce:1 wave:7 sidebands:1 difference:1 condition:1 hamiltonian:2 evaluation:1 t2:1 solution:2 standards:1 large:3 discrete:4 annihilates:1 optics:1 enforce:1 application:1 jump:4 rate:2 2aγ:1 pass:1 dynamics:2 carlo:4 aγn:1 plays:1 iterating:1 sum:1 method:5 evolving:1 unobserved:1 component:1 here:3 separation:1 directions:1 along:1 equations:2 change:1 simulating:1 institute:1 allows:2 dfγ:2 trial:2 resulting:1 correct:2 resonance:4 fourier:1 via:1 sγ:3 castin:2 replace:2 summation:2 apply:1 total:1 establish:1 rω:3 select:3 partitioned:1 use:3 proceed:1 would:4 distinct:1 rω1:8 few:1 type:1 theoretical:1 more:3 lowering:1 initial:2 operators:6 emission:3 berlin:2 transient:1 particular:2 provide:1 unraveled:1 cases:2 must:4 ρa:2 evolves:3 springer:2 equation:6 work:1 values:3 freedom:1 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quant-ph9807026.txt \|@word consider:2 fig2:1 fig3:1 computation:3 fig1:1 deterministic:3 answered:1 finally:1 tk:2 nodes:7 string:4 very:1 upstream:4 condition:2 entire:2 michael:1 solution:1 t0:2 t1:2 vector:4 small:1 enhance:1 second:2 implemented:1 machines:1 cursor:1 what:1 brackets:1 giving:1 consisting:3 respectively:2 answers:1 operating:2 others:1 represented:2 search:4 tapes:1 shift:2 vectors:2 leaving:1 symmetrical:1 implement:1 changes:1 followed:1 marked:3 replace:1 marker:1 apply:2 use:3 would:2 remains:1 contains:3 toffoli:1 next:1 encode:2 until:1 sort:1 reversible:4 particular:1 known:1 states:4 springer:1 ma:1 augment:1 modified:1 grover:2 following:1 example:2 numbers:1 figure:8 process:1 sample:1 indicates:1 performed:1 verlag:1 end:1 s1:4 s0:4 machine:15 how:3 answer:4 gate:1 ordinary:1 inputs:5 arcs:9 after:2 data:1 outline:1 whenever:1 register:25 sk:2 lengths:2 so:2 order:4 lsb:10 over:2 fall:1 symbols:4 through:2 statistical:1 write:3 writing:2 pending:1 good:1 halt:2 they:1 rotation:2 now:1 term:1 stopped:1 2a:1 2b:1 each:3 found:2 2k:1 square:1 detect:1 concord:1 related:1 fewer:1 quantum:12 operation:1 shown:1 network:1 space:1 since:1 denoted:1 newly:1 cause:2 shows:1 written:1 org:3 advance:1 pairs:1 created:1 could:3 computers:1 times:2 length:6 place:2 onto:3 first:3 xk:2 reversing:1 there:1 probability:1 encoding:1 number:4 done:2 fast:1 given:3 similarly:1 introduction:1 construct:1 indicate:1 too:1 bits:7 williams:1 shifted:1 tuple:3 reversed:2 exactly:1 simulate:2 alphabets:1 x0:4 x1:4 representing:1 diffusion:2 wide:1 roles:2 require:1 zero:2 arc:7 amplitude:1 pre:1 fashion:1 unchanged:2 manner:1 need:1 any:4 depending:1 efficient:1 answering:1 isolated:1 note:1 high:3 causing:1 tool:1 reach:1 falls:1 regular:1 but:1 cleared:1 inserted:1 observation:1 considered:2 implications:1 mechanical:1 registers:4 completion:1 copy:1 simulating:1 state:6 only:1 tape:1 explorations:1 handle:1 get:1 stop:1 runs:1 unaddressed:1 arxiv:4 traversed:2 fixed:1 set:6 constructing:1 physically:1 observed:1 see:2 computer:4 operated:1 satisfying:1 enough:1 various:2 reading:5 available:3 barenco:1 initially:1 ket:4 optional:1 realizable:1 reverse:2 many:3 qubit:1 com:1 asked:1 point:2 simply:2 iterations:2 table:1 ps:3 invert:1 mark:1 ai:1 ph:6 ak:1 empty:1 define:1 optionally:1 sufficient:1 those:1 case:3 will:7 replaced:1 procedure:1 unitary:7 ave:1 binary:6 perform:2 alphabet:3 make:1 clearly:1 shifts:1 quant:6 finite:4 evolve:2 used:1 http:3 i0:4 upon:1 numbered:1 database:1 expression:1 without:3 left:3 gates:2 just:1 less:2 rotated:3 transforms:3 questions:3 using:2 useful:1 rotates:1 enters:1 supply:1 source:3 other:2 input:30 remaining:1 format:3 read:2 possible:2 integer:2 bit:11 execution:2 rotate:1 necessary:3 output:23 replacement:1 right:3 sequence:4 conditional:2 some:1 back:1 specified:2 happens:1 broad:1 stops:1 conditionally:1 does:2 augmenting:1 o0:4 run:3 processing:2 step:2 simpler:1 about:1 o:12 simulation:1 range:1 involving:1 act:1 software:3 destination:4 into:3 references:1 elementary:1 utility:1 additional:1 assumed:1 initial:3 question:6 transform:11 long:1 gif:6 way:1 forward:1 was:2 function:4 complete:1 concatenated:1 jul:1 repeated:2 construction:6 encoded:5 removed:1 true:1 entered:1 applying:1 up:1 us:1 um:8 uo:7 un:1 ui:7 computing:1 defined:1 universal:1 ar:7 exist:1 effected:2 eventual:1 corporation:1 when:3 terminating:2 appends:1 node:25 repeat:1 superposition:3 symbol:10 problems:1 includes:1 a1:1 a0:2 important:1 augmentation:1 needed:2 structure:1 algorithm:4 assume:1 baker:1 fsm:21 strings:8 parallelism:2 demonstrates:1 abstract:1 validation:2 original:1 augmented:1

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